THE SECHELT A THESIS CIRCULATION B. THE THE THE Sc. We INLET REQUIREMENTS SUBMITTED UNIVERSITY (Physics)

FACULTY © accept DOCTOR to Scott h required the Scott OCEANOGRAPHY SYSTEM, this University Wayne OF AND IN OF Wayne OF thesis 1995 By GRADUATE in PARTIAL FOR PHILOSOPHY BRITISH Tinis, ENERGETICS standard as BRITISH Tinis THE of conforming Victoria, FULFILLMENT 1995 COLUMBIA DEGREE STUDIES COLUMBIA 1990 OF OF OF THE

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(EOF)

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accounted

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identified

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cur

the not

1 7 8 12 14 18 19 20

2

Acknowledgements

1 List

List

Abstract

2.2

2.1

Instrumentation

Introduction

1.4 1.3

1.2

1.1

of

of

Data 2.1.5

2.1.4

2.1.3 2.1.2

2.1.1

Data

2.0.2

2.0.1 Figures

Tables

Motivation

The

Shallow-silled

Fjord

oceanography

processing

estuaries

Endeco

Anemometers

InterOcean

Aanderaa

Cyclesonde

Hydrographic

Current

and

fjords

oxygen

Meter

RCM

S4

of

Data

surveys.

Sechelt

Moorings

meters

Table

Inlet

of

iv

Contents

xiv

vu

13

ix

17

U 1

5

4

3

5.1 Vertical

4.6

4.5

4.4

4.3

4.2

4.1 Tidal

3.3

3.2 3.1

Tidal

Introduction

The

Tidal 4.4.1

4.3.3

Friction 4.3.2

4.3.1

Internal

4.21.

Barotropic

Energy

Tidal

Choking

Inviscid

2.2.6

2.2.5

2.2.4

2.2.3

2.2.2

2.2.1

Energy

Choking

Diffusion

Energy

Jet

Choking

Derivation

Energy

Normal

Theory

Energy

Oxygen

Runoff Wind

Harmonic

Density

Sinks

Currents

Tide

tidal

with

Partition

Flux

Partition

choking

friction

flux

of flux

mode in

Model

normal

Sechelt

of

Analysis

of

of

dissipation

fitting

internal

the

modes

Inlet

barotropic

modes

expression

V

tide

93

93

92

88

84

84

53

79 67

39

64 60 55

54

53

46 44

40

36 34

33

30 27 21

A

7

6

Hourly

Conclusions 6.6

6.5

6.4

6.3

6.1

6.2

Low

5.2

5.3

Empirical

Deep-Water Mean

Wind

Runoff Filtering

Mixing

Vertical

Frequency

Data

Circulation

Efficiency

Diffusion

and

Plots

orthogonal

Renewal

Circulation

spectral

in

the

function

analysis

Basin

analysis

vi

157

152

108

136 131

146

127

110

108

101 94

6.5

6.4

6.3

6.2

6.1

5.2

5.1

4.6

4.5

4.4 4.3

4.2

4.1

2.2

2.1

The

The

The

Mean

Mean

Modal

Summary

1991

Modal for

Net

(b) for

Modal

Modal

Modal

Egmont The

M 2

Instrument

January January

K 1

up-inlet

and

first first

first

tidal

monthly

velocities

energy

fits

fits fits

fits

constituents

and

four

four

four

K 1

constituents

of

to to

(amplitude

(amplitude

uncertainties

baroclinic

diffusion

barotropic

Porpoise

the the

EOF

EOF

EOF

fluxes

discharge

and

velocity

velocity

eigenfunctions

eigenfunctions

eigenfunctions

in

net

for

calculations

Bay,

and

and

January,

used

tidal

the

volume

tidal

from

and

and

phase)

phase)

and

List

first

for

energy

the

parameters

perturbation

perturbation

the

barotropic

February,

fluxes

four

of

Clowhom

vii

for

for

for

for

for

for

flux

harmonic

Tables

modes

the

the

the

the

the

K,,

at

at the

=

K 1

M 2

Basin

Basin

Basin

from

April

station

energy

River

density

density

of

tide

Basin

tide

analysis

the

the

and

mooring mooring

mooring

dam

3

fluxes

M 2

profiles

profiles

mooring

(MW)

harmonic

May

for

and

in

in

in

January

for

K 1

of

of

April January.

February.

the

the

(a)

analysis

constituents.

M 2

M 2

K 1

to May

.

tide

tide and .

. of . .

.

141

142 140

135

130

103

83 81

96

80

74

74

59 31 16 6.6 The first four EOF eigenfunctions for the Basin mooring in May 143

6.7 The first four EOF eigenfunctions for the Salmon mooring in January 144

6.8 The first four EOF eigenfunctions for the Salmon mooring in February 144

6.9 The first four EOF eigenfunctions for the Salmon mooring in April . 145

6.10 The first four EOF eigenfunctions for the Salmon mooring in May 145

vi”

3.2

3.1

2.12

2.11

2.10

2.9

2.8

2.6

2.7

2.5

2.4

2.3

2.2

2.1

1.4

1.3

1.2

1.1

across

Relation

Choking

Power

Oxygen Wind

Clowhom Estimated

Sea-level

Basin

Salmon

Power

Power

Along-channel

Along-channel

Moorings

Temperature,

Inlet

The

Lazier’s

Southern

Sechelt

(75

record

densities

a

spectra

spectra

spectra

densities

values

sill

proposed

of

between

spectra

m)

River

British

deployed

monthly

flow

Inlet

from

salinity

of

of

of

(ml

Salmon

Basin

()

dam

through

from

Egmont

the

the

(as)

Columbia

amplitude

system

circulation

Salmon

1_i)

during

runoff

at

(from

along-channel along-channel

currents

in

and

the

selected

currents

from

the

a

oxygen

oxygen

from:

pressure

Inlet

constriction

the

List

daily

and

surface

reduction

the

for

at

Sechelt

depths

for in

Vancouver

of

(a)

selected

moored

discharge

inlets

time-series

for

ix

the

records Figures

January

Salmon

Basin

all layer

Sechelt

surface

Inlet

for

and

sources

with

Endeco

depths

for

currents

January

rates

phase of

Island

currents

experiment

shallow

(100

January

the

layer

(Trites,

from

for

oxygen

and

shift

Basin

for

for

January

sills

for

200

1985

January

of

1955),

January

January

cyclesonde

meters

the

m)

to

and

surface

and

1990).

Narrows

(b) tide .

. the . .

.

41 40

37

38

35

34

32

28

29

26

24

23

25

15

11

10

2 3

4.13

4.12

4.11 4.10

4.8 4.6

4.9 4.7

4.5

4.4

4.3

4.2

4.1

3.7

3.6

3.5

3.4

3.3

the constituents

Schematic

Net

tide January

In-phase

In-phase

Vertical

Horizontal

Perturbation TS

Log

Profiles

Is

Profiles

M 2 Tidal

Analysis Velocity

Model from

Tidal

Skookumchuck

Choking

diagrams

derivation

constituent

constituent

for

up-inlet

Brunt-Vãisãlä

January

currents

amplitudes

for

January

of

of

velocity

measurements

(a.)

of

coefficient,

(a.)

of

the

Basin

Basin

velocity

the

and

in

a

baroclinic

and for

density

of 31

generalized

single

versus

January,

for

for Narrows

modified

along-channel

along-channel

in-quadrature modes January,

frictional

to

at

in-quadrature

January

frequency

January

modes

February

cos

Boom

channel modes

hydraulic

in

(w(z))

tidal ,

February,

barotropic

February,

phase

Skookurnchuck

(u(z))

power

versus

Islet

(p(z))

profiles

inlet energy

10,

velocity

velocity

(b)

head

for

(solid

analysis

(b)

loss

topography-tide

1984

x

for

April

showing

perturbation

January

for

tidal

April

velocity

for

flux

across

January

line)

and and

January

and

January,

flux

Narrows

(MW) and

the

perturbation

perturbation

and

Skookumchuck

May

profiles

model

May

coordinate

density

Rapid

for

February,

factor,

for

(a)

of

July

Islet

profiles

the density

density

M 2

system

9

Narrows.

(dotted

April

M 2 and

and

of

from

from

tide

10,

used

and

the

(b) line),

.

1983

M 2

the

the

K 1

for

May

in

86

85

77

76 69

70 68

71 63

72 60

62

56

50

52 48

44 47

6.8

6.6

6.7 6.5

6.3

6.4 6.2

6.1

5.9

5.8

5.7

5.6

5.5

5.4

5.3

5.2

5.1

4.16

4.15

4.14

Filtered

Filtered

Filtered

Filtered

Filtered

Filtered

Filtered

Work energy

Smoothed net

(April-June)

Work

Eddy

Eddy

Eddy

Eddy Eddy

Eddy

Eddy

barotropic

Kinetic

versus

Along

Frictional

up-inlet

diffusion diffusion

diffusion diffusion

done diffusion diffusion

diffusion

done

channel

estimated

flux,

energy

densities

Salmon

Salmon

Salmon

Basin

Salmon Basin

wind

dissipation

tidal

against

against

baroclinic

E,

and

along-channel

along-channel

velocity

coefficients

coefficients

coefficients coefficients

coefficients

coefficients

coefficients

flux

power

for

along-channel

along-channel

along-channel

along-channel flux

(c) power

(o)

buoyancy

January

buoyancy

of

Basin

rate

in

spectra

the

tidal

profile

loss

Salmon

turbulent

for

for

for

computed

for for

for

for

(April-June)

energy

to

from

wind

wind

for

forces

forces,

May

December December1990

April March

February

January

of

wind

wind

wind

wind

May

Inlet,

(a)

the

xi the

and

and

flux

to

to

jet

up-inlet

and

and

and Salmon

and

tidal

using

W,

to

modified

June

January

May

currents

currents to

for

entering

to

April

currents

currents

currents

currents

1990

as

February

jet

March

the

January

1991

1991

a

(January-March),

of

during

to

function

to 1991

one

barotropic

station

in

in

Sechelt

January

March

(135-220

(170-215

in

in

in

in

1991

May

April

dimensional

(170-220

1991

to

May

April February

January

flood

May

of

3

(150-220

1991

Inlet

(120-220

as

1991

baroclinic

tidal

m)

m) tide

a

m)

(125-215

versus

function

(b)

(125-215

flux

sill

m).

Salmon

m).

model

model

tidal total

.

m).

of m). .

.

120 118

119 119 118

116

117

113

107 106

101

100

100

99

99

98

98

91

89 90

A.5

A.4

A.3 A.1

A.2

6.22

6.21

6.20

6.19 6.18

6.17

6.16

6.15

6.14

6.13

6.12

6.11

6.10

6.9

Along-channel

Along-channel

Along-channel

Along-channel

Along-channel

March

Along-channel

March

Along-channel

Temperature,

MSf

Profiles Mean

1993 May

2

Lag

Hourly

Coherence

Coherence

Coherence

Coherence

Coherence Filtered

Coherence

m

correlations

along-channel

constituent

along-channel

1991.

1990

discharge

of

densities

Basin

and

and

and

and

and

and

salinity

Salmon

Salmon

Basin

Basin

Basin

section

section

phase

phase phase

phase

phase

phase

between

along-channel

for

from

(o)

currents

currents January

currents

currents

velocities

spectra

spectra

spectra

spectra

spectra

spectra

and

currents contours

currents

in

contours

the

Salmon

discharge

dissolved

Clowhom

in

for

for

for

at

at

at

at

at

at

Salmon

velocity

for

in

in

of

of

Salmon

Salmon

Salmon Salmon

Basin

Basin

May

April

February.

xli Inlet,

the

the

density

January,

density

from

oxygen

dam

surface

surface

Inlet

for

for

and

May

for

the

for

for

for

May

April

and

and perturbation

.

in

May

April

January

February

February,

Clowhom

layer

layer

Sechelt

oxygen,

oxygen,

for

for

River

March,

Inlet

February

April

for

for

density

February

February

from

dam

April,

from

and

1957

and

and

and

the

the

to

161

161

160

158

159

151

150

148 134

133

129

128

125

125

124

124

123

122 120

A.12

A.11

A.9

A.1O A.8

A.7

A.6

Salmon

Salmon

Salmon

Basin Basin

Basin

Along-channel

densities

densities

densities

densities densities

densities

Salmon

(oj)

(crt)

(o)

(Jt)

(as)

(os)

for

for for

in

in

in

currents

May

April

February

the

the

the

surface

surface surface

in

XIII

the

layer

layer layer

surface

for

for

for

May

April

February

layer

for

May

167

166

166

164

165

163 162

thing

my

thanks

Michelle, in

to

Shore

discussions

data

at

analysed.

support

Jones, numerous

LeBlond

committee

this project,

I

I

would

am

tight

think

Tides

Personal

Many

direction.

thesis,

and

or

for also

Hugh

to

places.

two

during

first

about,

and

and

for

always

keeping

permitting

thanks

the

The

helpful

very

deserve

over

in

support

their

about

Maclean

Currents

for

like

summer

Geoff,

assistance

these

to

The

the

coffee. grateful

gave

giving

to

to

me

comments

discussions

Roger

many

marathon

instrument

Peter

defensive

thank

came

Shirley,

the

times

alert

me

and

(Institute

softball

Thanks

me

for

use

from

Pieters

good

thanks

Arjoon

Baker

and

in

Dr.

the

of

and

Dr.

of

Dan

many

drives

during

cover-ups the

limited

reason squad

for

to

the

opportunity

deployments

Steve

of

for

for

suggestions

as

Acknowledgements

Ramnarine

Pond’s

staff,

and

the

enlightening

Ocean

ways,

tidal

well;

his

his

and

the

for

Pond

to

beer

funding.

Susie

especially

helpful

help

from

get

rapids

playing

showing

in

data

support

and

Sciences,

xiv

garden/coffee

particular

for

away

to

became

during

and

in

deserve

the

from

analysis,

me

presentation participate

his

data

model

The

cards.

for

up

Mike

guys

for

during

on

guidance

many

Sidney,

the

my

to processing

much

the

a

other

the

I

was

on

Woodward

while,

most

preparation

Livvy,

thank

and

second

room

many

people.

many the

the

recognition

in

much

B.C.)

members

suggestions,

Drs.

and

of

the

and

final

hockey

Mr.

Jessie,

gang

water

the

and

dangers

family

appreciated.

in

advice

My

Sechelt

Susan

they

and

Dario

months

providing

games.

of

for

for

parents

Dexter

of

samples

team

this

for

Anne

and

never

giving

the

of

throughout

my

and

Allen

Stucchi

Inlet

their

nerf

thesis.

taught

were

of

many

supervisory

Ballantyne,

and

to

let

and

tide

me

that

preparing

and

program.

technical

footballs

Jennifer

me

timely;

for

Nessie

plenty

sister,

David

useful

gauge

me

were

Paul

lose

this

the a

finally

scholarship

and

their

air

and never

a

huge

is

I

for

Engineering

thank

cooperation

clearer

let

like

thank

the

me

to

the

program.

weekend

and

forget

you

acknowledge

officers

the

during

Research

to

the

hikes

perspective

Sally

and

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the

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of

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of

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taking

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research

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late

xv

of

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This

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me

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R.B.Young again.

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Finally,

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would

rubs,

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The

Fjord

sensors

1.1 of

and

versity

and inlet

residents

the

and

aquaculture

popular

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Sechelt

1.1).

each

A

Sechelt

continuing

glacially

its

close

waters

Fjord

estuaries

comprehensive

notable

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Sechelt

of

were

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year,

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spot

is

British

proximity

growing.

Peninsula

for

farms,

estuaries deployed

are

for

is

scoured

and

for

to

have

and

until

industry,

a

recreational

three

the

assimilate

fjord

moored

Columbia

particularly

Narrows

been

April

field

impressive

to

As

U-shaped

over

is

estuary

inlets

the

recreation a

communities

carved

study

current

1992.

popular

six

pollution

Department

lower

boaters

in

have

months,

on

shellfish,

the

tidal

of

walls

from

Hydrographic

the

meters

shallow

the mainland

and vacation

system

and

Introduction

rapids

will

southern

high-latitude

are

along

Chapter

Sechelt

beginning

waste

because

white-water

of

become

equipped

steep,

1

sills

(Sechelt,

at

Oceanography

the destination,

markets.

disposal,

Inlet Skookumchuck

mainland

surveys

connecting

inlet

of

1

and

in

important

river

its

with

system

December

Salmon

enthusiasts.

the

grow

relatively

the

were

Though

valleys

coast

and

temperature

sills

water

and

beginning was

their

issues.

made

and

the

Narrows,

which

of

1990.

over

rely

undertaken

calm,

not

quality

waters

British

number

The

Narrows,

in

increasingly

several

heavily

often

winter

productive

in

and

inlet

Sechelt

of

to

Columbia

January

of

conductivity

appear

Sechelt

also

the

by

glaciations.

Fig.

and

permanent

populated,

the

Inlet

attracts

outside.

on

spring

waters

1.2)

1990,

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Inlet

Uni

(Fig.

the

is

of a Chapter 1. Introduction 2

128°W 123°W 52 °N + + + + 52 jr L °N British

SeymourInlet Columbia

+ + Knight Io4et + + Bute -— Inlet Toba Inlet

Jervi ÷ + . Inlet Sechelt Inlet N Howe Sound Indian 44, 0 Arm • Vancouver ÷ Alberni÷ - Pacific Inlet U.S. Ocean Saanich Inlet

÷

48 °N ÷ 8°N 128°W 123°W

Figure 1.1: Southern British Columbia and Vancouver Island.

49.5°N

Chapter

—]

124°W

1.

Introduction

kilometres

S

echelt

Inlet

Figure

Porpoise

1.2:

Sechelt

The

Bay

Tzoonie

Sechelt

Inlet

system.

Inlet

0

o

.

I

LEGEND

Hydrographic

Cyclesonde Station

Aanderaa Geodyne

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123.5

F

0

W 3

the conserve

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water vigorous

tical

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large

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bottoms

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the

Chapter

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sharp

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dissolved

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term

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has

directly

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long

source

layer

of

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layer

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the

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Queen

been

(from

interface

counterparts.

made

1.

characteristics

residence

beneath

bedrock)

southern

gradients

at

northern

to

Introduction

end

Canada.

The

oxygen

of

are

onto

Department

surveying

fjord

accumulations

at

of

the

flow

with

Charlotte

salt.

of

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5

surface

Georgia.

between

the

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the left

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and

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the

the

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Oceanography

of

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high

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layers

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is

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are

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up

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km)

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the

layer.

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to

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layer.

kg

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water

basin

thirteen

gradient

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intervals;

remnants

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shallow

furthest

1951

the

m 3 );

limits

and

(see

Pickard

and

attributed

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of

surface

waters

of

to

estuarine

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saline

less

deeper

also

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southern

depths

have

created

Sechelt

have

Pickard

sill,

the

extent.

measurements

of

defined.

(1975)

Pickard

as

and

density

layer

and a

the

less

the

water

source

with

it

to

1961).

flow

at

Inlet

suggested

terminal

notes

inlets

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is

travels

dense

the

UBC

entrains discusses

the

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is

of

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fact

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fjords

head

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of

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temperature,

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the

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forces

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general

onto

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water

freshened

into

water

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from

the

northern

circulation

water

deep,

of

1980).

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channel

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dense

deep-water

to

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surveys

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than

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as

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in

Chapter

deep-silled

the

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a

Friction,

discussion

of

blocking)

Tidal

flow

of

strongest

modulate

energy.

deep-silled

amount

calculating

suggesting

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interactions up-inlet

an above

for

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outflow

waves,

of

over

1.

influence

inlet

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mixing

enhanced

and

internal

may Introduction

fjord

Stacey

increased

of

to

of

high

the

while

area

the

internal

remove

will

inflow

fjord,

dissipation

that

Stigebrandt

Edwards,

the

also

near

sill,

in

may

two-layer

on

frequency

due

when

be

high

(1984)

energy

hydraulic

Observatory

and

the

occur

the

to

during an

enhanced,

so

be

hydraulic

the

energy

to

frequency production

complete

reduced

the

ebb

did

two-layer

greater

choking

1980).

sill,

also

by

budget

with

flow

(1976,

variation,

sill

an

the

tide

friction)

processes,

from

the

studied

ebb

a

is

at

processes,

while

The

Inlet,

than

power

tidal

at

blocking

fortnightly

may

of

internal

shallow

1980).

circulation

breaking

tidal

of

the

tide

the

a

amount

internal

the

the

fjord.

flow.

using

accounted

short

the

block

withdrawn

barotropic

and

entrance.

frequencies.

and

The

amount

deeper

and

and

waves

of

removal

of

a

and

Although

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the

the

period,

of

the

inflow

can

internal progressive

waves

the

the

mixing

water

subsequent

generation

inflow

long

for

and

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exchanged

range

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from

tide outfiowing

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of

during

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exchanged

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energy

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tides

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from

the

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important

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the

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be

of

enhancement

exhibit

barotropic

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in

winds

a

from

tide

altogether.

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spring/neap

hydraulic surface

tide

internal

slowed,

found

simple

a

tide

during

shallow-silled

therefore,

near

(1980)

tide

on

and

over

the

can

the

sink in

to

the

water

flow

model

or

the

pulsations

barotropic

high

waves

a

tide

a

a

jumps

also

be

most

found

of

shallow-silled

perhaps

tidal

deep

bottom

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during

cycle

sill

modulation

the

barotropic

important

frequency

dominates

in

affect

based

near

periodic

provide

slowing

cycle

sill,

(plus

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fjord

that

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brings

flood

such

even

and

tide

the

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the

on

as

in

of

a 5

the

at

then

and

deep-water basin

and

diffusion near

increased,

salt

was

response when

as of

Inlet,

water of

For

changes

from

along

1980).

Chapter

times

the

270 the

Over

Low

sill.

example,

from

the

weaker,

either

spring

the

the

most

water

outside

Baker

the

upwelling

sill,

m.

Because

strength

of

If

frequency

time,

surface,

in

of

of

1.

the sill

lateral

However,

the

the

density

pushes

low

renewal of

tides

offshore

salt

the

there

enters

Introduction

(1992)

(Stigebrandt,

lower

upwelling

the

the

the

increased

mixing

runoff,

most

current

(Pickard,

often boundaries

on

of

no

sill

was

wind

density

it

changes

variations

the layer.

mixing

are

found

the

the

substantial

density

up

of

of

deeper

over

and

provide

off

inlet,

energy the

Alberni

highly

deep

shelf

or to

surface

Although

in

that

the

often

1961).

1976;

at

in

water

towards

changes

the

of

(Stigebrandt,

the

transfer

currents

outside

and

in

the

offshore

west

the

was

the

dependent

sill

current

Inlet:

increase

density

deep-water

the

only

Stacey,

in

sill.

the

extra

channel

Periodically,

trapped

is

coast

there the

the

in

circulation

the

of

vigorous,

during

the

were

For

water

new

runoff

inlet

structures

momentum

head

energy

gradient

in

1984).

of

mouth

was

strength

on

example,

1990),

provides

volume

water

very

Vancouver

in

of

is

can

neap

the

of

was

a

the

fjords

eventually

required

deep-water

significant

water

in

weak

the

of

have

density

was

wind

sinks

surface

tides were

of

not

fjords

transport

the

the

if

and

inlet.

decreases,

the

found

there during

a

Island

that

as

and energy

inlet

coherent

to

when

large

the

to

inflow

of

replaced

are

layer.

clear.

increase

replace

pump

renewal

The

is

is

runoff

currents

the

to

(Stucchi,

increases

was

times

mainly

effect

mixing

little

denser

for

is

mainly

suppress

timing When

water

As

with

measured. related

dense

vertical

by

the

(Gade

in of

mixing

can

on

the

were

driven

energy water

than

high

the

the

the

1983).

outside

from

old

the

fjord

and

deep-water

only

entrainment

river

to

diffusion

velocity stronger.

and

density

wind

stratification

stratification

basin

over

from

the’

the

the

by

strength

circulation.

is

take

In

discharge

Edwards,

the

reduced.

strength

resident

seasonal

the

upward

as

outside

Knight

water,

of

place

shear

away

inlet

deep

over

The

sill,

the

of

of 6

at

(Glenne

contaminate

the

the

oxygen

and

consumption

the

the

also

penetrate limits

water, striction

fastest

The

1.2

concentration

more

dissolved Depending

Chapter

the

In

Shallow

surface

degradation

basin

Narrows

oxidize

pose

tidal

Scandinavia,

entrance

dissolved

Shallow-silled

the

and

currents

to

and

over

1.

a

water

to

oxygen

exchange

rapids

trace

the

(particularly

waste

sills

hazard on

water

Simensen,

are

the

Introduction

of

the

of

to

intense

the

oxygen

oxygen

of

levels

on

is are

passable.

bottom

the

at

heavily

sill,

due

material

limited

used

residence

water

replaced,

to

the

water

Skookumchuck

not

deep-water

which

to

mixing

navigation;

fjords

in

1963).

than

as

coast

for

near

of

only

populated

decomposition

quality

the

exchange

density.

sinking

is

the

industry

is

time

the

the

subsequently

of

the

of

deep-water.

a

as

The

inlet.

the

hazard

British

usually

by

existing

shallow

existing

head)

of

slack

organic

As

waters

fjords

of

Narrows

inflowing

limiting

the

or

The

basin

a

recreation.

to result,

where

of

water

Columbia

existing

increases.

as

basin

shallow

has

low-quality

material

organic

that

The

reduced.

navigation,

water

5

the near

water

caused

m,

is

it

inflowing

water;

ability

are

basin

exchange

often

can

limits

depths

the

due

at

material.

with

is

used

During

a

interfere

16

entrance

decomposed

to

water

hence,

water,

significant

the

of

but

the

the

water

narrow

knots

for

at

the

of

only

volume

may

the

rare

relatively

sewage

New

may

the

it

during

basin

with

is

(800

to

sill

may

time

or

also

exchange

rarely

basin

water

water

be

Sechelt

shallow

can

of

and

fish

water

cm

and

be

renewal

that

displaced

be

the

fresh

reduce

water.

strong

oxygen

extremely

dense

s 1 )

communities

usually

waste

responsible

tidal

Inlet

the

events

constrictions to surface

.

the

assimilate

enough

tidal

waters

Bacterial

dissolved

exchange

The

problem

disposal

have

towards

contains

oxygen

where

low

layer

flow

con

the

for

or

to

of

in 7

gauged,

flow

due

Clowhom in

runoff

internal

nearly

because

Point

historically

depths shallow

shallow opens

The

1.3 when

(by tend

(thus

Chapter

the

One

Mean

Due

to

rates

dredging)

Sechelt

to

winter

to

basin

The

the

increasing

20 onto

the

of of

but

to

accumulate

(14

wave

sill

its

Porpoise

fresh

1.

are

River

the

%

the

basin

the

Clowhom

oceanography

is

been

m).

runoff

area (5

the

of

from Inlet

Introduction

monitored

earliest

dissipation.

glacier

inlets

free

to

to

water

the

at

is

lower

There

the

(Pickard,

considered

maximize

20

rainfall

system

Bay

fairly

communication

is

the

total

in

are

and

assimilation

fed

m),

descriptions

much

input

the

part

is

head

has

275

hourly.

shallow.

and

surface

no

Tzoonie

and

and

(Fig.

stagnant

1961;

been

of

smaller

the

into m

of

sill

of

as

presumably

one

the

Jervis

for

Sechelt

Salmon

one

1.2)

separating

tidal

The

Trites,

area

historically

Sechelt

capacity)

of

rivers

in

Sechelt sill

of

deep

than basin.

is

the

early

waters

Tzoonie

energy

Inlet.

and

separating

located

Inlet

1955).

Sechelt

Inlet

layer.

and

is

has

that

and

summer

its

Sechelt

The

of

110

between

Sechelt

flux.

disregarded

from

its

is

sloping

River,

the

50

Salmon,

of One

There

Inlet

m 3

dammed

maximum

section

Narrows

km

Salmon

basin

This

creeks

caused

and

method

s 1 ,

at

Inlet

Sechelt

system

bottom northwest

are

the

and

Salmon

approach

of

water

estimated

with

draining

for

two

by

is

Inlet.

and

Sechelt

runoff head

of

85

and

was

separated

power snow

runoff

makes

increasing

respect is

m

Sechelt

Inlets.

of

of

given

Salmon

to

is

However,

for

period

along

melt.

Vancouver,

Inlet

by

Narrows

tune

particularly

by

peaks

it

Narrows.

by

precipitation

to

The

a

Inlet from

B.C.

from

the

in

the

Inlet,

Input

the

likely

the

Carter

per

the

typical

it

Inlet,

flushing

inlets.

is

constriction

Jervis

Hydro

circulation

Nine

comprises

year:

they

B.C.,

is

summer.

place also

effective

(1934).

largely

is

basin

have

by

Mile

The

very

and

and

one

not

and rate

for

a 8

water

deeper

tidal

layer

as

seasonal

and

turbulent

sills

due

water

vations a

was

between

1985,

thirteen

physiographical

was

sharply

sampling

oxygen

In

Chapter

circulation

the

The

his

The

Sechelt

Farmer,

to

visited

(Stucchi,

water

present

and

induce

and

enters

inflowing

surveys

(Fig.

tidal

between

first

source

levels

density

(to

1981

times

1.

forms

and

into

two

density in

Inlet

nearly

inflow

detailed

1980).

as

density

for

in Introduction

1.3(b)).

four

and

causes

below

1980).

of

in

thinking

of between

a

the

a

Sechelt,

description

cycle,

shallow-silled

water

was

B.C.

1986).

turbulent

layer

the

consecutive

1986,

has

0

increases

deep-water

currents,

the

look

mixing

ml

visited

Horizontal

Because southern

inflowing

where

gets

been

just

that

four

Narrows

1961

1—1)

surface

at

jet

lighter

of

below

the

directly

that

in

once

cruises

this

and

the

and

which

inlets

years

Sechelt

during

of

inlets,

the

and

Sechelt

layer

water

and

pressure

density

was

hydrogen

breaks

the

by

1964.

the

in

starting

autumn

was

to

the

flow

observed

Princess

the

he

spring,

constriction

(although

tidal

a

and

brackish

Sechelt

(i.e.

Inlet

permanent

proposed

black

noted

down

as

is

The

UBC

gradients

Salmon

exchange.

largest sulfide

indicated

in

and

system

the

it

Louisa

by

area

Inlet

mud

1961.

that

the

Institute

floats

water

he

winter,

surface

current

to

at

Inlet

associated

normal

in

was

may

Narrows

feature).

were

sampled

caused

was

Using

explain

Inlet:

the

the

by

The

on

at

not

was

have

made

the

of

the

made

the

water

meters

the

winter.

sill,

density

hydrographic

appearance

in

Oceanography

by

revisited

given.

Inlet

the

arrows inflowing

from

surface

The

been

dense

these

with

the

by

the

(one

outside

similarity

in

Lazier

had

Lazier

oxygen

flow

stratification

the

anaerobic

misled

influx

shallow-silled

basins

homogeneous in

in

(Fig.

until

very

layer

each

of

Fig.

bottom.

becomes

the

(1963).

measurements,

proposed

turbulent

of

level

by

with

of

in

low

1981,

1.3(a)).

of

1.3.

penetrates

sill)

the

the

conditions

infrequent

1957,

1981

dissolved

dropped

shallow

(Smith

Sechelt

Only

mixed

highly

inlets,

obser

has

when,

deep

that

jets

and

and

As

a

a 9

perhaps

in

(consistent annual

average

Sechelt

Figure

0.4 mogenization

between

1 newal

sities

spring/summer,

Figure

Chapter

ml

late

Pickard

Lazier

kg

1_i

outside

in

m 3 .

cycle

winter

1.4

100

of

a

to 1.3:

Sechelt

November

1.

rare

had

shows

5

with

over

m

(1975)

Dissolved

is

to Introduction

the

of

or

and

event,

Lazier’s

evident

hydrographic

4

7

Lazier’s

Inlet.

the

when

early

the

sill

ml

stations)

Narrows

presented

1961

water

(a)

M

are

replacement

time-series

oxygen Temperature

at

densities

spring.

proposed

circulation).

between

high

and

200

column.

and

75

measurements

a

m.

March

(from

levels

m

The

summary

outside

at

of

November

At

show

of

circulation

75

the and

The

decayed

Lazier,

cycles

water

100

1962,

m

a

data

oxygen

the

deep-water

m,

similar

in

of

at

suggest

and

1963,

during

and

oxygen

sill

Narrows to

all

taken

mid-depths

for

contours

less

the

four

March,

are

annual

Fig.

that

a

at inlets

than

data

salinity

oxygen

low,

years

particularly

Inlet.

100

5).

and

cycle

while

show

show 2

occurs

and

with

and

ml

of

profiles

levels

sigma-t

The

marked

(maximum

J’

data

(b)

bottom

an

200

(b)

annually

shallow

annual temperature

again

strong

in

increased

m

from

indicate

values

winter,

changes

in

water

by

deep-water

Sechelt

cycle,

in

1961

in sills:

July

increased

from

winter);

late

a

when

renewal

in

deep

to

data

peaking

1962.

Sechelt

winter

(a)

(at

below

1964.

den

ho

for

re

no

an

by

is

in 10

0.5

1963,

1962, Inlet

Figure

Chapter

Narrows

degrees

(75

the

the

1.4:

m),

1.

renewing

renewing

cooler.

Temperature,

Inlet

Introduction

from

oxygen

cruises

The

water

water

oxygen

had

salinity

had

data

between

the

a

decay

indicate

density

and

same

1961

rate

oxygen

salinity

and

an

much

is

annual

greater

1964

for

greater

as

Sechelt

(Pickard

the

renewal

in

than

resident

Narrows

(100

(1975),

the cycle

and

water,

resident

than

at

Fig.

200

75

in

but

m)

3).

Sechelt.

m.

water.

it

and

In

was

Narrows

January

In

nearly

May 11

is

and

circulation

sill of

is

at the

forcing.

an

of

for

physical

estimate

at

(1994), non-physical

assimilative the

levels

Aquaculture gather

The

1.4

Chapter

given

given

the

the

the

effort

the

region,

The mixing

data

analyses

growing

study

Motivation

sill.

baroclinic

and

basin

formation

biological,

in

aim

who

of

study

to

processing

oxygen

1.

chapter

in

and are

The

by

the

address

of

of

capacity

waters,

Introduction

the

the

examined

aspects

population stocks,

Sechelt

quantified. blooms

this

deep-water

was

energy

tidal

inlet,

efficiency tide,

production

and

chemical

7.

thesis

the

to

techniques

and

particularly

circulation

of

of

Inlet

movement

the

of

answer

(b)

flux

goals

the

the

the

of

(c)

toxic

is

Chapter

what

exchange

turbulent

of

extracted

study

and

by

production

to

the

inlet

how

of

and

the

three

present

or

the

used.

the

are

physical

is

Sechelt

of

salmon,

possible

have

is

gill-damaging

consumption for

discussed

5

UBC

study.

the

are

questions:

the

phytoplankton

examines

tidal

from

Chapter

pollution

and

been

diffusive

presented

and

circulation

Peninsula

information

Department

have

jet,

sources

Chapter

analyse

the

discussed

assimilation

in

and

the

3

(a)

Chapter

tide

been

and

in

and

phytoplankton

addresses

in

of

diffusive

the

what

energy

2

the

will

affected

blooms

chapter at

waste

deep-water

presents

mixing

plagued

about

of

by

water

the data

eventually

4:

are

Oceanography

Sutherland

of

dissipation

the

first,

disposal

sill;

processes

in

the

6,

by

organic

collected

energy.

the

column.

by

sample

the

and

problem

wind

exchange

second,

inlet

(Black,

a

main

chronically

theoretical

region,

a

put

(Arber,

summary carbon

The

(1991),

system

and

data

in

in

by

sources

The

of

pressure

was

the

the

1989).

Sechelt

friction

characteristics

low

low

and

tidal

and

deep-water,

energy

1993).

goal

in

designed

who

low

as

discussion

frequency

frequency

of

of

discusses

Timothy

order

a

As

choking

Inlet

results

oxygen

energy

on

looked

in

of

whole.

well,

flux

The

the

the

the

in

to

12 to average specified a tromagnetic sor S4 current temperature and The to Currents CTD current of temperature-depth this The 1991 true the June current Instrument (InterOcean period, conductivity CTD Sechelt (see probe. vector 9 meters several meter 1991 time oceanographic section Fig. surveys meters hydrographic field Inlet sensors Historical average and interval 2.1). moorings were uncertainties readings S4). of set sensors study coincided from use the (CTD) A of are up of mooring The and two voltage tide Institute December stations began of around the were less surveys of types: spot velocity probe Aanderaas gauge the velocity. with are Instrumentation accurate deployed potentials was in direction the listed moored of were (Fig. coupled rotor the January data 1991 also components Ocean instrument. servicing Rotor-type made Chapter in and in 1.2) (Aanderaa, from landward deployed to instruments Table created readings general with Sciences 13 1990 cyclesondes April from approximately the of a 2.1. over and and 2 One region seaward water late by current 1992, than of the to cyclesonde) (lOS), The the continued the the Data compute could moorings advantage autumn those use sampling to were current sill sampling water meters of Sidney, monthly monitor average be the between provided on velocity. to inter-calibrated until and flowing so sill meter of the also rosette early B.C. interval that the from electromagnetic using the rotor April CTD January have by conductivity through S4 the exchange summer. The December system a the counts is 1992. and probes. conductivity- a temperature InterOcean that stall Tides and compute with an at During over water. it Three speed June elec 1990 each sen The and and can the a

decimated

the

data

The Winkler

the from

assembly

model

probe when

but

five

Inlet

mooring

A

increases

2.0.1

the

the

uncertainties

(--2

Chapter

series

During

A

upcast,

bottle

in cyclesonde

are

stall

temperature

are

cm

the

(station

Guildline

the

is

Sechelt

1015

not

Hydrographic

25

of s’

titration)

binned

probe

deployment

speed

2.

is

the

Guildline

salinities

to

a

hydrographic

hz,

bottle

rosette

discussed

for

lowered

cast,

Instrumentation

1

uncertainty

for

9).

Inlet

and

m

is

provide

the

problem

model

into

samples

vertically

the

intervals

samples

the

Some

and

bottle

Aanderaas

(stations

to

model

to

0.1

period.

4

cyclesondes

in

CTD

8705

produce

salinity

hz

a

between

the

m is

measurements

surveys

surveys

continuous

somewhat

from

cluster.

for

are

for reduced.

8709

profiling

bins

probe

CTD

analysis.

2-6),

One

the

and

taken

depths

and

(using

the

a

(0.2

CTD

5

was

8709.

second,

station

probe

are

two

Data

samples

and

cyclesondes)

CTD

while

for

The

at profile

m

made

similar

shallower

the

in

probe

several

20

bins

The

were

low

was

Salmon

probe

correction

was

independent

measuring

Guildline

m

from

continuously.

of

current

probe

for

used

was

made

to

from

located

temperature,

depths

at

under

than

the

January

those

Inlet

used.

for

each was

the

at

speeds.

Autosal

8709). of

currents,

50

just

all

and which

(stations

station

for

attached

the

density

bottom,

bottle

The

m,

surveys,

to

Initially,

the

seaward

later

rotor

Finally,

and

June

salinity

8400

the

sampling

0,

Aanderaa;

the

depth

profile.

7-8),

analysed

every

to

and

rotor

speed

located

1990,

except

salinometer

the rotors

the

of

the

and

and

the

are

the

5

probe

will

General

rate

for

prior

The

binned

m

density.

are

February

combined

one

in

downcast

for

sill

however,

not

the

thereafter.

for

Jervis

CTD

turning

to

and

oxygen

(station

in

at turn.

fall

Oceanics

the

the

data

Narrows

During

rosette

UBC).

probe

speed

Inlet,

1991,

when

main

8705

with

data

The

and

(by

are

1), 14 tJ: ‘1 I ,_io0- I E

r4)

200 -

300-

I I I I 40 30 20 10 0 Distance from the Head (km)

Figure 2.1: Moorings deployed during the Sechelt Inlet experiment. Depth scale corresponds to bottom topography and only approximately to the depth of the instruments. Table 2.1: Instrument uncertainties. Values for conductivity are given in equivalent salinity (indicated by (S)).

C,)

Instrument Cond Temp Press Oxygen Speed Dir Rotor (equivalent S) (°C) (dB) (ppm) (cm s1) (°) Type

— I Cuildline 8705 CTD — — .01 .01 1.5 —

Cuildline — 8709 CTD — .04 .02 5 .5 —

Cyclesondet .01 .02 .25 — 1.0 3.0 Savonius

Aanderaa RCM4t .02 .15* 5 1.0 5.0 Paddle/ (2.0 stall speed) (7.5 < 5 cm s’) Savonius

InterOcean S4 .01 .02 2 — 1 ± 2% of reading 2.0 Electro magnetic

— — EndecoO2 — — .2 .4 —

— Ceodyne Anemometer 2.0 (%) — — 2.0 (%) 5.0 Cup t For the cyclesonde, Aanderaa and InterOcean instruments the conductivity values given are the precision. The accuracy values are somewhat larger depending on how well they can be corrected to the CTD values. 0.02 for some instruments with expanded temperature range.

0)

currents

similar

every five

second

the

a

ity line

mooring.

sites

of

two oxygen

1991:

at

the

1991, A

2.0.2

Chapter

150

one

The

approximately subsurface

There

and

At

Three

Sill

S4

from

mooring

months.

will

two

m

one

then

surface

the

current mooring

to

mooring

temperature.

mooring

meter

would

Current

profile.

-20

2.

be

The

were

the

months

mooring

near

Sill

again

hereafter

was

Instrumentation

one

and

to

was

instrument

mooring

site,

be

meters

two

station

employed

with

in

180

75

between

and

one

too

at

30

Meter

sites placed

Salmon

one

moorings

m

m

Basin.

the

m

The

referred

subsurface

small

was

at

and

2,

depth

cyclesonde

was

landward

and

addition

one

2,

instrument

at

used

Moorings

a

December

deployed

two

Inlet

4,

to

Geodyne

No

deployed

50

30

near

(van

deployed

and

to

6,

be

Aanderaa

an

m.

cyclesonde

m.

was

mooring

9

as

of

of

accurately

Data

station

Leer

inflatable

profiling

and

Between

The

“Sill”

twice

three

the

a

normally

1991

buoy

near

Geodyne

at

et

12

sill

current

RCM4s

,“Basin”

closely

3

the al,

Aanderaa

(January

m.

and

was

(equipped

in

Egmont

current

were

bladder

1974),

December

measured

Basin

the

The

takes

April

deployed

buoy

and

spaced)

maintained

(recording

main

and

Geodyne

recording

meter

to

RCM4s

site.

between

less

to

oxygen

1992

suspending

with

March

(S.

“Salmon”

move

1990

basin

than

and

here,

One

was

Pond,

(see

an

at

current

mooring

meters

and

between

one

velocity,

up of

December

and

one-half

anemometer)

mooring deployed

since

208,

Fig.

Sechelt

and

in

pers.

respectively.

five

June

April

238

Salmon

meters)

were

it

2.1).

down

required

S4

January

depth,

hour

was

comm.).

1991,

and was

inlet

on

to

1990

current

serviced

The

June).

felt

a

the

Inlet.

to

268

identical

were

suspending

conductiv

(consisting

subsurface

an

and.

and

complete

servicing

that

mooring

depth

m.

Endeco

meters

placed

These

every

June

June

The

the

to

17 of

scalar

and

perature,

and every

the

clesondes

cyclesonde

to

quired. temperature-salinity

ing

UBC

to

the

digitally

The

cyclesonde

minute

The

2.1.1

2.1

Chapter

be a

On

Once

deployments.

units,

Pond

then data

portable

cyclesonde

vertical

MTSG

10

any

values

Data

the

while

Cyclesonde

CTD

m

recorded

linearly

removed

stream 2.

salinity

were

(1995)

data

plotted

mooring

mainframe,

to

below

processing

Instrumentation

are

resolution

mainframe.

profiling

computer.

measurements

operate

adjusted

point

collects

linearly

discuss

and

interpolated.

and

The

on

50

from

and

were

curve.

m),

cassette

corrected.

which

density

profile

(1

for

checked

the

temperature,

the

is

to

the

There,

interpolated,

hour

with

used

between

agree

30

raw

cyclesonde,

Glitches

interpolation

varies

data

of

and

at

tape.

days

every

an

to

for

data

the

conductivity

The

regular

with

Data

approximate

correct

were

5

beyond

spurious

data

before

3

were

and

channels

conductivity,

corrected

the

hours)

while

the

then

intervals

were

10

procedure

deep

examined

any

requiring

a

tape

velocities

m.

data

set

used

and

and

checked

in

drift

binary

CTD

sampling

was

Profiling

tolerance

each

(every

once

points

temperature

to

pressure

in

individually

for

read

servicing.

values

create

file

files

are

in

the

every

creating

5

binary

interval

(glitches).

using

once

were

vector

m

from

cyclesonde

were

and

at

time-series

5

between

the

minutes

every

converted

velocity

near

a

All

form

a

the

then

then

averaged

of

tape

linear

beginning

three data

profiles;

A

the

3

for

20

transferred

interpolated

sensors.

reader

of

while

glitch hours

records

fit

and

bottom

missing

channels

into

velocity,

hours.

in

to

essentially,

and

stationary.

50

10

allows

connected

is

engineer

the

once

The

m,

defined

m

end

bits

of

to

Baker

if

tem local

were

bins

and

the

cy the

the

per

re

of

in 18

same

adjusting

current

the

current conductivity

The

(

are

2.1.3

samples.

may

two

series.

(see

conductivity

before

pressure)

deraas

The

1)

2.1.2

Chapter

Because

were

12

vector Each

significantly

highest

InterOcean

Baker

be

method Aanderaas

m)

Seven

and

moored

contaminated

over

sensor

InterOcean

Aanderaa

compared

data

2.

A

the

at

and

averaging

and

after

straight

the and

the

Instrumentation

10

and

and

data

S4

as

set

were

is

Pond,

below minute

S4

mean

in

surface

with two

sampling

recorded

deployment.

that

temperature

temperature

points sampled

error.

to

electromagnetic

set

RCM

feature

average

lowest

S4

the

by

the

it

values

1995).

200

intervals.

to

layer

is biological

centered

Aanderaas

CTD

interval. conductivity,

record

m

not

at

values

of

of

to

This

at

and

10

has

The

the

every

to

the

prone

the

values

the

minute

make

The

a

on

Data

current

were

material type

large

seven

Aanderaas

one

The

CTD

current

the

Basin

10

(see

to

temperature

at

any

removed,

of

minute

minutes.

temperature

data hour

fluctuations

rotor

intervals

values

values

section

station

meter

filter

site

and,

meters

reliable

were

were

deployed

pumping

average

were

is

at

might

hence,

allows

2.1.2).

and

The

1,

useful

was

used

the

were

converted

and

adjustments.

but

adjusted

in and

the

advantage

beginning

include

filtered

accurate

subject

to

conductivity

of

seaward

all

from

temperature

showed

when

remaining

calculate

velocity

velocity

deployed

to

wave

one

to

to

dealing

to

measurement

hourly

too

of

and

of

create

the

intermittent

or

(some

and

the

the

action.

the

three

in

records

much

end

more

CTD

and

with

hourly

the

sill

values

spot

electromagnetic

an

of

also

were

conductivity,

variability

values (near

surface

hourly

values

In

sensors

deployment

of

readings

value:

of

erroneous

using

measured

addition,

averaged

the

the

station

which

taken

time-

layer

Aan

that

the net

the

of

19 in

from

in

Data

with

2.2

oxygen

the oxygen

cessing

The

2.1.5

coordinates.

filter

components

should

The

direction

2.1.4 presumably

densities

mean

was

Chapter

cm

nearest

impractical.

anemometers

conductivity Endeco

the

will

used

Data

s 1

density

values

data help

also

Endeco

Anemometers

constant

on 2.

be

between

and

for

current

includes

magnetic

presented

temporarily

to

in

were

Instrumentation

oxygen

increased

spectral

were the

all

reduce

oxygen

Instead,

relative

salinity,

reprocessed

Aanderaas

the

on

instruments

meter.

corrected

meters

a

the

tape

instruments.

in

frequencies

the

salinity

with

homogenized

SI

Geodyne

meters

to

the

oxygen

When

(similar

noise

units

recorded

standard

depth,

for

and

and

instruments

to

correction

were

the

in

correct inherent

(MKS)

the

values Data

will

buoys

to

and

situ

reprocessed

rotated

the

S4s

oxygen

sea

be

the

strong

temperature

for

changed

recorded

Aanderaas)

with

water

in

was

were

using

in

upper

cycles

in

to

the

and

used

the

wind-mixing

made

situ

geographical

and

a

data

wind

water

by

air

following

constant,

temperature

per

for

salinity,

are

no

when every

self-consistent

temperature,

were

day

the

direction

column)

more

given

compared

10

anemometer

processed.

(cpd).

events

exceptions:

using

typical

north-south

than

minutes.

as

every

values

and

observations.

were

the

Salinities

wind

2

by

salinity

%.

used

to

15

The

salinity

ensuring

The

on

identified

currents

those

data.

speed

minutes.

and

the

to

original

same

are

value.

match

processed

The

Practical

east-west

record

and

Velocity

that

derived

will

hourly

(which

wind

filter

pro

The

The

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the

be

of 20

the rotating

both

rotation

to 6.6°, of

with

component be

minimizes

to

are be

(i.e.

In

for

2.2.1

and

kg

the

Salinity

“January”

Chapter

9.5°

be

topographic a

made. performed

For

m 3 .

V

rotated

Monthly

the

UNESCO

fjord,

a

along

the

the

cases

component

quite

complete

(i.e.

the

subsequent

Currents

the

for

variance

Scale

V

2.

the

all

cross-channel

it

contains

in

of

21

close

component,

Salmon

data

by

Instrumentation

data

using

was

of

the

principal

the

(1983)

(no

depths

steering

rotating

presentation

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was

to

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direction

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decided

current

sets

units).

one

data

U

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data

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used

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at

component

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axis).

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the

was

from

for

=

was

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minimized).

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of

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of

calculated.

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mean

the

are

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of

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data

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by

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angle

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rotation

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the

for

data

the

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sets

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(V)

of

sea

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1985;

month

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principal

not

over

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the

are

is

rotation

angle

velocity

water,

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January

made

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angle

currents

possible,

variance

presented

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current

with

in

(U)

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from

were

which

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water axis

in

of

and

which

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site,

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a that

the

velocity 23

-6.6°

and

in

directions

then, salinity

changes

left

standard

are

and

small to

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column:

1986),

the

appendix.

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the

they

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in

with

presented

February

to

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discussed

principal

analysis

geographic

-U

component.

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21,

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likewise

section,

require aligned mainly

—

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mean

must

using

used

data

1000

that

may

by

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have

surface.

currents spectral

smoothed in

must,

is

components

(Salmon). for

the

in for

Chapter

plotted

each

both

Power

January

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cross-channel

a

therefore,

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value

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2.

on

over

spectra

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and

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nature

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a

diurnal

were

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shown

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9

strong

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are

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scale

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while

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others

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to

in

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changes

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filter,

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frequency

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the

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Figs.

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that

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in

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at

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the

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Fig.

near

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6).

and

to

depths

depths

curve

were

each

The

2.3;

the

2.5 22

currents

Figure

Chapter

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10

10

t.2.io

10

.10

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Q

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30

30 -30

-10

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-10

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10 -20

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20

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20

40

20

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2.2:

1/23/91

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2/1/91

2/1/91

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2/1/91

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2/8/91

2/8/91 2/8/91

.

are

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2/15/91

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2/15/91

2/15/91 ..R.A.

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in

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2/23/91

2/23/91

2/23/91

scale.

Positive 23

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Figure

Chapter

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E

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-20

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20 -40

40 -20

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2.3:

indicate

1/23/91

1/23/91

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(units

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2/8/91

are

the

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s 1 ).

layer

2/15/91

2/15/91 for

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January

1991.

2/23/91

2/23191

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2

surface

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to

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Salmon

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12

are

6.

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on

does

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with

the

shown

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instance,

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depths

only

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density

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not

depth.

order

February

of

dam

in

tidally

change

about

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reduced

fjords

Figs.

and

the

of

fluctuations

The

(see

Fig.

2

2

generated

the

10%

kg

are

significantly

2.6

m

1

and

density

Fig.

variability

2.9).

and

m 3

January

deeper

generally

and

as

Data

6.16),

February

large

at

Discussion

appear

2.7

records

internal

2

depths).

density

m,

respectively

coincides

between

as

and

highly

but

mostly

those

for

6

also

waves

which

of

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drop

selected

stratified,

Density

the

with

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at

with

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the

m.

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the

there

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the

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the

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to

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smoothing

in

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the

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scale

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at

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surface

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12

between

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outflow

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given

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27 of

Chapter

21

21

0

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E

E 22

E

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‘°

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22 20

20

21

22

20

21

20 22

22

10

18

14

10

14

1/23/91

1/23/91

1/23/91

2.

Figure

Instrumentation

2.6:

Basin

densities

2/1/91

2/1/91

and 2/1/91

-

Data

(o)

at selected

,-

2/8/91

2/8/91 2/8/91

‘nfl depths

-

for

2/15/91

2/15/91

2/15/91 January

-

1991. 28

Chapter

14

°

E

E

E18 22

22

10

18 10

14

18

10

14

1/23/91

Figure

1/23/91 2.

______

Instrumentation

2.7:

Salmon

2/1/91

densities

2/1/91

and

Data

(o)

in

2/8/91

2/8/91

the

surface

layer

2/15/91

2/15/91

for

January

1991.

2/23/91

2/23/91 29

may on

2.8.

included

the record

significantly

urnal

to

change rent

constituents. 4

the

constituents.

as

sampling

were

gauge

amplitudes The

2.2.3

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the

resolve

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The

monthly

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signals

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lower

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length

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clearly

choice

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constituents

in

per

spectra

2.

interval

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the

where

the

Table

are

bumper)

and

affect

tide,

day

Instrumentation

and

The

of

stratification

lowest

of

to

seen

often

had

one

phases it

—

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record

of

of 2.2.

aid

Mm,

density

inverse

the

(as

sufficiently

of

the

the

is

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(the

month

plotted

are

not the

the

that

frequency

six

the

discussed

stationarity

were

instrument

pressure

using

length

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tidal

coarsest

plot

of

months

records

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was

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with

and

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resolvable

analysis.

high

for

for

of

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chosen

below),

records

or

from

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sampling

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the

and

January,

interest

of

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interval,

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the

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harmonic

the

length

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preserve

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analysis

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from

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higher

record

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at

and

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to

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rate

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periods

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represents

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frequency

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length. (see

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hours),

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the

so

the

must

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that

that

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MK 3

high

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amplitudes

the

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with

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Nyquist

1972).

changes

the

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May

frequency

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were

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(overlayed)

Records

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it

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Figure Chapter cJ 0 ci C.) Cu 0 U) >

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Apparent

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British

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Instrumentation

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the

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the

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the

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1979).

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6.

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the

the

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the

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so

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two

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the

the

Despite

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Basin

January

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2.9.

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phase

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data.

large

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was

K 1 .

the

ap

of

33

to

of is

for

deployed

from

6. clearly

a

The

of year,

to

The

(1955)

2.2.5 speed

Figure Chapter

.

Co

good runoff

-1000 be -750 -250

-500

The 1000 the 250 500

750

level

runoff

the

fed

110

indicates

used

visible,

measure

2.9:

entire

Runoff

Clowhom

into

1/23/91

and 2.

1/23/91

reservoir

in

in

m 3

in

the

the

rainfall

Wind

Instrumentation

sW’.

its the

Sechelt

system.

and

reservoir seaward

of

early

effect

system

River

between

the

record

the

statistics

Inlet

summer

drainage

on

mean

The

flow.

is

remains

(Fig.

the

from

dammed

was

1985

hourly

2/1/91

2/1/91

flow

and

and

circulation

2.10

by

characterized

from

Salmon

and

nearly

Data

snow

the

is

(a)).

discharge

by

about

the

1990

drainage

B.C.

melt

constant,

Inlet

The

river

and

is

one-third

2/8/91

2/8/91

shown

by

Hydro, and

average

density

for

during

(Arber,

basin

Pickard

January

in

so

in

the

the

which

of

yearly

structure

area

the

1993).

Fig.

that

flow

early

(1961)

2/15/91

time

2/15/91

to

(units

keeps

2.10(b).

precipitation

estimated

statistics

estimate

The

winter

that

are

as

are

hourly

average having

presented

the

The

by

cm

from

the

by

rainfall.

moorings

flow

s’).

was

two

two

monthly

Trites

total

2/23/91

2/23/91

the

in

estimated

peaks

peaks

statistics.

dam

Positive

chapter amount

(1955)

Trites

were

flow

per

are are 34

Figure

Clowhom Chapter C,) L1 ix

LL

0 E

a, ix

Cu G) 0)

E c’J U, —

-

c’J

2.10:

2.

River

(B)

Jan

Estimated

Jan

Instrumentation

dam

Feb

Feb

(from

monthly

Mar

Mar

daily

Apr

and

Apr

runoff

discharge

Data

May

May

from:

Jun

Jun

rates

(a)

Jul

Jul

from

all

Aug

Aug

sources

1985

Sep

Sep

to

(Trites,

1990).

Oct

Oct

Nov

1955),

Nov

Dec

Dec

and

(b)

the 35

an higher

and is

longer

diurnal smaller

oxygen

The

(the after by

remains

sharp

appear

records

months

Egmont

Two

1991,

(outside

2.2.6

Chapter

contained

expanded

Another

phytoplankton

A

The

0.4%

change

high

oxygen

April,

spectrum

increase

and

than

than

are

to

and

than

show

time-series

beginning

Oxygen

steady

was

the

2.

values

at

correspond

April

higher

the

in

10

higher

in

feature

4

M 4 .

meters

deployed

Instrumentation

at

sill)

section a

cpd.

the

the

to

days)

marked

fluctuations

at

Egmont,

of

at

1991)

There

nearly

and

in

mean

between

low

with

the in

frequency

from

the

The

of

were

the

are

of

January

to

three

the

frequency

the

Egmont

very

and

high

the

is

value

the

6

water

the

inset

the

also

but

deployed

ml

other

very

power

4

times

remain

onset

the

four

end

data

spring/neap frequency

and

well

are

also

1’.

and

is

at

1991.

column

little

data

meter

likely

at

of

band,

oxygen

the

well

spectrum

5

for

over

show

of

After

defined.

Data

during

ml

the

larger

10

spring.

spectral

is

two

top

resolved

in

m

1_i

than

response

at

8

8.5%

record

presented

an

mid

meter

response

days.

tidal

on

months

right

the

the

than

from

An

increase

is

in

April,

around

the

Although

energy

study:

the

Basin

are

winter.

cycle.

analysis

and

deployments

of

in

December

The

along

Basin

(beginning

the

to

the apparent

in

probably

the the

in

K 1 ,

mooring

the

Fig.

one

outside

oxygen

At

winter,

time-series

with

The

amplitude

mean

low

the

of

Geodyne

increase

5.9%

Egmont,

at

the

2.12.

to

Basin

frequency

mean

lower

30

tidal

in

are

in

values

of

mid

decreases

indicating

was

variance

around

m

error).

December

these

shown

The

mooring.

in

response

on

oxygen

oxygen frequency

after

plot

March,

the

deployed

production

do

the

tidal

bands.

mean

variations

M 2 ,

(Fig.

in

about

shows

again

not

that

Egmont

fluctuations

Fig.

values

when

1990,

1.9%

at

frequencies

The

oxygen

peaks,

vary

once

2.11)

gradients

to

frequencies

mid

that

2.11.

of

there

at February

5

meter

decrease

(periods

mooring

strictly

for

oxygen

ml

March

MK 3 ,

shows 67.0%

which

value

Both

1’.

two

is

are

36

of

of

at a

jet

the

enhanced

and

wave amplitudes

as frequency

sinusoidally,

bottom.

the

right

tidal

the

Figure

Chapter

f 2 .

The

passing

LIJ 4

0

daily

0

shape C)

ES E7 Basin

C

not

of

currents

characteristics,

3

3

8

5

4

8

2.11:

the

peculiar

real

Similar

If

2.

oxygen

by

mooring

of

and

by

fall

plot

one

but

the

the Instrumentation

Oxygen

tidal

through

the

at

1/1/91

off

1/1/91

is

considers

shape flatten

first

oxygen

harmonics

Jan

fluctuations all

+

an

faster,

sensor, responses.

2

(top)

odd

the expansion

Jan15

odd time-series +

+

Skookumchuck

of

off

signal.

spectral

and

as

harmonic

2/1/91

harmonic

the the

then 2/1/91

Jan30 near

+

4 . f + are I

I

the

and

oxygen

at

spectrum

In

the of

Feb12

created

the from +

+

Because

Egmont

peaks

Egmont

fact,

eight

Data

oxygen

frequencies;

3/1/91

3/1/91

of top Feb27 +

+

fluctuations

Narrows

the

K 1 . the

I

days

are

of

of

in

the

mooring

are

moored

a

surprisingly

a

the

values probably

Mar20

fluctuation,

in square

+

÷

data

caused

4/1/91

4/1/91

May

are

spectrum the - Apr2 * I

+

will

may

Endeco

appear

(bottom)

marked

______

amplitudes

from wave,

Sf91

harmonics by

Apr17 increase +

1.

large

be

and

an

the

5/1/91

of

5/1/91 to

Apr30

oxygen explained

5111191

peaks (+).

+

÷

oxygen-rich I a

I

are

Egmont

have

can

peak

triangular

fairly of

May15

of

shown. The

* + 511191

be

occur

square

the

the

meters.

at

very

6/1/91 6/1/91

May29

by

inset

quickly

record

MK 3 +

+

harmonics

K 1

5115191

at

Times

their

turbulent

and sharp

wave, and

Jun15

on

the The +

+

to

is

from

triangular

the

origin.

M 2

probably illustrate

principal

of

near

data

but

fall

spring

upper

tides,

their

tidal

the

the

for

off

37 If

jet,

frequency

of

appears

may

until

ambient by

Figure

(dashed

Chapter

the

frequency

and

be

the

meter

2.12: I 0 0

0

over

to

lines)

level

the

jet

2.

spectral

be

recedes

to

oxygen

compensation

Instrumentation

Power

so

fast

at

is

changes

that

based

30

enough

harmonics

m spectra

and

values

the

on

to

in

plot

oxygen

the

18

that

0.05

oxygen

of

of

will

degrees

would

value

preserves

and

the

sharp Egmont

0.10

drop.

levels

returning

Data

were

of

be of

fluctuations

the

freedom

decrease.

oxygen

reduced.

The

slow, power.

frequency

jet.

oxygen-poor

actual

the

0.50

The

time-series.

(cp

The

(v

in

data

As

=

oxygen

response

oxygen

y-axis

18);

1.00

the

would

jet

the water

(0.073)

units

will

are

The

decreases

spectral

time

be

recorded.

remain

that

95%

are

smoother,

of 5.00

m1 2

is

densities

confidence

the

in

displaced

relatively

1—2.

10.00

strength,

If

Endeco

and

the

are

response

the

interval

by

steady

scaled

meter

there

high

the 38

to

friction

3.1).

two

McClimans

where

in of

(1963)

and tidal

the

than

phase

the

barotropic

internal energy

A

previous

account

Sechelt

tidal

The

sill.

sill.

models

42°

The

phase

15°,

there

and,

used

lost

and

for

oscillation

problem

In

Although

wave

tidal

some

Inlet.

for

tide

Sechelt

the

work

in

up-inlet

the shifts

exist

a

by (1977)

one-dimensional

the

some

generation

flow

attributing

M 2

rest

a

have

of

on

many

progressive

and

choking

most

Inlet,

and in

employed

tidally

across

to

tidal

cases,

of

constrictions

an

significant

the

the

fjords

K 1

British

phase

inlet

choking

at

gradient

the

of

tidal

a

entrance.

some

choked

reduction

the

a wave

the

connected

can

viscous

sill

changes

purely

constituents

Columbia

of

sill,

inflow.

differences

and

at

be

fjords which

component.

required

the

Tidal

Skookumchuck

However,

represented

and

channel

inviscid

how

Chapter

of

across

pressure

by

has

choke

the

possibly

coastal

39

Choking

the

constricted

for

respectively.

between

been

amplitude

the

model

model.

problem

some

The

the

the

gradient

3

by

inlets

sill

looked

internal

inviscid

barotropic

energy

Narrows

energy

a

to

at

the

Stigebrandt waterways.

pure

examine

of

have

Skookumchuck

of

along

This

tidal

at

tidal

loss

the

acceleration

hydraulic

standing

is

extensively

requires

phase

lost

chapter

tidal

range

surface

choking

results

the

the

Glenne

to

(1980)

shifts

entrance

tidal

wave,

wave

inside

boundary

jumps,

a

presents

in

tide

frictional

Narrows

of

was

in

choking,

a

which

and

combined

the

causing

if

shift

Scandinavia

landward

and

approached

channel

there

giving

flow

Simensen

a

friction,

are

in

outside

are

review

model

while

(Fig.

large

is

tidal

less

the

62°

the

no

to of

is

where

of

If

zh,

3.1

Chapter

the

one

the

Figure

then

Inviscid cross

i 73 (t)

constriction

considers

3.

Bernoulli’s

3.1:

sectionally

and

Tidal

Choking tidal

i 7 (t)

the

and

Choking

situation

equation

are

choking

averaged

uniform

of

the flow

Basin Outer

sea-level

in

can

through

atmospheric velocity

—

Fig.

be

U

gi 0 L

H

—)

seaward

applied 3.1 =

=

a

of

2g?7 3

constriction

grj without

I

the pressure

u

+ (assuming

— and

Basin tidal Inner

-, U

i.

the

landward

stream.

over

(Stigebrandt

drop

velocity

the

due

Thus,

of

region):

the

to

is

solving

frictional

(1980),

constriction,

negligible

for

figure

resistance,

upstream

U

and

yields

2).

(3.2)

(3.1)

U 2 40

phase is

the

sponsible

striction;

across

Figure

Chapter

reached

The

Figure

sea-level

shift

a

3.2:

sea-levels

sill

3.

i(t)

for

outside

3.2

across

Relation

(McClimans

on

Tidal

the

illustrates

is

either

the

filling

outside

the

the

Choking

sea-level

between

sill,

sill

side

and

a (1977), and

,

(similarly

of

sinusoidal

17 0 (t)

draining

are

landward

inside

the

amplitude

related

figure

constriction

the

when

of

= =

variation

3).

an

of

by inlet

.

--sin(wt--).

reduction

the

draining).

inlet.

the

i 0 (t)

sin(wt)

are

sill.

is

expression

in

is

the The

given

external

the

and

same

filling

The

sea-level

by

phase

cos

ratio

at

sea-level,

of

some

the

shift

=

of

seaward

h/h 0 .

inlet

tidal

time

of

i(t)

the

will

ranges

of

after

which

the

surface

cease

high

and sill

when is

(3.3)

con

tide

tide

the

re 41

where

A

dO

(—

Noting

which

channel.

S

tide

Chapter

topography-tide is

=

Following

Substituting

The

must

the

w

T

ranged

8

that

di, total

=

3.

This

inlet

be

2i-/w.

and

):

cos

Tidal

equal

McClimans

from

amount

relation

surface

integrating

(3.2) Using

=

Sh 1

factor,

Choking

inlets

to

Sh

h/h 0 ,

and

the

of

was area

= cosq!

=

water with A/j 2 [sin(wt)

,

tidal

(1977),

Sh

(3.3)

used

the

AJj 2 [hosin(wt)

from

landward may

=

little above

=

prism

entering

into

by

h/h 0 ,

=

the

be

S 1 h 2

A5mn2

let

4ircos

McClimans

sin 4

tidal

2ATVg’

(3.4):

defined

start

may

by

0

of —

= and

= the

£2

the

continuity;

choking

Si

be

to

wt (3.6),

_

by

fjord

AU(t)

—

sill,

written the

—

—

cos5 (1977)

cos 4

hsin(wt

and

(3.5)

to

end

through

dt.

(8

cos 4

8

those

therefore,

sin(wt

as

dO.

for

A

of

is

can

8

is

flood

the

a

—

dO.

with

the

be

the

—

set

phase

)]

rewritten

of

constriction

tide

cross

exposed

eight

dt.

landward

of

stream

Norwegian

the

sills

inside

during

at

area

of

low

the

of

fjords

tide),

flood

(3.7)

(.)

(3.5)

(3.4)

tide.

36

the

sill 42 Chapter 3. Tidal Choking 43

The integral on the right has a numerical value of 2.396. Finally,

Sjfl2 = 0.191 . (3.8) cos This relationship is plotted in Fig. 3.3, along with the tidal data from several Norwegian fjords.

One explanation for the deviation of the field data from the inviscid theory in Fig. 3.3 is that there is some contraction of the flow as it enters the constriction. McClimans states that, “Due to the abrupt change of cross sectional area in most inlets, the lateral

accelerations lead to a contraction of the flow”. The contraction coefficient, K, for flows through an orifice is defined as the ratio of the cross sectional area of the ensuing stream

to the area of the orifice, and ranges from about 0.5 to 1 (Lamb, 1945). Stigebrandt

(1977) shows experimentally that K = 0.75 is reasonable for most natural inlets; how ever, Stigebrandt (1980) states that for Nordasvatnet, which has L/R > 70, contraction

is not important, where L is the channel length and R is the hydraulic radius. For Skookumchuck Narrows, L/R 50, so contraction is not considered important, and K

is taken to be equal to 1. Contraction would have the effect of reducing the expected flow rate; therefore, in (3.4), U should be replaced by KU:

= 0.191K (3.9) cos . The “contracted” curve for K = 0.75 is also plotted in Fig. 3.3 and appears to serve as an upper limit to the field data. Deviations from this curve, as in the data from

Størstraumen and Framvarden, are most likely due to friction (McClimans, 1977).

The

of

becomes

additional

If

field

the

3.2

Figure

Chapter

friction o .2

0

one

o

8

theoretical

along-channel tidal

0 0

c

o

c

Choking

moves 3.3:

-

(Stigebrandt,

3.

is

0.0

averages water

I Choking

Ki

given

Tidal away

+ inviscid

M2

with

.Drammensfjorden level

+

by

pressure

Choking

(McClimans

from

coefficient,

slofjorden

F 1

friction

drop

1980)

curve.

0.2 = X\

I

the

X

rstraumen

WLr 6 ,

force

Bo

due

“Rrestva

Topography-Tide

completely

Sechelt

X

nflorden

cos

(1977),

due

to

‘Nqrdaasva where

‘, friction

—

to

en

0.4

X

Inlet versus I

—S

h

figure

W,

Storstraumen inviscid

—

Factor,

is

M 2

z.h

(as

is

topography-tide

balanced

4).

the and

= in

=

The

theory

i—.

X

U 2

wetted (Si/2AT)(hc’gf

------

0.6

Fig.

K 1

I

Framvarden

solid

by

tides

3.1),

of

the

perimeter

curve

tidal

are

force

factor,

h,

included.

0.8

(K=1)

choking

of

Bernoulli’s of

.

friction.

the

Data

corresponds

K=

channel.

and

K1

75

shown

The

1.0

equation

adds

(3.10)

force

The

are

an

44 to

runoff

S equation,

contraction

This

depend

friction

where

Resubstituting

Defining

friction.

the

bed

Chapter

is

Stigebrandt

pressure

the

stress,

new

respectively.

\

is

on

surface

If

the

=

3.

expression important.

z.h

),

(see

Tb,

2CdL/R.

Tidal

force

hydraulic

for

is

has

(1980) (3.12)

section

area

small

which

due

the

Choking

He

for

of

Equation

into

also

This

to compared

form,

radius,

showed

3.1).

the

the

the

the

(3.10)

includes

inlet,

expression

topography-tide

Tb

inviscid

water

R

that

(3.9)

=

u 2 =

to

=

and

and

pCdU 2 ,

A/Wy,

a —

the

level

if

zh

may

F

term

solving

curve

0.191

a

Q

1+

(l)I71o?1iI

may

depth

factor

=

and drop

=

be

where

one

ApgLih.

involving

CdU 2 L

Q

K

is

be

rederived

for

Rg

Qj

of

factor

+

is

sin

can

an

S

cos

used

the

Q.

Cd

U 2 ,

are

=

upper

solve

channel

QfT/aaS:

is

fresh

the

instead

the

represents

using

for

volume

limit.

water

non-dimensional

(i.e.

zih:

(3.13)

of

>

runoff

(3.2)

K

the

fluxes

0.2

a

to

is

set

flow

(T

in

yield

the

in

for

of

=

the

is

the

curves

coefficient

tidal

the

hydrostatic),

coefficient

case

continuity

tide

period,

(3.15)

which

(.

(3.13)

(3J2)

(3.11)

when

3

and

14

of

45

of )

of

the

point

following

Direct

3.3

by

the to

is

variability

constituents

constituent

a

give

Inlet

tide

Atlantic,

small,

and

water

a 0

length

Chapter

large

a

Ocean

ascertain

M.

If

Boom

flow

non-linear

0.10

factor

the

are

of

Tidal

tidal

the

level

measurements

Woodward

and

of

value

strongest

through

value

plotted

Sciences

3.

section.

for

Cd

the

Islet

tidal

in

it

amplitude

inside

on

as

the

could

are

Choking

Tidal

the

the

for

can

ebb

a

of

process,

in

and

forcing

nearly

friction

plot

Cd.

on M 2

amplitude

Skookumchuck

be

the

\

flow

the

(105),

(Tides

be

to

Choking

Rapid

(hence,

Fig.

ignored

and

However,

of

estimated

be

fjord

similar

mixed

outside

in

in

the

the

the comes

coefficients.

significantly

Sidney,

3.3

and

K 1

the

Sechelt

Islet

to

same

currents

harmonic

of Cd).

—

in

tides.

tides

to

be

channel

Currents

the

the

primarily

the

this

by

(3.15)

stations

Fig.

greater

amplitude

B.C.

Narrows.

For

tidal

constriction),

plotting

large

on

Inlet

analysis

For

in

Instead,

longer

3.3;

by

tidal

example,

Together

to

the

Skookumchuck

Division,

forcing

this

than

deviation

(Figs.

the

from

a

the

coast

good

the

The components

at

fails

range

than

Tides

outside.

the

curve

a

one

choking

at

3.4

with

the

model

single

then

approximation.

when

of

lOS)

the

the

entrance

from

of

and

and

constituent,

British

M 2

that

pressure

S,

sill

fresh

For

length

Narrows

channel

was there

will coefficient

3.5),

Currents

the

cannot

the

and

(see

passes

Sechelt

adapted

to

be

water

Columbia.

inviscid

deviations

is

K

the

of

Fig.

gauge

Sechelt

discussed

more

friction

were

be

the

as

constituents

through

data

section

Inlet,

versus

runoff

3.5).

analysed

it

flood,

and

curve

made

measurements

than

Inlet,

does

were

caused

model

The QfT/a 0 S

Because

the

used

of

could

in

that

one

would

in

and

in

the

compared

detail

causing

topography-

individually

M 2

1983

for

to

important

the

developed

by

point

the

cause

Institute

and

analyse

friction

suggest

Sechelt

Qj

=

in

at

North

mean

from

high

0.05

will

the

the

the

are

K 1

to 46

The

to

than

this

examining

made

a

Rapid

Figure

Chapter

simple

the

The

friction study,

currents

available

scaled

Islet

3.4:

model

model

3.

the

the

are

is

Skookumchuck

data Tidal

at

expressed

balances results

current

included.

based

courtesy

the

at

Choking

point

UBC.

from

on

Rapid

speeds

the

using

of

frictionally

Depth

of

the

pressure

Mike

Narrows.

strongest

should

linear

105

contours

Woodward

model

gradient

dominated

and

be

flow.

Locations

Islet

scaled

quadratic

are

runs,

Subsequently,

in

across

(Tides

9

to

metres.

hydraulic

it

of

was

reflect

metres

terms

the

the and

.

decided

sill tide

cross-channel

Currents

(7u

flow.

the

1Jo

by

gauges

and

105

the

that,

The

CduIuI):

frictional

model

section,

for

at

model

averages,

Boom

the

was

results

lOS).

purposes

bed

reapplied

Islet

stress.

rather

After

were

and

of 47

and

the

primarily

The

(3.16)

from

Figure

Chapter

I. -c

0

E

Although

The

x-intercept.

friction,

6-term January C’jJ 0

C%J

to

3.5:

pressure

determine

3.

near

arises

Tidal

acceleration

the

Tidal

31

the

head

dominant

to

32

from

x-axis:

amplitudes

Choking

the

February

(z)

1ÔF

the

values

effects

a

balance

uneven

and

strong

10,

at

of

34

become

flow

g/

6, 1984.

Boom

linear

leveling

for

-y,

speed

most

and

important

Islet

/

term

Julian

H+r

(u)

Cd

of

of

36

1

(solid

the

Day

the

reduces

(see

data

‘\

two

during

data

[6+7u+Cduluj}

Fig.

line)

are

gauges.

the

is

fitted

3.6).

periods

and

between

38

slope

in

The

Rapid

of

a

of

least

the

7-term

the

weak

Islet

pressure

fitted

squares

40

flow

affects

(dotted

curve

and

gradient

sense

the

(3.16)

small

line),

near

fit

to 48

the

where

average

were

to

tidally

using

Fig.

With

8, in

The

for

estimate

of

estimates

the

the

pressure

Chapter

y,

analyse

Fig.

the

The

channel,

the

raw

pressure

pressure

3.7.

modified

and

the

the

u

active

acceleration

3.6, acceleration

tidal

data lOS

=

head.

made

3.

fitted hysteresis

Cd.

of the

Umar the

77

the

Tidal

model

flow

corrections near

data

channel, Part

=

bulk

at

using

The

model

correction cos(wt)

7 1mar

velocity

UBC:

expected

the

from

Choking

of

of

friction

is

removed,

acceleration/deceleration

are

the

sin(wt)

origin

since

the

parameters

the

designed

is

then

the the

are

direct

before

the

velocity

is

velocity

over

that

effects

applied

(Fig.

tidal tide

applied

calculated

is

a

channel-averaged

velocity

fit

the

to

and

the

is

gauges

currents

3.6(a)).

and

of

the

on record

predict field

sea-level

only

sill

where

after

(3.16)

Ox

uA

the

plotted

property

observations.

using

calculated

may

and where

=

from

flow

an

To

the

shown

-150

is

inside

then

the

actual

gOt

of

correct

lou

made

against

in

maximum

Skookumchuck

the

of

velocity,

the

cm

Bernoulli

Skookumchuck

in

greatest

be

by

hysteresis

the

flow

s

to

velocity

Fig.

the

The

made,

conservation

the

find inlet,

<

is

data

A

actual

currents

pressure

u

3.6

interest

the

is

equation the

<

which observation

and

is

the for

were

source

Narrows 300

values

pronounced;

velocity

Narrows,

the

S

cross

to

expected

of cm

gradients

is

scaled

is

acceleration

(3.2).

mariners.

of

volume,

less

the

of

s

sectional

is

the

the

observations

are

surface

noisy

reconstructed

based

the

(Fig.

An

hysteresis

for

for

made

parameters

responsible

105

estimate

the

In

than

3.6(b)).

a

area

on

effects,

area

(3.18)

order

given

using

317

data

data

the

an

of

49

in in

gauge

by

Figure

Chapter

boat

data

3.6:

mounted

3.

were

Tidal

Tidal

(b)

Sechelt

Skooknmchuck

Skookumchuck

(a)

Sechelt

Skookumchuck

Skookumchuck

taken

EBB

current

EBB

currents

-1600

-1600

Choking

Rapids

Rapids

at

meter.

Boom

(Boom

(Rapid

(Rapid

(Boom

versus

1983

1983

Islet)

Islet)

Islet)

Islet)

Islet

The

hydraulic

and

solid

Speed

.500

Speed

-500

Rapid

lines

head

[cm 1 ]

[cm1

Acceleration

are

Islet

Acceleration

across

the

stations;

terms

model

Hydraulic

Hydraulic

FLOOD

Skookumchuck

FLOOD

terms

1600

1600

not

included

included

fits.

Head

velocities

Head

[mm]

[mm]

Narrows.

were

measured

Tide 50

may

radius.

of

the the

stress.

friction

for

(3.16) analysis of

the

flows

depending

flood

be

currents events,

that

of

Chapter

the

the

the

Equation

The

185

the

origin

inviscid

tip be

Umax

over

tide

to

quadratic

stream; inlet

Stigebrandt’s

Numerically,

cm

flood

effects.

overestimated

of

values

the

(chapter

the

were

3.

of data a

=

Boom

on

s 1 .

maximum

water landward

reef

data

7lmaxWS/A.

Tidal

(3.16)

the

and

the

scaled

of

For

the

yielded:

Because

south

term

the

two

is

4).

geometry

Islet

ebb

level

Choking

simplicity,

assumes

an

ebb

drag

R/2L

before

model

separate

in

by

of

overestimate.

tides

of

value

(Mike

drop

flow,

Using

the

the

(3.16)

Boom

coefficient,

about

of

fitting

that

(Fig.

need

maximum

of

sill.

0.01,

is

Woodward,

only

however,

the

water

the is

Umax,

Islet

taken

12%.

the

to

3.1),

sill.

From

actually

by

meaning the

tide

drop

Cd,

S

be Cd

Considering

during

level

a

the

For into

= flood

=

however,

factor

gauge

flood

is

=

scaled

(3.18)

found

0.03

0.04

in

pers.

example,

broader

channel-averaged

0.08

drops

(Cd

account,

that

water

events

flood

current

m 2 s 2

ms’

of

data

for

and

separately,

+

0.24.

includes

comm.).

in

the

in

R/2L),

tide the

level

are

and

to

the

the

in

Stigebrandt’s

the

arguments

flood

in

obtain

The

and

Skookumchuck

used

is

case

definitions

is

the

value

due

where

an

strongest

in

The

is

best

and

in

of lOS

flood

inviscid

7max

convergent

order

exclusively

the

of

flood

ebb

fit

maximum

in

R

data

Cd

subsequent

and

current,

model,

section

of

of

tide

to

just

tide

obtained

water

(3.16)

H u

Narrows

is

examine

w

and

may

is

near

770

to

for

the

downstream

3.2

the

channel

the

was

the

level to

,

several

be

cm

value

concerning dissipation

the

coefficient

the

by

hydraulic

the

it

frictional

different,

the

found

s 1 ,

drop;

is

middle

fitting

scaled

water

of

flows

bulk clear

tidal

the

Cd

51

of

to if

presented

may

Tides

The

Figure

Chapter

With

solid

be

and

3.7:

calculated.

the

3.

in

line

Currents

Velocity comparison

500

fitted Tidal

is

the

Choking

values

section).

velocity

The

measurements

to

Sechelt

frictional of

+

It

other

the predicted July

Acceleration

friction

energy

Rapids

dissipation in 9,

1983

Skookumchuck

by

parameters,

sinks the

terms

1983

in lOS

included rate

July

chapter

model at

10,

the

Narrows

Skookumchuck 1983

dissipation

4.

(courtesy

for

July

of

rate

Mike

Narrows

9

due

and

Woodward,

to

10,

friction

will

1983.

be 52

the

Three hours

elevation

elevation

energy

the

the

the

the

(Vancouver and part by from

resulting

A 4.1

potentially

The friction.

kinetic

internal

largest

sill generation

only

of

the

later

sinks

Energy

in

is

removal

the

across a

tide

such up-inlet

the

dissipated

energy

than

sink small

for

Harbour),

tide

In

barotropic

deep

large

is

the

narrow

that

Sinks

of

landward

the

of

on

high

extracted

amount

a

energy

flux energy

energy

basin

a source

progressive

sill,

high

by

sloping

tide

much

and

of

energy

friction

the

waters

flux

the (<

flux

tide

outside

from

of

of

at

deep-silled

barotropic

of

the

energy

bottom

5%)

turbulent have

the

is

inside

Tidal

flux

the

the

internal

(Stigebrandt,

in

sill

balanced

by

the

sill

been

up-inlet

Vancouver

barotropic

is

for

itself

frictional

has

Skookumchuck and

Narrows.

Energy

balanced

inlets Chapter

tidal

mixing

tidal

identified:

tide

been

(de

53

along

by

tidal

energy (e.g.

(Freeland

jet,

Young

1976).

identified

internal

tide

harbour,

dissipation.

Partition

in

Judging

by

the

4

energy

and

an

Knight

frictional

results

internal

flux

sides

inlet

and

Narrows

the

and wave

flux

but

as

from

into

Pond,

internal

and

in is

and

the

In

Farmer,

dissipation

hydraulic

internal the

between

a

generation

Sechelt

the

Indian

Observatory),

phase

primary

bottom

may

barotropic

1987).

phase

tide.

occur

1980;

shift wave

Arm-Burrard

Inlet

First

disturbances

of

in

source

The

shifts

Dissipation

and

the

the

of

Stacey,

is

generation

two

Narrows

tide.

breaking

the

the

very

dissipation

sill

inlet;

in

of

or

surface

surface

region,

greater

mixing

Energy

large.

1984)

more

Inlet

The

due

and

and

of is

was

the

relationship flux

showed

of

Farmer

tions When

4.2

up-inlet identified

found

turbulence

however,

all

directly of

generated

and flux,

to

Chapter

the

Observatory

One

of

internal

This

phase

that

from

Zedel

but

seaward

Barotropic

the

surface power

that

how

assumption

(1980)

flux

to

chapter

the

4.

contrary

estimates

the

energy

shifts

in

at

(1986)

at

a

the

hydraulic

phase

and

of

surface

Sechelt

is

the Tidal

small

surface

elevations

of the

showed

extracted the

deep

across

Inlet

describes

sill

the

flux

discusses

and

shifts

sill

to

Flux

Energy

barotropic but

that

of

have

displacement

Inlet.

basin

sill

tide.

Stigebrandt

and

into

do

processes

de the

the

how

significant

determined

Freeland

fall

across

Model

not

Young

from

a

Indian

energy

Sechelt

how

sill

the

Partition

This

water,

flux

In

out

transfer

and

are

tide

addition,

partition

the

it

between

the

(e.g.

section

(1986)

of

may

and

Arm.

fluxes

and

large.

and

Inlet

internal

and

barotropic using

sill

quadrature

from

are

hydraulic

Farmer

mixing

be

Aure’s

may

velocity

differ

estimated

is

This

of

presents

5

related

a

of

tide

tide

used

balanced

and

high

modified

tide

energy

be

flux

pressure

energy

by

gauge

(1980)

(1989)

tide

15%

to

important

is

at

frequency

jumps)

by

under

an

a

analyse

produced.

may that

section

at

more

between

some

of

by

data

angle

analytical

used

claim

via

a

the

gauge

frictional

certain the

provide

sill,

are

general

progressive

phase

may

energy

in

the for

internal

2

high

that

included

the

deriving

the

were

(see

measurements

diffusive

power be

conditions;

model

another

angle,

currents

frequency

inlets

three

dissipation

flux

used

derivation

Fig

in

waves

quadrature.

loss

internal

their

in

in

4.1).

to

for

which

tidal

,

processes.

the

the

source

infer

and

and

in

are

estimating

phase

internal

their

Freeland

internal

fjords

of

is

energy

turbulent

near

have

not.

tidal

waves,

the

the

presented.

the

of

analysis

relation

the

Stacey

energy

phases

Nearly energy

Stacey

where

strong

phase

eleva

waves

sinks

tides

and

it

sill;

the

jet

54 is

in

the

are

along-channel

where

along-channel

and

averaged

The

4.2.1 flux

in

when

difference

width

de

(1984)

Chapter

the

tidal

The

Young

The

average

illustrated

Farmer,

theory.

net

considering

inlet,

p

along

generalized

average

velocities

Energy

ranges

is

flux

4.

over

(1986)

between

the

energy

u

the

Tidal

1980):

of

coordinate.

component

a

in

and

mean

is

over

tidal

tidal

further

inlet.

flux

the

Fig.

(ui,

not

flux

the

Energy

the

a

total

cycle

density

energy

u 2 )

of

must

negligible

tidal

tidal

over

4.1;

model

The generalized

U 1 ?7i

the

of

and

If

power

Partition

(denoted

range

a

the

be

cycle

above

velocity

the

through

tidal of

= barotropic

so

tidal

out

tidal the

—

2ir

velocity

in

that that

1

at

can

P

relationships,

cycle

of

Sechelt

J

heights

the

section

fluid, by o p2

=

and

may

heights

quadrature

be

the

a

an derivation

U 1 77 1

fJ

would

section

shown and

i

quadrature

be

g

tide

overbar),

is

Inlet,

1

pgdA,

dwt

is

extracted

and

surface

the

are

be the

2)

to perpendicular

=

however,

by section

surface

it

assumed

zero.

by

be

acceleration

2

1

discussed

is

is

some

elevation

assuming

assumption

necessary

given

from

Therefore,

2,

elevation.

sin

did

phase

to

which

the by

.

in

be

not

were to

a

(Garrett,

tide.

due

the

linear

to

angle,

independent

proves

the

was

if

take

re-derive

following

in

energy

to

Since

inlet

not

change

quadrature, gravity,

&

into

to

1975;

required,

the

be

channel

is

account

the

dissipated

derivation

important

in

difference

of

Freeland

u

channel

energy

x,

is

(4.2)

(4.1)

then

(A),

and

the

the

the 55

2 w(S 2

Expanding

calculated

To

Equation

area

Figure

chapter

get up-inlet

—

the 4.1:

S)/A 2

4.

(4.1)

by

the

barotropic

Model

Tidal

of

conservation

evaluated

trigonometric

the

(from

Energy

for

sill.

part

the 11 1 =ij 1 sth(0t)

the

1=

u 1 A 1

at

a 1 cos(t

of

Partition

balance

generalized

of

section

fluid

P terms

—

F,

u 2 A 2

-

the

volume

of

JJ

A 1

1

and

becomes

volume

=

barotropic

phase

pgii 11

( 1 S 1 )

equating

12

between

u 2 =

Section

2 sin(ot

2 cos(oX

flux

analysis.

sine

2

tidal

+

at

sections coefficients, -

-

dA 1 .

section

velocity,

S 2

represents

1

2):

and

and

u 1 ,

2.

is

From

noting

the

used;

entire

Fig.

that

u

4.1:

can

surface

(4.4)

(4.3)

be

= 56

expressions

combined

lost

surface

tide

implying

Normally,

Using

Chapter

gauge

from

(4.5)

elevation

that

4.

with

the

the

data

for

and

Tidal

=

the barotropic

barotropic

i

? 1 A 1 cos

the

11 1 A 1

in

(4.6),

between

energy

and

Sechelt

approximation

Energy

sin

=

e

+2i 1 i 2 S 1 (S 2

the

tan

become:

extracted

tide

= =

tide

Inlet

Rapid

velocity,

=

=

Partition

-1

tan

+

inside

inside

i 1 S 1

2 wS

support

iiiwSi

(i 2 S 2 ) 2

—1

Islet

from

an

€t 1

I 2 wS

—

i 71 wS 1

sin

+

the

=

+

and

S)

inlet

and

+

i 2 wScos

this

the

i 12 wS

i

2 wS 2 sin

2 (S 2

inlet.

cos

sin

Porpoise

+

=

+

the

is

surface

approximation;

i 72 wS 2

, 2 w(S 2

,

2

very

‘i

cos phase,

—

S

+

+

If

q 5 i

S)

close

2iS(S 2

u 2 A 2

the

tide

cos may

Bay +

—

+

+

i 2 w(S 2

,

u 2 A 2

S)

expression

up-inlet

to 2i 2 SiS

sin

be

imply

may

,

being

sin

2

eliminated the

—

cos be

—

42

S)

that

small

of

2

S)cos 2 .

in

found:

cos(ç 1

cos

section

for quadrature

.

there

phase

u 2 from

—

at

2

is

2)]

differences

is

4.8,

little

section

small.

(

and

energy

(4.10)

(4.9)

(4.8)

(4.7)

(4.6)

(4.5)

The

2

the

in

57 is

M 2 previously

the

energy

(

‘72

and

total

sidering

then

(Freeland

(see

further

Moreover,

Substituting

Chapter

is

42

The

In

The

and total

=

Fig.

the

available

significantly

MW)

is the

P’7i/S)2

flux

to:

K 1

total

tidal

the

no

power

available

2

4.

3.2).

and

past,

considered

if

tides

will

may

longer

change

Tidal

(4.9)

it

amplitudes

available

tidal

Farmer,

Using

loss

occur

is

the

only

are

smaller

tidal

assumed

a

and

Energy

power

would

in

development

shown

small

this

be

to

when

+

surface

power

(4.10)

energy

1980;

considered

be

(i 2 S 2 )2

and

expression,

than

and

angle, be

Partition

in

that

the

the

the

into

and

de pgw1S2

Table

elevation,

sin flux

,.

phase

total

+

P

P

ñ 2 S 2

Young,

the

of

phase

(4.3),

the 2i, 2 SiS 2 cosq

=

is =

an

was

From

the

4.1.

flow

(4.12)

available

pgwi 2 S 2 sin.

not

1

pgw77 1 S 2

1

shift,

>>

energy

average,

sin

shift

the

the energy

2•

The

1986).

2 , pgwfS ‘i

through (4.13) ,

‘2

becomes

Si, percentage

,

total

If

across

total

where

flux

is

power.

(4.13)

since

sin2çS

flux

then

However,

45°,

it

power

2

the

sin

given

power

is

the

pgwS2

expression

but

the

the

and

were

evident

(tan_i

constriction

Therefore,

of

sill

loss

tides

by

power

loss

this

will

as

derived

are

expression

becomes

[

computed

interact

power

the

that

be ‘7 1 Si

was

related

was

loss

only

in

tide

2 wS 2 sin

considered

is

with

the

made

a that

+

expression

reduced

and

half

dissipative

by

becomes ‘7 2 wS 2

(4.13)

maximum in

2

was

ñ 2 /i3i

without

cannot

this

of

equal

cos

what

such

extracted

to

from

manner

reduces

choked

be

(4.13)

to

(4.12)

(4.11)

inlet,

truly

tidal

cos

that

con

was

the the

, 58

intuitively

wall.

and

the 90°

to

the

to

length

(4.9). results.

which

be

on

eters

differences and

Table

Chapter

be

zero

Figure

considered

The

the

sill.

the

sill;

tidal

Porpoise

50

At

Three

are

have

4.1:

Constituent

is

as

modified

tide

model

when

km

For

section

directly

currents

4.

reaches

4.2(b)

used

correct

Al 2

K 1

Al 2

between

dissipation

from

approaches

is

locations

the

Tidal

ç

Bay

separately.

being

behaviour

and

to

shows

=

1,

tidal

analysis,

proportional

head

a

for

are

calculate

(courtesy

the

90°

Energy

K 1

maximum

the

0.8980

0.9992

held

large

for

in

(m) flux

to

barotropic

how

tide

rates

no

90°.

sections,

quadrature

sill.

section

in

back

Individual

the

water

model.

Partition

phase

the

then

extreme

the

computed

of

When

0.7

1.4

Figure

at

(rad

to

width

model

enough

the

total

a

the

1

x

becomes passes x

shifts.

w ,

tidal

were

value

s_i)

iO

iO’

Tides

the

are

( 4.2(a)

surface

choking

of

ebb

behaves

available

parameters

=

from

so

phase

the

chosen

the

used

of

0). and

and

42.1

61.5

a

that

(°)

shows

inlet

standing

sill,

area),

(4.13)

that

Hence,

situations

to

flood

shift

for Currents

for

very

barotropic

compute

Total

and

will

is

the

from

and

as

of

approaching

events

=

dependent

little

the

(MW)

Power

the

wave

a

be

the

34.3

13.9

comparison:

45°,

Available

the

function

should

division,

the

model

taken

sill

the

tide

water

as

can

length

energy

where

harmonic

effectively

section

fractional

across

occur

yield

on

returns

as

of

is

100

lOS).

of

the

Power

S 1 /S 2 ,

constant

fluxes,

actually

5,

the

physically

from

MW.

(MW)

1

during

the

10

28.7

analysis

13.7

surface

is

The

a

power

becomes

inlet

and

moved

Loss

sill

result

then

the

and

getting

(so

tidal

spring

25

approaches

is

expression

oscillation

of

loss

thç

decreases

plausible

84

km assumed 99

which

that

seaward

%

Egmont

a

param

phase

based

solid

from

tides

past

the

is 59 Chapter 4. Tidal Energy Partition 60

0 20 40 60 80 0 50 100 150 200 fl\0 (degrees) Distance of Station 1 from SIN(km) Figure 4.2: Analysis of the modified barotropic tidal flux model using an inlet of constant width with the sill located 50 km from the head. (a) f as a function of q for section 1 (see Fig. 4.1) located at 5, 10 and 25 km from the sill. (b) The behavior of as a function of the distance of section 1 from the sill (q = 45°). of the sill. The total available energy in the barotropic wave landward of section 1 will increase as the surface area 1S + 52 increases. Therefore, the energy lost over the sill (a constant) will be proportionally less than the total upstream energy the further section 1 is moved away, and the tidal wave will begin to look more like a standing wave. Therefore, as section 1 is moved arbitrarily far away, should (and does) asymptotically approach zero.

4.3 Internal Tide

Based on tidal amplitudes of 1 to 2 m, barotropic tidal currents at station 3 (Fig. 1.2) in Sechelt Inlet should be on the order 2 cm s’ or less; however, tidal currents are often 10 cm s or more, particularly in the upper water column. Figures 4.3 (a) and (b) show the baroclinic (zero mean) 2M tidal velocities at station 3 (Basin) for January both “in phase” and “in-quadrature” with respect to a fixed reference phase. Figures 4.3 (c) and

from

length

and is

mid-basin ray

approximation).

must

and

use ocean

the were

January.

crossings.

the

much

stretches were

then

were

the

(d)

Chapter

the

The

Webb

The

slope,

of water

0.O4

(2)

show

barotropic

tidal

the

described

everywhere

computed

removed

Brunt-Väisälä

transformed

scale

the for smaller

variations

WKB

internal

boundaries

4.

the

the

w//N 2

column.

(1986)

amplitudes

its

value

dynamic

for

Figure

of

Tidal

domain.

associated

water

the

approximation

bottom

than

from

in

currents

in

of

The

tides

be outlined

terms

in

K 1

a

The

4.4

into

N 2

Energy

mode

the

(and

column,

similar

frequency

each

superior

2

the

first

constituent,

and

of

variations

=

illustrates

Since

modal

(de

two

of

baroclinic

domain

M 2

at

the

Knight

iO

profile

method

requirement

the

phases

a

Partition

Young,

fashion,

some

orthogonal

perturbation

dynamic

and

sill)

an

to

may

decomposition

requirements

and

the

rad

inlet

must

to

is

Inlet

to

the

the

depths,

from

must

compared

be

fluctuations.

w

1986),

about

eliminate

bottom

the

but

s 2 ,

is

resulting

modal

checked

does

K 1

be

(Webb,

may

the

the

be

wavelengths

profiles

the

the

slow

H/VH

density

velocity

to

and

justified.

not

tidal

harmonic

slope

be

mean

for

decomposition

to the

ray

normally

the

with

by

effect

the

1985)

examined

generally

-0.02

such

using

The

frequency.

slopes

slope

comparing

profiles.

to

=

barotropic

was

and

velocity

respect

130 of

ensure

seen

and

baroclinic

a

analysis

on

not

requires

a

the

for

of

perturbation

justification:

km

reference

by satisfy

the

the Indian

at

removed;

To

the

lowest

to

based

reflection

Using

profiles

(Webb,

comparing

basin

a

mode.

bottom.

main

calculate

all

M 2

at

fixed-depth

an

currents

either

modal

Arm

baroclinic

all

on

infinite,

a

constituent

phase;

floor

basin

typical

contain

the

The

1985),

the

depths

density

about

(1)

(de

requirement,

a

the

solutions

barotropic

variations

stratification

are

density

velocity

floor,

the

the

flat-bottomed

Young,

instrument

compared

near-bottom

Kelvin

modes.

the

several

at

larger

profiles

ray

mean

is

where

station

vertical,

profiles

(WKB

profile,

slopes

1986)

away

mode

wave

than

The

0.08

zero

was

the

for

to

N

of

61

is 3 (a) (b) (c) (d)

I.

-4 -2 0 2 4 -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 1) -3 -3 V (cm V (cm ) Density (kg m ) Density (kg m ) Figure 4.3: Profiles of Basin along-channel velocity and perturbation density from the M2 constituent for January 1991; (a) in-phase velocity, (b) in-quadrature velocity, (c) in-phase density, and (d) in-quadrature density.

t%Z (a) (b) (c) (d)

t

C,

C,-.

E C or-Q to

-0.3 -0.2 -0.1 0.0 0.1 -0.3 -0.2 -0.1 0.0 0.1 .3 -3 V(cm.1) V(cm1) Density (kg m ) Density (kg m ) Figure 4.4: Profiles of Basin along-channel velocity and perturbation density from the K1 constituent for January 1991; (a) in-phase velocity, (b) in-quadrature velocity, (c) in-phase density, and (d) in-quadrature density.

0) CA3

vertical

to

frequency

the

The

shallow

an

The

4.3.1

of

34

Chapter

29.,

gravity.

The

the

ewt

km

unperturbed

field

equations

above

and

shallow

and

where

Theory

water

dependence

variables

4.

of

Now

18

horizontal

the

Tidal

criteria.

p

equations

km

for

water

one

density,

is

disturbance,

of

for

the

are

Energy

the

can

normal

for

modes

equations

p01

dynamic

variables.

horizontal

average

assume

all

(e.g.

po,

(u(x,y,z)

Partition

variables,

v(x,y,z))

varies

modes

1

w(x,y,z)

and

p(x,y,z)

po(—iwv+fu)

po(—iwu—fv)

LeBlond

and

density

po(w 2

(normal)

a

ux+vy+wz

separate

The

velocity

form

N

with

2 respectively.

—

the

following

is

I

of

of

N 2 )w

and

z.

the

=

=

=

modal

the

shallow

into

the

(u,

f

Mysak

Brunt-Väisãlä

D(z)P(x,y)

D(z)i -Z(z)P(x,y).

water

is

v),

solution

the

=

=

=

=

assumptions

the

decomposition

vertical

water

Sechelt

(uh(x,y)

following

0.

—p

column

Coriolis

(1978),

ZWPz

V’(x,y)

which

equations

velocity

Inlet

and

frequency

(8.16)

parameter,

horizontally are

will

may

g

reasonably

made:

lead

is

(w),

reduce

to

the

be

(8.19)).

to

defined

and

derived

w

acceleration

a

and

to

is

separation

satisfies

pressure

the

vertically

Assuming

by

from

angular

N 2

both

due

(p);

the

of

= 64

by

the

are

essentially

Condition

The

12

dependent

Chapter

knowing

is

Additional

Equations

the

mode.

boundary

the

vertical

angular

4.

The

reduces

(4.18)

equations,

the

Tidal

(4.16)

information

conditions

solutions

time

mode

velocity

is

to

Energy

to

necessary

evolution

shapes

Z(0)

where

(4.18)

for

of

for

about

Partition

=

the

p(x,y,z)

the

h

and

represent 0

(4.16)

&Z

dz 2

ÔZ

of

tiZ

iwUh

only

for

earth,

is

Z(—H)

horizontal

the

the the

—

the

the

at

are

modal for

—

u

N 2 _W 2 z

Z

perturbation

eigenvalues

and

separation

baroclinic

2!2

=

=

an gh

the

=

=

V.U

eigensystem

x

the

—pohP(x,y).

_hU1L(x,y)

structure

velocity

8 Po

az

computation

Oh

0

0

Boussinesq

at =

— —

modes.

=

constant

are

density

and z

of

VP

gh

proportional

=

where

the

0.

pressure

approximation

of

with

field.

water

the

the

the

Since

column

terms

solutions

barotropic

to

dimensions

the

are

can

has

phase

to

be

mode,

been

the

attained

of

speed

system

(4.20).

(4.19)

depth,

(4.18)

(4.17)

made:

(4.15)

(4.14)

4.21

4

and

.1

of

6 65

form

the that

was

field

speed where

solution

channel

ing

we

Chapter

The

solutions

The

can

satisfied

an

is

variables

of

of

f

modified

c”

vertical use

(4.16)

flow;

cross-channel

=

to

the

4.

22

(4.14)

(4.21)

dependence):

to

would

mode Tidal

therefore,

are:

sin

and

find

eigensystem

by

to

and

Energy

and

varying

be

wn(X,y,Z)

is

the

p(x,

u(x,

Z(z).

relate

the

(4.15)

flow

Z(z)

vertical

U 0

the

y,

y,

Coriolis

Partition

the

is

The

in

the

z)

z)

cross-channel

is

is

x

P(x,

V(x,y)

U(x,

an

solved

density

a

the

sin(),

eigenvalue,

=

=

vertical

density

=

fjord

arbitrary

parameter,

y)

y)

_?N2(z)Z(z)p(x,y).

set

—ha

iwZn(Z)U(iwxfy)/c

for

perturbations

= is

jUocnN2(z)Zn(z)e_M

=

=

of

dZ(z)

profile,

eigensystem

each

n

expected

Kelvin

velocity

0

Uocnex_h’,

U 0 e”

=

scaling

c

(1,2,...).

Z(z).

=

U 0 e”

N 2 (z).

is

waves:

\/ç,

constant.

(V”(x,

the

to

to

Using

resembles

be

latitude,

the

Indeed,

the

much

y))

vertical

the

boundary

The

is

finite

a

set

smaller

c,

if

simple

final

N 2 (z)

=

velocity

to

centered

\/7

zero.

solutions

condition

than

harmonic

were

field

is

The

the

difference

the

constant

(assum

general

for

(4.18)

(4.24)

(4.25)

along-

(4.23)

phase

(4.22)

wave

the 66

the

The

is

4.3.2

from

temporal

salinities

necessary.

TS

deployment

types

diagram,

ability by scalar

to

February the

about agrams

made

peratures

Chapter

omitted,

the

mixing

For

following

The

diagrams

layers

normal

the

between

from

gradients

150

three

and

each

Normal

(Fig.

N 2 (z)

CTD

were

changes)

4.

150-275

and

from

The

from

above m)

since

small

the

modes

period,

month,

layers

orthogonality

Tidal

interpolated

made

that

profiles

4.5).

April.

February

log

profiles

the

moored

the

no

and

mode

undergo

scalar

m).

and

N 2 (z)

Energy

is

of

described

current

surface

turbulent

from

The

and

these

constant

high

water

In

(which

the

There

were

instruments

gradients

fitting

and

the

Fig. TS

profiles

a

the

moored

to

moored-instrument-averaged

annual

Partition

conditions:

meters.

layer

transformation

seen

obtained

April

diagrams

1

is

are

averaged

by

jet

in

CTD

4.5,

m

a

(4.23) temperature

data

not

intervals

in

that

(10-150

profound

(the

variability

instrument

due

three

Averages

the

and

profile

always

using

were

were

very

show

mainly

temperature

to

density

then

distinct

m);

(Fig.

(4.25)

available

change

small

produced

from

averages both

reliable

that

of

(0-10

and

averages.

(III)

plotted

to

the

4.6);

profiles:

cold

may

temperature

tail

CTD

there

water

salinity

the

in

m);

temperature

in

and

from

they

by

at

on

the

on

to

be

the

deep

data

The

is

(II)

TS

types

the

the

the

relatively

(I)

temperature

salinity

normalized

represent

middle

throughout

moored

a

surface

diagrams

basin

lower

TS

the the

adjusted

high

and

beginning

changes

are

diagram

surface

and

mid-depth

the

and

data

salinity

layer

water

instruments. layer

visible

warm

hybrid

salinity

salinities

so

were

upper

the temperatures

-

above

were

because

salinity

and

of

layer

that

for

with

water

year,

corresponding

end

profiles

water

compared

layer

March

layer

end

values

adjusted

they

150

with

little

of

and

and

of

between

(TS)

the

of

(below

m. driven

water

made

rapid

obey

large

1991

vari

tem

were

that

and

the

TS

di

to

67 if a,

(‘.J

The

1991

denoted

Figure

(III)

Chapter

first

J

in the

fFp(z)p(z)(1V 2 (7J 2 )dz 4.5: January

Salinity Figs.

Wn(Z)Wm(Z)(N 2 (Z)

as

bottom

four

4.

follows:

TS

Tidal

(4.7) normalized 6

(Ill)

diagrams layer

1 H

Energy

to

(I) (4.9). 1 c’J

un(z)um(z)

(150-275 the

18

baroclinic

for

Partition upper —

2226

w 2 ) January, February

Salinity

m).

dz

dz

layer w(z), = = =

(Ill)

February,

(0-10

o. u(z)

— m),

1

and

April

(II) p’(z) . Salinity

= the . April

(I) •

and 1

.

modes

middle 1 26 (N) 1

.

(MKS

May

are

0

layer

1991. units)

— c’J plotted

18

(10-150

The

nm n •

22 for Salinity . =

May layers .

‘I’ m

.

January m), .

.

(4.28)

(4.27) (4.26) .

(II)

and

are 68

for

Tables

(ar’,

constants, of

Figure

1991.

Chapter

E

normal

the

o

c’J U)

o o

If

c’j

o

the

ama9)

-6-5-4-3-2

4.2

January

4.6:

Log

4.

assumption

and

modes

a

B-V

Log

and

Tidal

and

4.3

I

req

M 2

the

Brunt-Väis.lä

show

(i.e.

b,

Energy

and

in-phase

may

is

the

u(z)

made

K 1

U) o

c.J o

o b

0

be

coefficients

Partition

data.

=

=

=

-5-4-3-2

and

found

Log

that

frequency

jw)

1 H

B-V

in-quadrature

the

I

by

req

au(z),

for

velocity

computing

the

profiles

in-phase o U)

0 cI 0

0

p’(z)

field

perturbation

-5-4-3-2

for

the

Log

=

can

January,

B-V

and

inner

be

Ireq

in-quadrature

described

dz.

products:

bp(z)),

density February, 0 U)

0 0 c’J U)

0 0

profiles

as

then

-5-4-3-2

Log

velocity

a

April

superposition

B-V

the

(b’ 1 ,

treq

and

complex

profiles

(4.29)

b’’)

May 69 0

0 U) I

0 0

-c 0 0) U) (3

0 c’J0

0 c..JU)

—10 -5 0 5 10 Velocity (m s1)

Figure 4.7: Vertical velocity modes (w,(z)) for January 1991. Only the first four modes are shown. 0

0 U)

0 0

-c 0. 0 ci) U,

0 0 C’]

0 U) C’]

-0.4 -0.2 0.0 0.2 0.4 Velocity (m s1)

Figure 4.8: Horizontal velocity modes (u(z)) for January 1991. Only the first four modes are shown. -4 o

Mode 1 8- Mode2 Mode3 Mode 4

0 L() C%J

I I I I -0.06 -0.02 0.0 0.02 0.04 0.06 Density (kg n13)

Figure 4.9: Perturbation density modes (p(z)) for January 1991. Only the first four modes are shown.

column.

water

are

January; four

of

Because

complex

to

approach

the

where

was

Chapter

,

the

The

create

The

plotted

Since

The

orthogonality

lowest

computed.

column,

velocity

a

inner

velocity

When

fraction

coefficients,

the

the

the

4.

a

must

=

modes.

for

new

The

a’ 1

superpositions

Tidal

weighting

product

weighting

since

comparison.

and

no

1

be

fractions

For

set

and

of

1 H

+

surface

condition

taken

Figures

perturbation

Energy

the

there

of

iama9,

velocity,

b,

u(z)u*(z)dz

perturbation

method

orthogonal

variance

u(z)u(z)dz

function

function

such

to

of

is

layer

4.10

Partition

and

the

no

compute

of

(4.26),

the

that

may

the

orthogonality

data

variance

and

that

the

density

for

total

for

=

functions,

first

only

density

=

modes

4.11

the

are

each

=

C(z)

the

variance

1

j

four

be

that

available,

profiles

density

present

1 H

total

mode

a,a

p’(Z)(n(Z).

are

used

profiles

is

modes

C(z)

each

condition

unity,

variance

real

=

is

explains

au(z)

are

function,

when

the

mode

one

=

found

are

so

included

M 2

(a’) 2

p(z) 1

the

data

that

must

which

reproduced

contributes

of

for

velocity

variance

p(z),

by

the

u(z)

the

are

au(z)

use

in

the

exists

system.

-w2

+

velocity

available

Tables

a

is

and

inner

(a”) 2 .

=

least

not

of

to

over

well

u(z).

dz,

and

density

p’(z)

the

4.2

product unity,

squares

One

and

a

using

over

find

total

partial

and

By

is

density

approach

proffles

a

the

the

given

only

4.3.

variance

fitting applying

different

method

entire

water

(4.32)

(4.31)

set

(4.30)

data

the

for

by

of

73 is

perturbation

Table

perturbation

Table

Chapter

Mode

Mode

4.3:

10

4.2:

9

8

5

6 10

7 4

3

2

1

8

9

6

7

5

4

3

2

1

4.

Dimensionless

Dimensionless

density Tidal

(cm

density

(cm

10.3 42.7

11.8 27.8

20.1

13.6

16.2 65.3

10.3

20.1

42.7

c 11.8 13.6 27.8

65.3

16.2

8.3

9.3

c 7

8.3

9.3

s)

s)

Energy

profiles

profiles

-0.021

-0.023

-0.007

-0.057

-0.096

-0.020

-0.017

-0.002

-0.016

0.039

-0.034

0.022

0.029

0.161

0.395 f{u}

0.019

0.061

0.180

0.109

0.024

{u}

coefficients

coefficients

Partition

for

for

-0.029

January

-0.009

0.018 -0.036

0.022

0.013

-0.105

0.022

0.007

0.007

January

0.003

0.021

0.033

{u}

0.013

0.006

0.017

0.029

0.063

0.047

0.059

{u}

from

from

%

1991.

%

1991.

Variance

the

the

Variance

77.7

13.1

45.4

30.7

0.4

1.0

0.3 0.3

0.7

4.9

0.0

1.6

0.6

0.6

0.4

0.6

6.9

7.9

1.5

5.4

modal

modal

{p’}

fits

?{p’}

-13.5

fits

22.3

-2.0

-1.7

-2.0

-4.3

-4.4

-1.9

24.2

31.8

-1.9

-0.3 17.7

-0.2

2.3

3.3

0.3

2.8

4.8

5.8

to

to

the

the

{p’}

Z{p’}

-20.6

-10.7

-0.4

-1.1

-2.4

-8.8

-0.1

22.5

-1.4

-1.5

-9.2

4.5

0.8

0.3

3.8

0.7

1.6 8.2

1.2

1.8

K 1

M 2

tidal

tidal

%

%

Variance

Variance

37.3

22.5

24.3

26.8

32.9

25.9

velocity

0.1

0.3

0.1 0.1

2.8

2.9

9.6

velocity

0.2

0.3 0.3

2.1

9.0

1.5

1.0

and

and 74

travelling

Since

station:

may

of

mode.

The

barotropic

computed

profiles

In

velocity

brings

structures ling

procedure

Chapter

the

March,

If

The

velocities

be

modes

u(z)

one

data.

The

considerable

used

are

data

and

4.

wave

separates

and

of

effect and

the

=

vI 2

(Webb,

incomplete

The

Tidal

to

velocity

perturbation

U 0 h

from

were

was

causes

make

absence

and

fit

on

January

the

Energy

vertically

found

the

the

the

uncertainty

K 1

1985;

some

and

a

modes

and

p’(z)

density

constituents

waves

u(z)

of

harmonic

minus

and

to

density

profiles

de

Partition

p(z)

S4

density

assumptions

be

averaged

therefore

Young,

to

= =

instruments

into

sign

structure

negligible

to

the

=

is

are

p(z)

u(z)

analysis

profiles the

up-

U 0 cp.

to

in

data.

were

shown 1986).

and

appear the

modal

unsuitable

and

about

N 2 Z,

through

by

compared

surface

Taking

the

for

in

[a’e

described

[ae”

down-inlet

in

far

Since

fits

only

the

mean

January,

the

Fig.

the

the

using

the

layer,

the

surface

for

number

in

much change

—

+

4.3

subtracted

largest

to

stretching

(4.34).

in

origin

ae”]

the

travelling

the

the

the

(M 2 )

February,

chapter

of

layer

inner

in

of

density

least

absence

contributors

the

(x

sign

and up-

.

=

to

of

means

difference

product

squares

waves,

2

y

of and

Fig.

remove

the

April

variations

=

were

of

c

0)

water

down-inlet

surface

in

4.4

that

a

and

to

at

method.

used

the

method.

the

simple

(K 1 ).

in

the

the

column

the

down-inlet

May

barotropic

the

measured.

layer

to

mooring

variance

vertical

travel

model

(4.34)

modal

(4.33)

create

1991.

data

The

was 75

are

using

Figure

January

Chapter

...I.up

The

fitted

,

0

e’

0

the

..dn

4.10:

two

1991.

4. to

___

first

):

-4

velocity

each

Tidal

In-phase

four

The

mode

-2

Energy

mode

dotted

(in-phase

V

(cm

(a)

(a)

to

0

fits

s

{u}

yield

Partition

and

lines

obtained

2

and

four

in-quadrature

represent

=

=

= =

in-quadrature)

4

independent

by

{ae’

{a7e:’

the

the

inner

(b)

0

approximations 0

—

— +

equations

and

ae’}.

velocity

product -4

I

two

perturbation

-2

method.

profiles

in

four

V

to

(cm

(b)

0

I

the

s unknowns

of

profiles

the

2

density

M 2

4

given

tide

profiles

a,

for

by 76

stead,

mode

tudes

removed, from

amplitude

tide

If by

Figure

Chapter only

-C

E

using

The

for the c..J U) 0 cl Q 0 U) 0 U) 0

0

accounted

the

4.11:

the

January

normalized

the

head

4.

there

and

function

and

0.0

velocity

first

In-phase

Tidal

a

before

phase

is

1991.

for,

0.1

no

four

as

Density

Energy

functions

data

Z(z)

need

since

they

for

getting

(a)

The

mode

0.2

(a)

(kg

are

both

and

to

was

were

normalizing

Partition

dotted

m

fits

available,

0.3

include

of

a

in-quadrature

an

normalized

fit;

previously

u(z)

obtained

lines

up-

0.4

however,

it

and

and

one represent

in

the

the

by

for

down-inlet

p(z)

in must functions 0 -C

0

E

with

(b)

the

fitting

determining each c’.J U) 0

c,1 0 0 0 8

0

perturbation

the

inner

were

assume the

—

mode,

approximations

procedure.

0.0

removes

density

wave.

not

product

something

used

and

the 0.1

I

Density

With

data density

their

amount

method.

the

to

0.2 (b)

I

determine

(kg

the

one

functions

relative

about

to

m

profiles

the

barotropic 0.3

of can

I

variance

the

profiles

compute

scaling.

0.4

the

u(z) of

I

reflection

the

ampli

mode

given

each

and

M 2

In

an 77 were since assumptions months of to the upon reflection flux 3. case, to Although third different in from a, the dimensionless. ([aPJ 2 p(z) p(z) Chapter contributions the modes The Tables Prior The down-inlet fitted for qP, there difficult the modes; reflection. the have were energy — reflection of the contributions and second studies 4. (see [a9 2 )c coefficients velocity the 4.4 for amplitudes observation. was units computed K 1 were Tidal the flux fourth and the Tables to flux no constituent, By transferred mode The first using of distinguish coefficients for necessary is M 2 4.5. information and is Energy of velocity creating very mode proportional the mode greater 4.2 overall for individual by of and appears density the fits the small and each (4.23) also Partition K 1 appears dynamic from and on concerning u(z) of up-inlet dynamic in than in 4.3). mode about appears constituents (higher to fits the the Tables the and density, modes other be to 1.0 and first are other to The lower (4.25), mode undergoing may the the flux undergo may modes modes important 4.4 scaled modes p(z) the four may M 2 making surface hand, up-inlet be must layers, fitting and represent number with does modes variability in compared to even in properly. at significant fact 4.5 are be the this very layer the the U 0 not from employed energy this more greater are dominated to of be = M 2 point amplitudes a fashion, strong change modes the (Webb, transfer 1 greater the procedure the to is so). and Since m reflection flux dominated M 2 each of tabulated than ratios s. the reflection K 1 Contributions reflection. travelling significantly the and in 1985). each than by of other The least the of profiles mode a/a’ was energy the coefficients K 1 the landward the Z(z) down-inlet fits, functions Because in by squares first data up-inlet not fitting n. up up-inlet The terms are its the between for is Values mode. and over simple; are to contribution significantly distribution of normalized, each second coefficients that the technique, the of u(z) of tabulated down station flux, the flux energy: station energy In modes modes of mode; result some four this due and but and the 78 3.

The

energy

density

From

4.3.3 uncertainty

to

the

4.5).

waves

suggested

ten

the

fit

amplitudes.

as

the

the for

included

inlet

Chapter

fit

the

to

fitted

From

comparison

modes

residual

variability

observations.

overbar

the

in

If

the

the

were

original

flux

per

Energy

order

the

complete

4.

in

the

amplitudes

modal

data,

to

were

very

unit

in

of

data

the

represents

variance

The

be

Tidal

variance

to

the

in

the

signal,

sufficient

to

but

fitting

help

area fit

similar

solutions

flux

signs

from

the

modal

data

the

This

Energy

internal

to

the

observations. the

behaved

of

without

of

using

analysis

the

of

inner

the

process.

an

set.

an

to

sum

behaviour

these

mode

internal

by

amplitudes,

average

for

data.

Ea=—po(u

Partition

those

surface

internal

modes

the

The too

product

of

ensuring

velocity

in

amplitudes

it

fitting.

their

A

modal

many

2

absence

much

found is

When

least

over

layer

modes

apparent

was

Because

may

wave

______

method.

individual

and,

modes

and

the analysis,

In

that

by

wavelength.

the squares

observed,

+v

were

be

of

is

addition,

will

the

same

perturbation

hence,

data

given

number

the

the

computed.

that

--w

for

omitted

be

inner

least

total

fit

the

variances

way

at

the

such

the

by:

)+

the

particularly

of

the

the

amplitudes

The

product of

fit

as

squares

first

variance

the

2poN

energy

that

from

barotropic

modes

surface

when may

272

From

density,

internal

dynamic

four

will they

2

the

result

method

fitting

flux

too

of

was

modes

far

Gill

would

in

of

cancel

least

the

the

waves

many

the

mode

estimates.

the

exceed

reduced

modes

in

(p.

procedure

solution

energy

mean

(see

account

squares

up-

unreasonably

density

to

modes

generated

would

140)

give

the

and

Tables

was

much

to

density

is

the

variance

procedure,

for

down-inlet the

four,

fits,

performed

have

minimizes

were

the

4.4

most

greater

energy correct

at

(

when

same

to

large

used

as

.5)

and

and

the

be

79

of

of is Table 4.4: Modal fits (amplitude and phase) for the M2 tide. Fits using both the inner product and least squares method are shown.

Inner Product Least Squares

Month Mode c, a a q çb!’ Reflection a a q Reflection (cm s—’)

1 65.3 3.28 2.49 40 -150 0.76 3.14 2.36 40 -150 0.75 Jan 2 42.7 3.99 0.80 -37 177 0.20 4.00 0.71 -35 -175 0.18 I 3 27.8 7.70 1.39 -17 136 0.18 8.12 1.69 -17 142 0.21 4 20.1 4.31 0.79 50 -79 0.18 4.73 1.25 45 -117 0.26

1 64.2 3.72 2.12 44 -151 0.57 3.74 2.14 44 -151 0.57 Feb 2 35.5 6.59 0.58 -18 106 0.09 6.79 0.57 -17 103 0.08 3 24.2 6.57 0.61 30 74 0.09 6.77 0.60 28 71 0.09 4 17.1 6.39 1.04 126 -33 0.16 6.18 0.46 123 -48 0.07

1 58.4 5.10 2.29 44 -126 0.45 5.26 2.02 40 -115 0.38 Apr 2 37.4 5.92 0.61 -10 59 0.10 6.26 1.01 -9 31 0.16 3 25.5 11.04 0.40 -1 114 0.04 10.60 1.04 0 131 0.10 4 17.9 4.29 0.84 51 -71 0.20 3.39 1.50 55 180 0.44

1 72.7 4.12 2.56 46 -168 0.62 4.12 2.51 47 -168 0.61 May 2 39.3 7.99 0.88 72 102 0.11 8.00 0.85 -45 78 0.11 3 30.1 10.42 0.61 104 -117 0.06 10.42 0.65 -38 -57 0.06 4 21.0 6.02 1.06 64 -148 0.18 5.06 0.35 34 -105 0.07

00 Table 4.5: Modal fits (amplitude and phase) for the K1 tide. Fits using both the inner product and least squares method are shown.

Inner Product Least Squares

Month Mode c a qP q Reflection a’ a çb Reflection (cm s’)

1 65.3 4.75 2.19 -16 54 0.46 4.96 2.17 -15 57 0.44 Jan 2 42.7 2.26 1.43 17 -8 0.63 2.50 1.51 13 -4 0.60 3 27.8 3.35 1.34 180 3 0.40 3.70 1.59 173 -10 0.43 4 20.1 4.06 2.39 -135 145 0.59 4.25 1.34 -145 134 0.32 F

1 64.2 5.02 1.84 -26 23 0.37 4.96 1.96 -26 21 0.40 Feb 2 35.5 2.66 2.62 -5 -26 0.99 2.68 2.90 -6 -25 1.08 3 24.2 2.64 0.49 -149 50 0.18 3.08 0.79 -153 -175 0.26 4 17.1 2.04 3.86 -87 147 1.89 2.53 2.55 -129 166 1.01

1 58.4 7.00 4.11 -19 57 0.59 6.98 4.15 -17 60 0.59 Apr 2 37.4 3.67 3.81 0 61 1.04 3.50 3.70 4 64 1.07 3 25.5 5.39 0.63 172 23 0.12 5.95 0.51 175 -175 0.09 4 17.9 3.17 4.42 -122 168 1.39 2.86 4.39 -106 128 1.53

1 72.7 6.68 2.67 -30 28 0.40 6.71 2.77 -30 27 0.41 May 2 39.3 2.37 2.04 -53 1 0.86 2.76 2.23 -56 5 0.81 3 30.1 4.82 0.30 -177 140 0.06 5.39 0.20 -174 101 0.04 4 21.0 1.20 2.34 56 114 1.96 0.12 3.00 171 90 25.0

may

found

up-inlet

fluxes

modes

where

follows

may

The

over

approximate

wave larger

20

wave

the

radius

sill

Chapter

The

cm

A

start

inlet

energy

stem

the

be

is

with

measure

from

of

(u(z,

than

are

s 1 ),

of

(Gill,

ignored

energy

energy

made

depth,

the

4.

off

width

the

from

compared

a

t)

the

flux the

with

phase

as

Tidal

the

p.

M 2

p’(z,

barotropic

by

of

flux

flux

velocity-pressure

for

plane

inlet

the

= H,

(<

141):

is

modal

and

a

the

integrating

t))

simply

Energy

all

speed

2

and

estimates

Rossby

from

fact

c 2 U 2

width.

to

km),

represents

net

waves

modes

K 1

p’(z, energy

(4.37) width,

°

that

mode

January

of

up-inlet

tidal Ecu,

f

Partition

the

radius 1

H

The

and

t)

and

from

m

the the

W(z)

in

effect

density.

W(z),

is

where constituents

=

an

s 1

highest

adjust

Table

analysis;

the

approximately

modal

baroclinic

to

of

energy

the

integral

i:

j

{cZ 2 (z)

has

May.

on

2

energy

of

c

km.

modal

—p’(z’,

(4.6). Taking

to

the

W(z)

a

the

significant

is

flux

flux

Rossby

both

The

the

the

over

The

shape

density

inlet

from

velocity

The

estimate

+

analysis

(u(z,

t)g

independent

rotation

the

group

disagreement

methods

w 2 Z(z)

one

cross-channel

500

(recognizing

dz’,

radius

the

data

of

real

t)

mode

expression

tidal

km;

and

the

p’(z,

speed

inner

are

part

is

are

of

+ of

show

wave

because

appears

an

cycle.

perturbation

t))

the

about

N2(z)Z(z)j

also

of

of

of

product

approximation

between

dz

10

each

that

the earth

the

dependence

for

a is

plotted

The

general

km,

twice

negligible.

to

it

plane

mode. modal

i2

term

is

slowly.

be

net

fits

which the

=

much

as

density

the

in

waves

dz.

up-inlet

and

increase

to

decomposition

large

two

Fig.

of

fourth

is

The

based

the

An

larger

integrating

the

estimates

still

is

4.12.

as

fields

internal

normal

used

energy

Rossby

Kelvin

in

(4.37)

(4.36)

those

(c

much

on

than

the

as

82

to a

interfere

to

the

Inlet.

in found

and

sink

tidal

total

as

theoretical

and

on

K 1

Table

Chapter

0.01

Sechelt

Indian

p’(z)

The

a

assertion

constituents

Salmon

for

p’.

energy

flux

5%

by

4.6:

kg

strong

the

Apr—May

May—Jun

Feb—Mar

in

Jan—Feb

with

Month

error

4.

de

Arm

suggests

Inlet

m 3

Net

model

(4.37)

tidal

Inlets

flux

Young

Tidal

that

the

diurnal

in

which

per

up-inlet

would

never

in

flux.

velocity;

may

of

the

K 1

is

that

Energy

month

January,

0.055

0.077

Flux

0.035

0.026

(1986)

the

nearly

decreases

be

tidal

mixing The

sea

exceeded

be

baroclinic

the

MW

circulation,

less

(Modal)

±

±

±

±

somewhat

breeze

when

energy

Partition

in

<

twice

currents.

0.006

0.004

0.008

0.002

energy

February,

vigorous.

up’

energy Indian

by

0.2

no

M 2

(see

>

that

fluxes

tidal

0.009

flux 0.030

0.015

0.012

MW

flux

deep-

and Flux

larger

Arm.

per

chapter 0.02

To

of

April

The

energy

MW

of

for

errors

that

in

Indian

±

±

±

±

unit

((up’))

understand

or

kg

the

spite

0.004

0.003

0.008

than

0.003

Since

Sechelt

bottom

and

mid-water

uncertainties

2) m 3

volume

flux

internal

are

Arm,

of

could

stated

May

the

per

at

based

0.101

0.044

0.036

the

Flux

0.035

Inlet

density

combined

station

the

one

of

1991.

potentially

large

month.

tide

MW

renewal

in

(Modal)

are

±

±

±

basin

±

on

extent

would

Table

in

0.010

0.004

0.004

0.004

in

is

about

estimates

Modal

a

3

calculating

Sechelt

not

5%

water

(MW)

This

basin

K 1

takes

expect

to 4.6.

create

error

50%

the

0.039

0.052

0.015

0.022

Flux

flux

which

difference

is

for

volume

Inlet

The

place,

for

dominant

MW

as

lower

that

errors

in

±

±

±

±

currents

quantities

((up’))

(a)

the

large

fact

0.006

the

0.007

0.003 both

0.003

decreases

in

the

M 2

barotropic

in

of

are

supports

K 1

that

contrast

as

velocity

Sechelt

Sechelt

and

mixing

energy

which

those

based

tidal

such

the

(b)

by 83

and

section

can

developed

and surface

Burrard

of

is

When

4.4

energy

Richardson

flux

contamination

by

sensitivity

To

suggesting

the

ratios

currents

Chapter

eventually

the

In

50%

assess

It

be

currents

(2)

Farmer,

(including

Friction

chapter

was

channel

of

a

estimated,

tide

is

of

the

Inlets,

and

strong

surface

are 4.

in

the

by

the

observed

tests

that

results

number

to

two

Tidal

should

contaminated,

Freeland

(b)

dissipated,

1980;

impact

5,

friction

can

water

does

and

the

flow

the

some

were

elevation.

parts:

currents

provided

from Energy

cause

M 2

was

Stacey,

not

equal

energy

(mixing

that

passes

column

of

run

in

and

contamination

contributions)

(1)

the

significantly

the

shown

going

the

the

the

the

above

using

Partition

Farmer

flux

If

a

through

that

wind-generated

dissipation

1984;

ratios

efficiency)

sill

flow

derivation

the

due

ratio

K 1 /0 1

into

to

of

region

current

12

a

response

to the

equal

to

de

(1980),

of

good

of

heat

m

become

a

affect

K

internal

vertical

by

Young, ratios

the

was

constriction,

enhanced

has

for

model

3

of

profiles

parameterization

and

the

to

forcing.

to

the

the

to the

.—

the

been

currents

O

were

turbulent.

15%

sea

both

mixing

±5%.

tide

power

diffusion,

1986).

used

Sechelt

energy

general

tidal

calculated

with

by

breeze

of

quite

is

constituents

for

friction

compared

the

lost

50

Hence,

on

currents

processes.

flux

Using

(a)

Inlet

frictional

Skookumchuck

%.

Energy

the

different

giving

total

is

due

currents

estimates.

of

for

present

basin.

The

it

estimated

from

to

the

friction

available

were

was

to

Knight,

friction an

is

extracted

The

change

dissipation

the

dissipation

down

the

the

concluded

estimate

above

in

compared

change

power

is

sides

same,

the

total

Narrows.

Observatory

power

in

to

available.

in

from 12

the

surface

about

total

and

energy

in

lost

expression,

the

of

m

expression

that

sill

(Freeland

to

potential

the

the

reduced

bottom

ratio

by

energy

K

region

12

layer.

wind

This

flux,

flow

and

flux

/01

the

m,

84 of (a) (b)

0.12 . 0.12

0.1 ‘-e-i 0.1 14—i Nonnal Mode 1+-I No’maI Mode 1+-i

0.08 0.08

0.06 0.06 It I 0.04 0,04

I 0.02 0,02 I

0 0 • 1.1.1.1.. 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Julian Day (1991) Julian Day (1991)

Figure 4.12: Net up-inlet baroclinic tidal energy flux (MW) for (a) M2 and (b) K1 constituents in January, February, April and May 1991.

00

where

(see

where

(4.38)

Beginning

4.4.1

the

Figure

Chapter

derivation

Fig.

E

and

h(x)

4.13:

Derivation

=

4.13),

4.

with

pgr

(phu 2

is

Tidal

Schematic

the

of

(4.39):

the

frictional

channel

+

Energy

shallow

of

pg7) 2 ).

dissipation

of

j

X2

a

Partition

power

depth,

x 2

water

Integrating

single

--dx

OE

x 1

loss.

equations

an

channel

+

+

at

expression

energy

pghur (4.40)

— —

=

(pghui)

inlet

for

—g

I2

equation

Ohu

from

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rectilinear

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showing

=

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the

0,

can

head

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be

0.

coordinate

to

obtained

the

mouth

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system

adding

of

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(4.41)

(4.40)

(.

(4.38)

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86 in

integration

dimensionless D(x),

tion where

no

Integrating

where

becomes

be

Equation

inlet

third

third

(4.41)

The

Chapter

cross-channel

explicitly

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due

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(i.e.

terms

was term

w(x)

D(x)

the

over

to

4.

term

(4.42)

/ät

case

parameterized

can

over

is

friction.

is

a

has

represent

included

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friction

tidal

zero,

the

where

is

be

the

the

implies

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=

the

width,

Energy

reduced

cycle

0,

dimensions since

surface

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coefficient

time

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the

see

that

the

H

by (indicated

there

Garrett,

energy

pgWoHij+

Partition

in

rate

to

is

area

=

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--

ÔE

u

u,

friction

dissipation

x 1

h(x 2 ),

and

of

is

of

or

ãu

i

of +

fluxes

v 2

no

and

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1975): drag

—

the

+

8

by

x

water

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and

energy

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is

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(pghu,)

D,

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Jo ôq

an

at

I

coefficient.

fX2

only

in

x 2

due

W 0

of

and

the

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+

overbar)

equations

w(x)puDdx

quadrature

(see

flux

energy

and

=

D(x)

important h(x)

=

to

boundaries

/öt

and

+

0.

w(x 2 ).

boundary

puD

Fig.

averaging

through

(1980)

Farmer,

and

per

by

0,

=

=

4.13).

in

The

including

0),

=

unit

in

assuming

0.

as

to

the

a

0,

the

friction,

one

over

1980).

D second

solid

balance

width

The

lossless

=

sill

obtains:

a

CduIuI,

boundary.

a

tidal

no

Equation

dissipation

region,

term

and

stress

the

the

case.

dissipation

cycle

energy

the

first

is

where.Cd

term:

the

the

second

(4.40)

(assuming

term.

Averaging

function,

limits

loss

dissipa

(4.45)

in

(4.44)

(4.43)

(4.42)

then

is

The

and

can

the

of

87 a

jet

the

will

Not

4.5

rate

would

the

the flux.

dissipation

over

derived. in

by

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value

calculate and

Chapter

will

surface

(4.13)

From

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surface

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constriction,

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all

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the

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suggest.

comparable

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advected

of

dissipation

flood

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fitted

in

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4.

for

the

in

the

the

negatively

elevation,

rate

layer.

the

a

Jet

the

each

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linear

form

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Fig.

of

dissipation

turbulent

period,

values

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frictional

due

narrows:

into

the

and

flood

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in

good

of

Energy

3.5 rates

importance

regression

to

uncertainties

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buoyant

the

magnitude

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the

of

thus

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for

event

advected

approximation,

energy

the

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uncertainty

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dissipation

rate

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Partition

sample

justifying

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found

P 1033

with

of

due

by

during

is

of

is

to

the

mixed

1.1

term

(4.46)

the

in

and

dissipated

=

tidal

respect

to

the

in

parameters

±

data

pWoL[’y(u 2

picking

rate

the

in

result

friction,

six

a

given

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0.1

tidal

the records).

flood

the

were

water

use

months

is

plotted

that

to

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somewhat

value

amplitudes

energy

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values

of

directly

compared

surface

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from

assuming

of

in (4.13).

(3.16),

(7

+

elevations

of

in

of

the

the

From

in

CdM 3 }.

=

such

tide

flux.

the

Fig.

Cd

water

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0.04

fact

estimated

higher

the

to

from

inside

gauge

each

sill

as

that

form

4.14

the

that

and

the

dissipation

can

and

average

and

the

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than

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theoretical

it data

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and

of

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a

width

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considered

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the

outside

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0.08),

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estimate

of

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and

a

one

the

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the

dissipation

phase

a

regression

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jet.

width

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jet

energy

model,

energy

under

(4.45),

(4.46)

given

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were

shift

now

are

the

of 88

observed The

made for

with responsible

line

from

versus

Figure

Chapter

U-

0

0

0 C

1d

0 0

0

Lazier

the

is

currents

strong

six

0

0

c’J

CD 0

0

8

at

the

estimated

formation

4.14:

the

months

below

4.

(1963)

least

0

for

mixing

entrance

Tidal

Frictional

are

the

the

squares

was

of

power

of

quite

middle

Energy

inflow.

at

tide

the

the

mooring

the

loss

dissipation

fit

strong

20

middle

gauge

first

sill.

layer

to

Partition

from

to

the

data

at

with

density

propose

in

the Theoretical

data

20

the

rate

taken

the

modified

m

40

characteristic

(slope

layer.

computed

that

during

cyclesonde

Barotropic

in

the

1984

=

Direct

barotropic

flood

1.1

tidal

Flux

were

using

±

60

profiling

three-layer

measurements

(MW)

jet 0.1).

tide,

used

the

in

tidal

Sechelt

and

one

for

current

flux

density

a

the

80

dimensional

strong

Inlet

model.

of

analysis.

meter

the

profiles

was

return

tidal

Flood

(Fig.

responsible

sill

The

100

jet

of

flow

events

model

4.15).

inlets

were

solid

is 89

surface

is

where

ergy

indicates

maximum

was

Figure

Chapter

the

I

Stigebrandt

measured

flux

CJ 8-

U) 0.

0-

tidal

p

4.15:

area

of

is flow

4.

flood

amplitude

the

a

landward

Along

Tidal

turbulent

towards

with

and

average

in

Skookumchuck

Energy

channel

a

Aure

cyclesonde

in

of

the

tidal

density

the

the

-10

(1989)

head

Partition

velocity

inlet,

sill.

jet:

of

of

profiling

derived

Narrows

A 3

the

the

profile

is

inlet,

inflow,

Velocity

the

the

current

of

at

cross

positive

following 0

the

w

9:00

(cmfs)

is

meter

sectional

tidal

the

pm,

velocity

expression

jet

angular

May

approximately

during

area

12,

is

frequency

towards

10

of

1991.

flood

for

the

estimating

sill

Negative

three

tide.

the

of

and

sill.

the

The

hours

Af

velocity

tide,

the

profile

(4.47)

is

after

the

en

ij 90

to

of gauge

and

energy

barotropic

Figure Chapter

-‘ w

LI.

barotropic a,

0

the C 0 >, C 0

‘C

As

the 0

LI)

pressure

tidal

with

flux

4.16:

surface

4.

0

tidal

of

jet.

the

Tidal

Kinetic

tidal

the

data.

tidal frictional

flux.

turbulent

flux

Energy

energy

flux.

The

The

in

20

Fig.

dissipation

jet

slope

Overall, Partition

tidal

flux

flux

4.16.

of

Barotropic

of

jet

at

the

about

the

There

was

each

across

40

linear

turbulent

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estimated

event

5%

is

the

a

Energy

regression

of

nearly

sill

is

the

jet

Flux

compared

60

for

described

tidal

linear

entering

(MW)

each

is

0.05

energy

relation

inflow

to

in

±

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the

section 0.01.

80

flux

period

theoretical

between

can

Inlet

4.4,

using

be

versus

the

the

attributed

100

estimate

the

jet

kinetic

total

flux

tide 91

that

internal

where

the

work

bottom;

be

was

its

in

of

Columbia

very flux.

the

through

the

The

4.6

100

Chapter

the

the

energy

shown

The

The

The

energy

proposed

progressive

kinetic

is

MW

different

barotropic

The

against

the

The

water

dissipation,

dissipated

energy

progressive

dissipation

waves

in

Skookumchuck

4.

on

to

in

majority tidal

coast

flux

Sechelt

energy

Energy

heat

column.

chapter

Tidal

the

by

buoyancy

effects

near partition

jet

is

internal

(e.g.

tidal

Stigebrandt

extreme

in

and

dissipated

and

is

flux

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Energy

by

of

internal

the

Sechelt

Partition

on

5

responsible

The

Seymour

mixing energy

the

friction

progressive

that

of

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forces

for

the

tide.

Narrows,

the

tidal

the

three-layer flood

Partition

Sechelt

tide,

mixing

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the

Moreover,

as

breaking (1976)

in

flux

tidal

at

in

Inlet)

energy

heat.

the

tides.

transfer

the

for

which

the

is

in

while

internal

Inlet

jet

deeper

to

in

much

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the

Sechelt

water

where

density

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probably

the

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near

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the

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a

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of

the

larger.

in

inlet.

comparatively

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mechanical

column

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almost

profile

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waters.

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much

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strong

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completely

very

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of

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seen

primarily

0.5

energy

the

by

the

The

is

and

small

smaller

middle

large

available

jet,

%

tidal

dissipated

the

in

partition

internal

inefficient

of

mechanism

an

other

which

from

generation

the

amount

balances

with

mixing

in

even

in

of

Porpoise

dissipation,

barotropic

fjords

magnitude

waves

three

the

in

accounts

values

smaller

mainly

and

deep-silled

at

is

internal

for

the

distinct

on

of

on

transferred

the

that

this

approaching

tidal

Bay.

progressive

the

the

by

amount

for

tidal

sill.

and

transfers

transfer

most

sloping

friction

tide British

energy

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fjords

layers

have

flux

5

will

to

of

92

to

% to

analysis the

pares

Rf

baroclinic

and This

is

vertical

the asserts

salinity

becomes

basin

Vertical

diffusion.

5.1

inefficient.

This

breaking

baroclinic

Aure

transfer

the

0.05

water

Introduction

that

both

diffusion

by

diffusion

chapter

more

potential

(1989) Salt

—.

tide

Stigebrandt

the

becomes

0.10

of

decrease

of

susceptible

tide.

The

is

is

the

energy

mechanical

discusses

diffused

found conditions

for

in

the

baroclinic

energy

ratio

deep-water

An

Indian

warmer

flux

the

which

and be

estimate

of

upwards

to

Richardson

the

change

deep-water

R 1

Arm.

the

the

energy

Aure

intrusions

drives

and

tide,

results

is

basin

work

0.06

driven

of

less

Vertical

in

(1989).

which and

the

from

the

the

of

saline

number,

water

density;

against

Chapter

in

of

heat

turbulent

by

the

flux

water

in

dense

the

Norwegian

93

turbulence

turn

Diffusion

is

with

diffusion

for

internal

Richardson

generally

buoyancy

as

column

water

Rf;

deep-water

gets

5

diffusion

time.

the

Stigebrandt

fjords,

its

that

analysis

density

tide

and

to

The

diffused

energy

to

number

the

enter

in

to

is

renewal.

and

the

changes

fjords

much

do

estimated

decreases,

in

from

over

available

(1980)

de

downwards,

work

Sechelt

is

larger

comes

Young

made

the

the

in

Stigebrandt

against

temperature

and

energy

sill.

the

barotropic

Inlet

than

primarily

energy

following

(1986)

Stigebrandt

basin

In

so

molecular

buoyancy

and

this

fluxes

that

in

(1976)

found

water

com

from

tide.

way,

and

the

the

the of

recently

becomes

quantity leaving

surface.

negligible;

and

i

tion

(i.e.

the

greater

a Turbulent

5.2

Chapter

=

fashion

In

(1,

form

(4)

equation

no

many

Vertical

2,

only

source/sink

advection),

it

than

is

In

3);

5.

(following

analogous

has

diffusion

however,

assumed

studies

the

repeated

the

Vertical

are:

the

become

deep-water,

Diffusion

K,,

molecular

(1)

of

then term.

of

Gargett

to

to

along-channel

term

Diffusion

local

indices

turbulent

scalar

apparent

be

molecular

term

ac

(1)

conservative,

If

in

time

a

diffusivity.

though, (1984)):

seawater

indicate

+

(3).

time

(2)

U—

K 3 =

rate

diffusion

that

diffusion,

ac

vanishes.

ac

(2)

If,

at

period

gradients

of

along-channel

K,,

a

in

properties

=

change

sum

term

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Kh

processes,

is

az”

0

0

a 11 ac

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over

Horizontal

chosen

(4)

complete

are

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of

a 0

0

constant,

vanishes C,

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ac

that

not

to

the

K

I<,

0

0

(2)

when

gradients

traditionally

the

+

always

index.

turbulent

is

scalar

advection,

gradients

(4)

F,

above

considered

but

there

and

The

small,

varies

conservation

may

the

is

assumptions,

diffusivity,

across

no

terms

conservation

(3) been

be

systematically

constant.

especially

deep-water

turbulent

considered

parameterized

in

the

the

equation

channel

the

However,

conserva

equation

near

diffusion

renewal

is

small,

scalar

much

with

(5.1)

the

are has

94 in

March renewal

surveys. was

horizontally

de

relative

than

amount of

salinity

et

waves

band

assume

where

mixing

the

Chapter

at,

0.8

Young

The

evaluated

Brunt-Väisälä

one;

1995).

internal

and

of

<

Rf

in

to that

energy

data

technique

The

of

a

q

5.

however,

and

is

the

Sechelt

April

energy

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<

(over

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Rf

the

area

in

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wave

gradients

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is

general,

many

is

flux

that

from

frequency,

function,

the

a

in

Inlet

and

used frequency,

q

constant,

spectrum

the

must

(1988):

Richardson

the

Diffusion

fjords

was

deep

the

a 0

there

is

for

are

basin-averaged

internal

confined

be

is

breaking

rare,

basin),

A(z),

and

larger

the

e

found

less

the

limiting

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N. of

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K,,(h)

more

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lakes

diffusion N’°

the

number

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than

conservation Gargett

wave

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to

to

of

ocean

=

determined

in

scatter

value

(K,,

(where

the

=

be

2

the

field.

(It

for

Ujh

in

temperatures

1991,

1

and

and

a

upper

study

local

order

interior,

throughout

salinity.

—A(h)

site

N’°).

in

R

K,,

f

Holloway

If

A(z)Sdz

a

equation

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the

internal

dependent

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for

150

was

=

from

the

a 0 N-)

temperature

density

is

m.

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dissipation.

the

hydrographic

and

not

the

(1984)

‘

(5.2),

N’ 5

wave

The

budget

water

constant,

salinities

have

constant

intrusion

to

period

(K,,

field,

decrease

integrated

show

data

typical

column.

from

method

Gargett

then,

charts.

between

that

N° 5 );

from

determined

q

because

occurred

temperature

could

with

exponent

if

vertically

For

and

several

described

the

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time

for

December

be

the

the

Holloway

between

source

internal

greater

by

broad

values

(Pond

errors

CTD

(5.4)

(53)

and

and

the

by

95 of

given

errors

below to

affected

values

aS/az

vertical

the

1990

both

Table

Chapter

Apr—May

Dec—Mar May—Jun

Mar—Apr

Feb—Mar

Dec—Jan

Jan—Feb

March

The

Month

The

diffusion

and

by

the

associated

125

of

5.1:

at

results

by

gradients

CTD

the

K

1991

5.

temperature

depth

March

in.

advection

Summary

were

fitting

analysis.

125—215

135—220 170—215 Vertical

170—220

150—220

120—220

125—215

Depths

data

was

of

(m)

h

with

1991

extremely

the

of

were

the

routine.

below

diffusion

scalar

(normally

Diffusion

of

the

was

longest

and

made

Levels

diffusion

19

18 21

10

11

15

19

slopes

50

judged

salinity

scattered

quantities

The

m

using

period

study

shallow)

—6.69

—7.13

—7.46

—7.23 —5.94

—6.42

—7.46

were

temperature

of

calculations

to

data.

the

ao(T)

data

(Figs.

where

have

(normally

binned

±

±

±

±

±

±

±

are

least

0.17

were 0.56

0.48

0.23

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0.45

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the

5.1

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m

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summarized

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+

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the

10

were

5

values

are

deep-water

ao(S)

m

results

m.

estimates

±

±

±

±

±

from ±

±

the

intervals.

analysed

0.13

0.43

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0.31

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0.20

Depths

in

of

of

standard

December

Table

the

were

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0.93

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1.35

data

deep-water

of

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obviously

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q(S)

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±

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1990

The

and

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winds

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waves

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study

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K,,

5.

tidal

and

1990

single

possible

for

the

for

reliable

and

±

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and

that

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salinity

by

salinity)

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0.35

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q

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large

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frequency;

limit

N

Stigebrandt

even

overall

that

be

results.

(mean

March

(1988)

suggests

Diffusion

fraction

(1.35

of

other

for

if

are

the

and

Inlet

the

q

energy

temperature

±

1991,

reported near

=

the

The frequency

>

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standard

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1

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best

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flux wind

0.93).

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q

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values

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energy

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6.2).

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the

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29

chapter

the

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data

internal

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periods

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value

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0.01

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are

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97

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to

Figure

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1990

Chapter

February

solid

solid

to

5.2:

5.1:

January

>

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0 Lb

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line

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1

10

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a

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squares squares

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the

January

the

data

data 98

S:

line

Figure

April

solid

to

Figure

Chapter

March

represents

line

1991

5.4: 5.3:

CM

> 5.

0

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0 CV

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U,

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E >

c

1991 0

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to 99

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Figure

Chapter

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1991

1991

5.6:

5.5:

0

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the mode

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5.3

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1990

Chapter

>

magnitude,

baroclinic

90%

net

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to

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Mixing

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5.7:

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stratified

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1991

Robinson

measured

energy

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both

(125-215

chapter

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differ

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fluid

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(1969)

perturbation

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Basin

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Figure

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freq

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M 2

lines

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(rad

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4.12),

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s

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()

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towards

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the

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energy

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the

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of

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that

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in

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principal

since

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“well-behaved

energy

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b,

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was

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modal

be

it

along

mouth

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buoyancy

(5.5),

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5%

was

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error

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102

by

of

in

at to Table 5.2: Modal energy fluxes (up- and down-inlet) for the first four modes of the M2 and K1 constituents. The total up-inlet flux is compared to the work done against buoyancy. I

M2 K1 Total Work Phase Up-inlet Against Month Mode Speed Up-inlet Down-inlet Up-inlet Down-inlet Flux Buoyancy Flux Flux Flux Flux (cm s’) (MW) (MW) (MW) (MW) (MW) (MW)

1 65.3 .0189 .0109 .0397 .0084 Jan—Feb 2 42.7 .0093 .0004 .0030 .0012 .0834 .0065 3 27.8 .0089 .0003 .0017 .0003 +.0083 ±.0001 4 20.1 .0010 .0000 .0009 .0003

1 64.2 .0228 .0074 .0415 .0055 Feb—Mar 2 35.5 .0141 .0001 .0023 .0022 .0872 .0041 3 24.2 .0043 .0000 .0007 .0009 ±.0087 ±.0001 4 17.1 .0014 .0000 .0001 .0005

1 58.4 .0338 .0068 .0637 .0220 Apr—May 2 37.4 .0133 .0001 .0057 .0055 .1344 .0078 3 25.5 .0136 .0000 .0032 .0000 ±.0134 ±.0004 4 17.9 .0007 .0000 .0004 .0005

1 72.7 .0431 .0167 .1136 .0181 May—Jun 2 39.3 .0270 .0003 .0024 .0018 .2135 .0109 3 30.1 .0206 .0001 .0044 .0000 ±.0214 ±.0005. 4 20.1 .0023 .0001 .0001 .0003 I

linear

iments of

column

substituted

when

from

vertical

(Table

0.30

from

0.21

barotropic

it

the

of

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basins,

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believed

Chapter

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is

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The

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shown

MW)

MW.

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both

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breaking

were

suggest

efficiency

5.2).

unaffected

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of

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the

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function internal

against

the

internal

estimate

will

(0.043 water

internal

tidal

occurs

(4.45)

is

estimated

Since

given

smaller

upper

and

comparable

latter

process,

approximately

relationships

be

energy

flow

±

a

felt

buoyancy

tide

and

of

Sechelt

mainly

tidal

the

jet

0.009)E bound,

for

tide

being

150

than

E

to

mostly

basin:

could

tidal

same

value

were

flux

the

constituents

(Fig.

m).

vertical

was

to

on

Inlet

for

confined

total

u,

is

jet

forces

attained

much

the

baroclinic

be

+

Stigebrandt

of

in 42

there

regions

calculated

was

5.8)

much

the

(0.002

basins the

the has

generated

MW.

internal

mixing.

power

wave

chosen

yields larger

was

is

to

deep-water

flux

a

smaller

is

of

a

from

±

larger

The

the

were

baroclinic

energy

estimated

estimated extracted

sloping

basins.

0.001).

from

Richardson

fluxes

the

than

(1979)

to

in

upper

maximum

the

than

said

volume

be

relation:

such

the

flux.

the

since

diffusion

in

bottom

the

asserts

Since

tide

to

125

from

the

to

for

moored

Indian

a

fluxes

depth

be

basin.

than

number

laboratory

be

m.

energy

produced

total

the

R 1

the

that

less

topography.

not

analysis

estimated

Arm

In

is

Indian

four

in

instruments

M 2

energy

The

efficient

more

the

chapter

a

the

extracted

in

measure

(0.13

periods

and

despite

the

exper

effects

energy

water

Arm,

were

than

flux

104

K 1

jet

for

to

A

at 4,

show

underestimate.

if

the

However,

that

depth

choice

the variance.

From

constituents

the

Combining and

determined compared

section

and

work

the

work,

Hence,

Chapter

the

There

Two

other

water

Another

background

advantage

the

0.034±0.010

station

a

the

mixing

done

that

of

Wo,

relationship

4.3.3:

the

additional

mixing

the

tidal

harmonic 5.

this

is,

Estimates

column

to

is

the

flux

all

against

by

of are

measure

upper

3.

Vertical

effect

0.002

the

covers

constituents.

(a)

of

(5.5)

course,

K

of

energy

Richardson

rate

the

Two

work

the

is

an

respectively,

being

sources

versus

analysis

extends

bound MW.

similar

buoyancy

low.

using

key

of

of

a

estimate

Diffusion

estimates

of

measures

done

little

J?f

considerable

is

work,

Rf

contributors

Hence, independent

confined

an

N

for

should

of

to

of

may

shallower

The

number

against

less

adjusted

uncertainty

relationship

the

14

what

the

up-inlet

from

and

for

second,

the

be

of

than

integration

=

tide

be

to

R

made

the

Stigebrandt

(4.37)

buoyancy

0.002±0.001

uncertainty

the

has

range

multiplied

to

the

than

gauge

area

half

of

of

and

the

net

and a

background

should

lower

the

station

held,

by

value

and

function,

of

of

150

W 0

tidal

up-inlet

data,

more

comparing

in

0.03

the

energy

up-inlet

layers,

in

(b)

m

and

by

(5.5).

of

be

and

the

energy

MW.

3

water

Sechelt

that

important

M 2

to

the

0.80 noted.

(Fig.

the

A(z).

estimates

Aure

0.08

0.043

rate

flux

lost

and

Because

the

of

the

net

to

assertion

column,

the

flux,

station

for 5.9).

Inlet,

K 1

between

from

of

integration

Although

(1989)

Rf

allow

estimate

modal

and

net

uncertainty,

work

they

Rf

contribute

is

for

150

the

This

station

R 1

found

up-inlet

for

and

could

3

found

by

flux.

W 0

are

m

is

(Fig.

the

“background”

=

the

of

the

Stigebrandt

estimate

it

was

0.002±0.001

stopped

0.034

not

and

to

the

be

generation

These

could

for

3

M 2

contributions 80%

tidal

5.9),

be

comes

the

considered

the

were

R 1 ,

work

inlets

and 0.082±0.016

-

to

0.082,

be shallowest flux

which

only

were

at

of

but

from

the

given

K 1

done

argued

150

R 1

(1979)

whose

rate

to

ones.

MW.

point

total

they

tidal

both

and

was

the

has

105

the

m.

an

in

of

in of

the

that

the

high

for

rate

(the energy

diffusion

W Figure

Chapter

=

comparison

year. energy

units

of

these

frequency

0.002

flux,

work

5.8:

was

it

5.

of

internal

flux

+

may

E,

iV

Work

is 0.002

0.004

0.006

0.008

0.012

Vertical

0.014

driven 0.043E.

0.01

internal

due

of

0

to

for

contribute

0

m 2

the

waves

the

done

primarily

January

by

Diffusion

used

high

Sechelt

wave

the

had

against

by

frequency

to

internal

0.05

W

to

field

an

to

Stigebrandt

the

data).

=

May

energy

wind;

buoyancy

(0.056

generated

constant

1991.

tide.

internal

Stigebrandt

however,

Barodnic

flux

±

0.1

Their

and

The

0.011)E

background forces,

‘—

at

TdaI

wave

Aure

10%

the

dashed

results

another

Fhix

and

sill.

as

W,

flux

+

(MW)

0.15

(1989)

large

0.0018

line

de

Aure

suggested

as

remains

rate

possible

Young

a

for

is

as

function

of

argue

the

the

W 0

work.

0.2

relatively

least

and

source

baroclinic

were

that

Pond

of

squares

converted

the

of

baroclinic

steady

energy

(1989)

0.25

tidal

background

regression

to

flux.

during

found

is

tidal

MW

the

106 If

mates

of

Figure

W

W Chapter

= net

—

(0.002

(0.002

are

5.9:

up-inlet

5.

shown: ± 0.0022

0.004 00e

::

Vertical

Work

± 0.001)

0 0.001)

0

baroclinic

(a)

done

+

Diffusion

+

the (0.082

..

/

(0.034

against up-inlet

0.05

tidal

±

±

0.016)E).

1. J

energy

buoyancy

O.010)E) flux 8aroctkdc

0.1

derived

flux

forces and

That for

Flux from

Net

(b) January

(b)i. up-inlet (MW) 0.15

Modal

the the

Flux net < f1

i-—*

of

to

u(z)p’(z)

modal station

0.2

May

zzz

flux

1991. 3

>

as

(regression (regression

0.25

a

Two

function

esti

107

is is

frequencies

frequencies

The

a

variability

6.1 variability.

the

The

current

wind-driven

The

runoff

filter

channel

tions

and The

cutoff

The

water

method

determination

shorter

low

approach

with

with

Filtering

have

and

main

currents,

frequency

frequency

column.

periods

are

a

higher

0.8f The

wind

on

circulation

cutoff

period

of

goal

also

taken

the

low

mean

and

<

densities,

records

than

greater

of

frequency

Results

presented

circulation

of

of

f

circulation.

pass

tides

the

here

spectral

<

the

0.929

circulation

in

the

f.

filtering

low

to

and

effect

Knight

than

is

from

wind

cutoff,

The

determine

cyc

Low

to

frequency

in of

fluctuations

is

25

analysis

of

0.929

an

examine

Baker

cutoff

an

taken

and

day 1 .

and Inlet,

chosen

hours.

Frequency

runoff

f,

effort

empirical

runoff

were

the

cyc

Chapter

the

to

(1992)

frequency

using

analysis

in

The

to

to

The

the

be

deep-water

day’.

108

strength

set

caused

records

Knight

smooth identify

that

data

coherence

orthogonal

25-hour

used

data

to

Circulation

is

6

zero

part

was

similar

by

to

were

Inlet,

and

statistical

were

the

and

determine

renewal

diurnal

chosen and

cutoff

of

extent

and

low-pass

data

explain

the

function

Fourier

however,

to

a

cosine

that

period

circulation

phase

not

used

period

cycle

coherences

of

the

the

presented

the

filtered

transformed,

only

(EOF)

proved

taper

a

eliminates

spectra

are

effect

dominant

wind

spectral

winds.

to

also

which

using

was

be

to

analysis

that

more

influence

in

between

discussed.

identify

low

The

applied

this

filter

all

has

a

wind

modes

then

difficult.

spectral

enough

diurnal

thesis.

along-

of

varia

with

over

and

the

the

the

the

for of Chapter 6. Low Frequency Circulation 109

to exclude the diurnal and shorter period variability, but also to fall in a relatively low

energy frequency band to reduce the ringing caused by cutting the spectrum off sharply in a band with significant amounts of energy.

Raw and smoothed power spectra were generated for each time-series. A discrete Fourier decomposition of the function F(t) (t = nLt, where Lt is the sampling interval) may be defined (see Press et al (1986) for a complete discussion):

N/2 F(t) = a 2t)cos(2irf + b sin(2irft), (6.1) th where f, is the discrete frequency and N is the number of samples in F(t). The value of the power spectrum at a frequency, f, is then defined as

P(f)f = (a + b), (6.2)

where if = 1/(Nzt), and f = izS.f. The spectra were smoothed over 9 frequencies using a boxcar filter, giving each spectrum 18 degrees of freedom. The 95% confidence interval for the spectral value, S(f), with v degrees of freedom is

2 S(f) S(f) 2 S(f). (6.3) Xzi,O.025 Xv,o.975 In this case, i’ = 18, x80025 = 31.53 and Xs,o.97s = 8.23. The power spectra are plotted on a logarithmic frequency,. axis so that the lower frequencies are expanded. In order that the area under each band remain proportional to the total energy, the spectral values are scaled by their frequency.

Another useful method of examining the relationship between two signals is through their coherence spectra, C(f), and phase spectra, (f). First, the cross-spectra of two time-series were computed using the series’ Fourier coefficients, a2 and b. The co- and quadrature spectra of time-series F(t) and F’(t) are defined by

and influence

Studies

width

6.2 herence

the

were

smoothed time.

the

smoothing

coherence

The

Chapter

=

The

method

coherence

Pond,

coherence

smoothed

Wind

1

The

over

of

—

squared)

coherence

on

6.

many

0 • 05 M,

over.

of

number

1976).

allows

all

outlined

the

Low

two

of

coherences.

squared

using

circulation,

N 3

British

two

is

where

the

Frequency

The

processes

of

was

plotted

squared

by

hypothetical

a

estimate

degrees

wind

boxcar

chosen

Columbia

and

Jenkins

M

with

particularly

=

phase

must

stress

which

Circulation

Q 3 (fjzXf

of

C 3 (f)zf

C 2

sf,)

2/(v

of

filter. to

an

and

freedom,

•

(fJ

what

be

mainland

time-series

be

— — spectra

transfers

arctanh

occur

—

9

Watts

The

-

an

2).

smoothed

(similar

is

=

near

C(f)+Q(f)

—‘

termed

95%

ii,

P(f)P’(f)

at

The are

(—3

y-axis,

fjords

(1968),

momentum

is

the

the

with

C,(f)

then

to

confidence

2N 3 , 95%

—

surface

the

over

the +

same

have

ab:).

no

the

chapter

bb)

defined

where

noise

95%

power

true

a

confidence

shown

frequency

(Baker

through

band

noise

interval

level

coherence

N 3

spectra),

as

9.3.

that

is

of

level

and

is

When

the

the

interval

frequencies,

the

is

is

the

Pond,

(Chang

computed

number

and identically

would

water

level

wind

coherence

the

has

1995;

column,

lie

above

has

et

frequencies

frequencies

a

5%

since

following

a!,

constant

a

Buckley

1.

(or

strong

1976),

of

which

The

and

the

the

co 110

are

winds

—U variance.

the of

be

poorly

proximity termed

month

are 4

masses important

energy

in

disturbances

pressure When

and of

compensation surface

also

Chapter

m

the

the

argued

water

The

anti-correlated

cross-channel

component

shown

it

from

causes

is

wind,

along-channel

is

the

records

correlated:

at

becomes

“winter”

0.43.

waves.

anemometers

gradients not

at

6.

The

that the

of

diurnal

in

wind

in

one

mixing

and

unusual

Low

in

the

the

The

Fig.

air/water

can

from

correlation

the

is

the

While

is

end

more

and

the

warmer

Salmon

Frequency

wind

used

correlation

and

steady,

develop

result

at

at

depression

2

in

January

6.1.

of

energy

the

for

Salmon

to

zero

zero

aboard

pronounced

the

the

higher

the

at

variance

10

interface. currents

from

April

seasons,

and

For

the

Salmon,

upper

direct

lag,

between

completely

day

lag.

inlet.

of

Circulation

to

is

wind

frequencies.

surface

the

in

the

convenience,

these

Basin

to

the

band

stronger,

March

Because

at

the

layer

effect

deep

The

June

when

Geodyne

surface

than

one

Smoothed

linear

to

the

Basin

bands

topography

are

anemometers,

currents

compensating

to

leak

in

through

(Salmon),

record

would of

the

during

along-channel

the

balance

the

but

the

correlation

pressure

wind

is

is

The

into

daily

buoys

the

source

water

normally

64%

the

+U

will

wind

expect

and

cooler

shear-generated

stress

diurnal

the

January

sign around

the

heating

and

as

component

be

measured

gradients

compensating

column

of

power

the

cross-channel

flow

wind

large

termed

coefficient

a

indicates

April

seasons.

much

is

comparable

Salmon

negative

seabreeze,

along-channel

felt

the

and

to

can

stress.

spectra

as

to

to

of

caused

Basin March

the

near

“spring”.

cooling

be

reach

that

is

June the

that

and

turbulence

is

correlation.

used

coherent

wind

flow

Synoptic

the

low

Basin

to

only however,

(v

mooring

of

the

right

cross-channel

by

(Salmon

deployment

or

of

=

the

will

at surface,

frequency

at

spring

Despite

the

two

the

—0.21.

greater

18)

winds;

Basin

to

approximately

with

along-channel

only

scale

accumulation

and

interior

components

allows

the

can

for

and

A

winds

baroclinic

the

the

last

than

breaking

possible

and

It

the

weather

bottom,

in

become

content

will

Basin)

Basin

could

wind.

some

close

fact,

until

land

two

the

are

the

111 be

for

of

error

along-channel

chapter

Since dominant

and

currents

the

are,

currents records.

the

energy

in

51.4%

of

the

the

diurnal

explanation

near

Chapter

wind

spring,

the

The

comparison

Unfortunately,

A

diurnal

spring

winter

spring

not therefore,

the

in

the

variance

total

of

constitutes

4

energy

band

filtered

from

records).

remain

associated

The

Basin

6.

the

assumed

actual

and

forcing

winds

winds,

value

seabreeze

variance

for

Low

variance

the

increases

diurnal

winds

almost 47.5%

analysis

flux

(the

anemometer.

the

as

along-channel

is

effect

in

Frequency

wind.

for

and

the

After

that

strong

21.8%,

7.3

with

due

Salmon

non-negative

Basin

of

(divided of

the

inseparable.

almost

band

of

wind-driven 3.6

times

of

the

shows

at

the

the

to

The

the

the

the

diurnal

times

during

the

the

January

40.9%

wind

individual

Basin

winds

energy

Inlet.

Circulation

Salmon

disappears

strong diurnal

as

sensitivity

that

wind

into

Salmon

velocities

as

large

contamination

the

correlation

period

wind

and

contributed

energetic

During

currents

individual

the

actually

and

appears

outflow

wind

outflow

tides

as

spectra,

20.6%

site

spring

variance

February tests

(see

the

currents

are

the

in

occur

by

associated

as

exceeds

to Basin

winds

section would

as

winter,

of

to

shown

Salmon

monthly

outflow

2.1

the

half

the

be

is

before

the

in

the

very

probably

times

in

data

low

spring

spring.

smaller

spring

of

in

be

variance

barodinic

2.2.4).

that

the

37.7%

in

the

winds

wind

with

closely

frequency

early

or

a

records)

are

Figs.

between

topographically

surface

Basin

energy after.

of

diurnal

By

than

the

not

conditions

of

high.

However,

are

February,

the

in

together

contrast,

the

6.2

tidal diurnal

included

winds.

It

the

are 1.1

50%,

wind

low

layer

to

winter

band

Salmon

appears

to

the

times

included

wind

fluxes

frequency

the

energy

6.7.

the

in

is

in

seabreeze The

the

the

energy.

surface

and

due

from early

generated

frequency,

as

diurnal

in

5%

wind

then

mentioned

surface

energy

diurnal

The

energetic

those

spring,

to

constitutes

at

estimated

the

February,

currents.

winds

In

variance

that

the

the

and

filtered

period

in

terms

tides,

three

layer

band

eddy

lack

and

and

top

the

the

112

the

in

in as CD —‘q

I-1:j

S(f) f*S(f) f*S(f) &CI) I n —. 0 1000 2000 3000 4000 5000 6000 0 10000 20000 30000 40000 50000 0 5000 10000 15000 20000 I I I I I I 0

0• C) CD CD’ >0) 0 -D 0 CD Ia 00) .1’) 0 0 a .,.. —. —- a, (I 0 (Th LQ. 0 Co 0 0 p ‘CD 0 0 ..-, o 01 01

01 01 CD CII

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0 •0

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0 cn 001 •-‘. p 8 ‘a 1%) 10 CD —. 8 lr C-I

0 .p p. ,p 0 0 8

‘-I ÷ O CD

, Q_ C.,.

baroclinic

giving

inlet or,

freely

a

January

that

they with

6.7). days

6

below

the the

record

dam of

initial

during

record

records

appears

Chapter

freely

m.

decreasing

The

perhaps,

In

deepening

increase

Salmon

is

the

appears

are These

(330

oscillating

a

the 4

increase

(see

approximately

the (Fig.

oscillating

phase

m.

phase

could to

to

wind.

limited

6.

modes

m 3

Salmon

high

period

oscillations have

The

Figs.

by

in

Inlet

Low

density

6.8)

s’)

twice,

of

have

speed

speed

response

the

in

In

effect

frequency

basin

the

thickened.

discussed

to

2.6

may Frequency

density

from

on

along-channel

baroclinic of

January,

strong

been

the once

pycnocline

for

of coincides

strong

and

February

of

20

scale

be

last

Salmon

the

2

the

to

the

triggered

beginning

km prone

2.7) indicates

outflow

m

fluctuations

in

high

for

the

There

internal

seiche

winds,

seiche

strong

Circulation

wave

record.

chapter long,

is

approximately

with

4.

from

to

oscillating

Inlet

frequency

due

velocities,

The

wind

by

whose

internal

is

of

a followed

is winds

and

the

on

wave

mixing

an

to

homogenization

about

the shows

One

4

the

decrease

January

event.

(see

large

the

(approximately

the

increased

wavelength

sudden

did

may

same

fluctuations

possible

currents

seiching,

an

23

decrease

period

by

a Figs.

and

discharge

not

a

short

The

oscillating

cm

be

week,

in

a

30

order

the

discharge

significant

substantially

high

response

produced.

2.6

s 1 .

period

(Fig.

of

explanation

are

where,

period

subsequent

in

is

of

and

the

and

of

of

frequency

at

twice

seen

the

the

the

6.4)

water

magnitude

flow

6

do

of

oscillation

2.7),

of

under

in

of

and stratification

same

surface

decrease

the

down

not

For

that

fresh

and

the

increasing

with

affect

from

increase

12

for

and

seiche

appear

fluctuations

example,

the

as

once 6

of

to

m

water

layer

a m

these

mode

the

the

the

Salmon

is

as

(-..‘3

right

is

12

period

and

would

on

roughly

likely

to

the in

Clowhom

m,

densities

filtered

density

due

and

from

kg

oscillations

May

be

3

conditions,

stratification

the

12

but

or

theoretical

of

Inlet. m 3 ).

to

in

be the

correlated

caused

m

the

seiche

4).

30

about

2 the

mixing;

in

that

density

density

at

period

below

days,

dam, River

(Fig.

May

The

The

The

2

2

114

by

in

of

m

is

m

a 2

indicates

corresponding

Fourier

unfiltered

phase

moorings

Geodyne

for

signature

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sity face:

along

from

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the

the

may

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seiche

Chapter

node

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part

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upper

records

be

the

the

seiche

the

spectra

can

frequencies

near

coherence

computed

of

an

that

buoy

6.

isopycnals

CTD

are

in

inlet,

current

layer

the

be

internal

in

having

the

for

would

the

Low

shown

were

the

examined

density

in

to

low

data,

which

January

density

thickness.

center.

January,

Frequency

the

and

wind

velocities

from

frequency

smoothed

also

created

a

phase

would

in

the

2

coarsest

phase

across

would

Figs.

is day

have

records

hydrographic

using

The

two-layer

and

leading

only

speed,

be

Depending

for

period

and

spectra

be Circulation

the

some

6.10

over variability

May, location

displaced

a

all

field

the

suggests

a

simple

the

interface,

the

node

four

to

is

signature internal

April

shown

during

between

sampling

9,

winds

6.15.

c

currents.

data;

of on

giving months

—

for

model:

most

in

that

and

the

the

in

the g

Salmon

the

Because

phase

were

p

wind

in is

at

mooring

Figs.

May

a an

thickness

is

(from

isopycnal

of

times

the

simplifying

95%

the

the

the

internal

gridded

the

speed

and

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Inlet.

acceleration

isopycnal

6.8 ends

the

average

noise

the

in

Salmon

in

currents

and

of

anemometer

lies

question.

data

displacement.

of

seiche

Salmon

cyclesondes).

to

level

the

Salmon

the

between

6.9,

water

a

displacement

mooring are

upper

3

for

of

inlet,

is

due

hour

do

shown.

Inlet

0.31.

a

the

column

The

Inlet

possible

not

to

layer

failed

16

and

sampling

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deployment.

gravity,

is

The

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lack

and

show

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into

Coherence

nearly

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positive

that

density,

on

near

filtered

explanation

and

54

of

a

number

significant

the

would

and

two-layer

is

cm

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the

halfway

Salmon

chosen

strong

phase

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h 0

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6/23/91

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cutoff 6/23/91

-

frequency 117

frequency

Figure

frequency

Figure

Chapter

6.5: 6.4: a 0 0 . (40 0 .e (4 620 Eo Eo 6 0 (.4 -100C 6 -10CC -500 If

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along-channel

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2/8/91 A 2/8191 — \_‘ \I

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2/23/91 A

2/23/91

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Figure

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Chapter

6.7:

of

6.6: of C4O

0,

20 E ‘C

E 0

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00 -20 -40 6. -20 40 -40 -20 20 40 -40 -20 20 500 40 20 40 20 40 -20 401 -20 -20 40 .401 -20 20

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6/15/91 6/15/91 - ‘—-- —-- —r S.— “—

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in

5/23/91

5/23/91

April. May.

—

6/23)91

6/23/91

The

The

cutoff

cutoff

fre

fre 119

Chapter 6. c’i — c16 c’J 8 — c’i c Elo; co 1! E

E Low 20 22 22 10 20 20 22 12 14 16 18 12 10 10 18 12 14 18 20 22 10 12 14 10 18 12 10 12 14 20 18 22

18 20 22 Figure 10 12 10 12 18 14

18 Figure 1/23/91

1/23/91 Frequency ______—

-

6.8:

6.9:

6/1/91 Filtered

6/1/91

Filtered Circulation 2/1/91

2/1/91

densities

densities 6/8/91

6/6/91

2.18/91

2/8/91

(o)

(o)

in

in

Salmon 6/15/91

6/15/91 Salmon

2/15/91

2/15/91

Inlet, Inlet,

- January.

2/23/91

2/23/91 May. 6/23/91

6/23/91 120

time

could

level,

at

clinic

forcing

squared

are

the day

f lying

squared greater

with

f

with frequency, frequencies

semidiurnal

The

the

strong

Chapter

best.

The

At

typically

The

coherence

diurnal

band

scales 0.8

0.8

relatively

the

a

and

in

flow.

be

the

slightly

phase

(0.5

frequency

wind-generated

(0.64)

One

cpd

at

coherence

drops

the

the

two

6.

the

at

Basin

it

greater

4

sea

However,

will

to

tides.

0.2

is

Low

100

is

possible

m

vertical

processes.

connection

very

for

at

off

high

difficult

0.7)

at

more

breeze

0.4,

is

to

mooring

be

m

0.65

Frequency

periods

slightly

2

sharply

band,

than

squared

near

Both

0.5

in

m. at

although coherence

coherent

than

migration

explanation

the

and

cpd.

May.

all

(if

cpd

In

surface

one

zero.

0.16

between

in

wind-generated

different

coherences between

not

depths

the

until

its

April,

between

The

both

(2

day.

At

Circulation

with

harmonics

at

impossible)

surface

at

In

to

currents

208

208,

of

phase

208 f

there

the

April

For

May,

around

for

5

the

the

the

in

1.5

m,

the

day)

m

238

diurnal

example,

0.5,

the

nature,

near

currents

deep

spectra

velocity

and is

wind;

and

the

in

with

wind

having

appear

and

a

low and

band.

the

and

to

April

the

coherence

May,

strong

currents 2

separate

the

and

days.

with however,

268

coherences

diurnal

and

tidal

ranges

show

do.

if

bottom

zero

strong

there

to

the

Below

exception

the

semidiurnal

m,

the

coherence

peaks

be

currents

The

that

crossing and

highest

wind

there

from

the

squared

and

is

currents

compensated

spectral

because

are

4

a

those

deep

at

the of

Fourier

m,

response particularly

semidiurnal

appears

of

0.44

barely

0.57

9

coherence

at

deep

at

over

the

frequencies

and

a

of

coherence

lines

at

at

diurnal

peak

they

2

to

(April)

0.7

components

coherence

the

both

m

the

currents

12

above

0.54.

to

at

near

for

just

is

occur

m

of

surface

survey

9

be

with

strong

frequency

sites

stretched

by

and

for

and

0.49

m

the

squared

the above

The

is

an

a

were

lag

f

at

the the

squared

semidiurnal

is

diurnal

0.51

deep

increase

near

95%

is

period

associated

coherence

coherence

the

the

relatively

wind

tenuous result

0.5

0.8

to

over

bands.

values

(May)

baro

the

noise

wind

same

shift

cpd,

cpd

and

121

for

for

on

in

of

2 a Chapter 6. Low Frequency Circulation 122

c.)) L4) C%J .1.... .J I I I I I I I I. 0) o : I . •11 I :t’ :

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period (days) period (days) nt 5 2 1 0.5 0.33 0.25 nt 5 2 1 0.5 0.33 0.25 .9 180 E E7 I E0 - :5 0 -180 -H-H

.95 .9 E7 I :5 . 0 .95 180 -:---: - .9 I

. - -

U --- . — .——

.95 180 ------& c ::: : H I e 0 ——.-.---. a> I -- I 180 C a> a> I Cl, .95 a> 0 :-- C _b:. -- L-L---k -180 --H--- - a> I 0 C) I 4-: ----4--- V - .95 E .9 07 I :5 U..--_- z

95 V .9 E V 01 .5 Zt: .95 E E180 ° .7 V... . V -180 0 0.2 0.5 2 3 4 002 0.5 1 2 3 4 frequency (cpd) frequency (cpd)

Figure 6.11: Coherence and phase spectra for wind and currents at Basin for May. The dashed line in the coherence plot is the 95% noise limit. The error bar shown for the coherence at each depth is the 95% confidence interval. I. ______

Chapter 6. Low Frequency Circulation 124

period (days) period (days) InS 2 0.5 0.33 0.25 Iiif, 5 ? 1 0.5 0.33 0.25 .9 C :5 .3 C.. ------EEEiiS3E .95 H I :1 . c _%_._. Lzzx - 184-4 . 1 -- 7WE .3 W fN. :_ 0 ° .95 .9 °‘a7 * I 6 S... . - .3 Y--J11i--v. z.?c. .95 .9 18 ------a - csj .7 ‘-r-_%. .3 180’! 0.20.5 1 2 a 00.20.5 2 3 4 frequency (cpd) frequency (cpd) Figure 6.12: Coherence and phase spectra for wind and currents at Salmon for January. The dashed line in the coherence plot is the 95% noise limit. The error bar shown for the coherence at each depth is the 95% confidence interval. period (days) period (days) InS, 1 O5 0.33 0.25 Iiif, ? 1 05 0.33 0.25 .9 180j ----;;w. 7C . c01_ —, .3C... ------.95 — j;--4—s’. - •%.6 : - 84

L 180f . E-z---- .7 I Of 5 T W . 80f__ _.. 0 :4 ° .95 .9 18------I ---- I I s °‘87 : :5 I .: T . .3 -18 C ;._f —v-. .95j .9 C cJ .7 —.5 .1 .3

O.2 0.5 1 2 3 4 ÔO.2 0.5 2 3 4 frequency (cpd) frequency (cpd) Figure 6.13: Coherence and phase spectra for wind and currents at Salmon for February. The dashed line in the coherence plot is the 95% noise limit. The error bar shown for the coherence at each depth is the 95% confidence interval. ______

Chapter 6. Low Frequency Circulation 125

period (days) period (days) Inf,5 ? 1 0.5 0.33 0.25 nf 5 2 1 0.5 0.33 0.25 .9 ----.. 5 7 —

-184- V V-

.95 .9 18

V 57 - V :5 - -1 -. —-T v_’ __%_._ -‘ . z7t -1 -.-‘----- 0) = .95 (I)0 .7 ‘ 5 AdA 3 a -. ------0 C) .9 57 - °‘ : ol .3 is4-- .95 I_ 180f—-.. .9 I ;.— S c..J .7 oj - .‘...... -‘- - : .‘. %- .3 - ÔO.20.5 1 2 3 4 00.20.5 1 2 3 4 frequency (cpd) frequency (cpd) Figure 6.14: Coherence and phase spectra for wind and currents at Salmon for April. The dashed line in the coherence plot is the 95% noise limit, The error bar shown for the coherence at each depth is the 95% confidence interval. period (days) period (days) h’if 5 ? 0,5 0.33 0.25 Inf 5 2 1 0.5 0.33 0.25 180 .9 j V -_ - 57 ° C%J -— - .3 iaoF V - .95 .9

57 V - ‘ :5 — -% .3 ‘ — 4 -‘ 0) z .95 a) 18 ._ Co0 g V 57 V o :5 :.ot • .3 a) -184 _., t. ---“-- V 180H

V o o I V 4 •.%‘

- ----. S •. V I ,- V - : — C -----Jz- 00.2 0.5 2 3 4 00.20.5 1 2 3 4 frequency (cpd) frequency (cpd) Figure 6.15: Coherence and phase spectra for wind and currents at Salmon for May. The dashed line in the coherence plot is the 95% noise limit. The error bar shown for the coherence at each depth is the 95% confidence interval.

in

at positive

below

reflected water

pycnocline

phases

the

9

of

at

depths

0.78

The

low

strongly

May

with

coherence

coherence

the

by

to

Chapter

m

response

Basin

February

depths

In

changes

1800

The

filtered

frequency

wind

also,

phases

respectively,

shows

phases

general,

column.

2

at

below

phases

m.

Salmon

in halfway

in

negative

6.

but

forcing.

the

below

squared

with

may

April

the

current

The

to

a

in

at

near

and

Low

the

sharp

peak

the

4

the

band,

stratification,

down

coherence

2

the

surface

have

m

wind

and

through

2

April,

m

peak

zero

coherence

Frequency

for

and

surface

Migration

peaks

m

are

and

coherence

wind

peak

in

with

to

May

frequencies

deepened,

are

response

for

at

coherence

May

negative

6

where

layer density

m.

and at

below

of

the

6

both.

small

coherence

flow.

suggest

m

0.68

between 2

are

Relatively

Circulation

thickening

of

deployment

the

phase

frequencies

m

the

in

for

records

the

In

(< the

allowing

nearly

for

in

near

greater

at

April

wind

the

peak

f

April,

January

0.5).

main

spectra

9

zero

almost

squared

the

m

0.5

possibility

0.8

strong

response

identical

that

(0.73

coherence

in

currents

is

than

crossing

the

the

The

pycnocline.

are

cpd, because

very

February,

cpd

of

all

(0.78)

the

values

coherence

wind

positive

at

coherences

the

0.5

phases

and

is

f

small).

surface

0.5

of

to at

and

stronger

does

cpd.

of

Salmon

and

squared

to

values

a

of

those 9

cpd),

0.8,

a

mentioned

deep

the

in

transfer

down

0.50

m

change

not

February

The

is

Since

layer

each

would

wind

except

near

spread

near

data,

in

baroclinic

than

the

to

explain,

values

coherence

to

April.

there

0.70;

thickened

of

in

the

is

momentum

coherence

6

the

with

the

become

earlier

weak

in

the

m zero

(0.87)

evenly

bottom

at

however,

noise

is

February,

(they

Basin

however,

With

four

compensation

high

4

an

crossing

for

squared

in

m

are

in

over

incoherent

indication

level

squared

all

are

months

this

coherence

(below

were

response.

the

February,

deeper

near

f

the

most

positive

the

where

elsewhere.

section,

depth

exception

at

0.80

0.5

phase

0.8

200

lack

2

for

values

in

of

flow,

from

m

with

cpd,

and

The

cpd

and

the

the due

the

the

126

m)

all

at

in

of

is is

can,

between fresh

prevented poorly

fresh

unable

Knight

shortly

expects

would

and

correlation

from

inlets

perhaps

precipitation

6.16).

April

River

and

The 6.3

Chapter

Changes

The

the

therefore,

mean

autumn).

water the

water

are

averages

Runoff

occur

were

It

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not

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6.1)

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(1992)

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the

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instrument

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January

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0 U-

50

0

211/91 2/15/91 f1/91 3/15/91 4/1/91 4/15/91 5/1/91 5/15/91 6/1/91 6/15/91

Figure 6.16: Hourly discharge from the Clowhom dam for the period of January 21 to June 18, 1991. Data were smoothed using three passes of a 25-hour moving average filter. leads 2

Figure Chapter m along-channel the 6.17:

current

6. Low Lag response.

correlations Frequency

>.. 2 C currents

.1.

.0.

;°•.•Z : •0. I I .C

.

-48 -8

in

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baroclinic

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tive mode

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Stigebrandt linear

Table

1991

Chapter

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change

2

numerical

the

6.1:

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(1980)),

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the

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(1984)

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May

Apr

Feb

Jan

stratification,

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Hydro).

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Fig. The

tion.

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6.18.

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Mean

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90

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6.

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place

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February,

January,

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between

exchange

Circulation

mid-depth

single

the water

velocities

Fig.

Each

of

surface

down

in

mid-depth

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Island.

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February,

seaward

to

profile

Fig.

3.4).

about

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February,

month

the

say

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to

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with

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6.18.

likely

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is

February

12

volume

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meter

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by

in

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April

other

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the

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180

surface

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and

months,

90

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the

layer

hydrographic

The

two-layer

is

m

m).

seaward

be

to

cyclesonde

caused

May

four

the

are

to

being

is

between

properly

enough

water

outflow

a

Without

substantially

surface

plotted centred

steered

months

niid-depth

1991

mean

conserved

by

exchange

flow

beneath

cross-channel

with

about

are

the

deployments

measure

surveys

surface

is

fresh to

the

from

along at

of

shifted

shown

complex

one

observa

50

a

renewal

surface

30

higher

return

at

at

150

water

20

m,

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flow

side

(see

and

the the

the 131

to

to

m

in is Chapter 6. Low Frequency Circulation 132 outflow. The compensating layer beneath would be a combination of the compensation due to entrainment and a residual flow caused by the currents associated with the tidal jet. The broader two-layer exchange flow underneath is probably caused by pressure gradients arising from the mixing of the water column near the sill by the tidal jet. The tidal jet mixes buoyant water from near the surface with the water outside the sill to form a water mass which is denser than the surface layer, yet almost always lighter than the deep resident basin water. The new water mass enters with significant kinetic energy which is dissipated as the jet water mass is mixed with the basin water. As a result, the deep isopycnals are tilted down towards the sill, and a mid-depth flow is driven towards the sill (see Fig. 6.21, March density). To conserve mass, a return flow is set up underneath. Hence, the kinetic energy of the tidal jet is ultimately responsible for maintaining the tilt in the deep isopycnals, which, in turn, drives the deeper two-layer flow. Harmonic analysis of the along-channel velocities shows that the MSf tidal velocities may be as large as the 2M tidal velocities in the upper 150 m of the water column, and about half as large as the 1K velocities (see Figs. 4.3 and 4.4). Since MSf currents driven directly by astronomical forcing are negligible, the presence of measurable low frequency tidal currents indicates that non-linear tidal interactions are important. The vertical structure of the 1MS velocities in January, shown in Fig. 6.19, represents a multilayer flow down to approximately 120 m, with much smaller velocities between 120 m and the bottom. In general, the MS velocity structure is principally a two-layer flow down to depths of 75 to 120 m, with small velocities near the surface; the zero crossing may be anywhere from 20 to 50 m, depending on the month. The perturbation density amplitudes for the 1MS constituent are comparable to those of 2M and .1K The largest 1MS density amplitudes occur in the surface layer where the density gradients are relatively large. - - - Sill — Basin Salmon 0 r

0

8

E

c..J Feb

-6-4-20246 -6-4-20246 -6-4-20246 -6-4-20246 -6-4-20246 1) Along-channel V (cm i1) Along-channel V (cm ‘) Along-channel V (cm s1) Along-channel V (cm Along-channel V (cm 1)

Figure 6.18: Mean along-channel velocities for January, February, March, April, and May 1991. The solid lines are from the Basin mooring, the heavy dashed lines are from the Sill mooring, and the light dashed lines are from the Salmon mooring. Seaward flow is positive. (a) (b) (c) (d)

0

Q ‘4,

E

clQ to I

0 0 C’,

U, C’,

-4 -2 0 2 4 -4 -2 Ô 2 4 -0.1 Ô 0.1 0.20.30.40.5 -0.1 6 0.10:20.30:40:5 1) -3 -3 V (cm V (cm s ) Density (kg m ) Density (kg m ) Figure 6.19: Profiles of Basin along-channel velocity and perturbation density from the MSf constituent for January 1991; (a) in-phase velocity, (b) in-quadrature velocity, (c) in-phase density, and (d) in-quadrature density.

which

get

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in

the

and fresh

and

Sechelt

Chapter

February

an

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channel.

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B.C.

May

the

water

is

accurate

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volume

variations

Basin,

portion

considerably

Table

reasons

in

Hydro

1991.

6.

the

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A

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6.2:

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data

6.1)

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the

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on

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possibility

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Month

velocity

volume May

to

of

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mean

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Table

mean

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as

this

The

30,

the

second

the

both

which

m.

in

of

mode

9

crossing

70

at

bulk

chapter.

variance

The

most

April.

the

and

uppermost

In

variance

which

in

months

about

and

and for

flow

mode

contributes

May,

flow

first

dominant

each

(70

(35%)

60

of

10

its

Based

180

with

is

disrupts the

m;

in

The

to

3

(outflow

and

there

to

month.

correlation

(27%)

across

represents

between

m,

the

m.

80 however,

is

variance

layer

15

outflow

second

on

second

nearly

and

mode

%)

Basin

is

%

little

This

the

is

the

the

138

no

In

(0

of

of

at

a

9 a

the

driven is

The

mode

Inlet estuarine

of

appearing in

column

represent crossing

February. The

of

zero

data,

6.7

the

variance

becomes

contribution

circulation.

April

Chapter

mode

response

the

the

surface

The

to

wind-driven

wind

layer

crossing

by

changes

the

eigenfunction,

mode

6.10).

remaining

buoyancy-driven

(which

four

the

1.

at

is

strongest 6.

circulation

the

dominated

second

is

in The

currents.

not

It

about

to

intense

given

However,

moving

months

Low

The

near

to

bulk

the

is

in

the

is

consistently

second

unlikely

the

low

each

not

variance

mode

first

Frequency

analysis

5

inflow

the

2

motion

in

mixing

m),

m,

variance

of

may

frequency

towards

it

measured);

mode

data

the

inconsistency

the

mode

mode,

surface would

accounted

the

estuarine

and

that

of

be

first

difference

of

(2

of

near

set

in

in

new dominant

of

better

the

a Circulation

to

the

in

be

the

however,

January

the

the

layer

and

mode

counter

variability

mode

6

the

water

the

the

upper

tempting

head

%).

same

EOF

Salmon circulation.

for

is

established

data

sill.

in

change

in

wind

in

is

always

mode

18

With

at

and

its

the

in

flow

layer

has

not

mode,

analysis

May.

As

from

to

mid-depth.

accounted

January,

placement

is

data

to

surface

February

a

possible

in

in

35

represents

beneath

the

in

negatively

strongest

say

seaward

Since

sign

the

it

the

One

in

%,

response

exception

and

is

appears

that

Salmon

Salmon

and

Basin

layer

of

able

April

explanation

the

in

for

and

in

is

not

the

The

this

flowing

a

in

the

Sechelt

mode

all

to

correlated

57

largest

in

to

uniformly

data,

first that

the

and

in

the

Inlet,

second

site

of

mode

accurately

months. May

to

third

movement

the

poor

January,

3,

79

mode

May,

fourth

the

were

surface

the

Inlet

contribution

but

and

makes

%

Basin for

mode represents

mode

definitive

correlations

with

apparent

moving

of

also

but

in

is

The

in

using

the

mode

the

identify

February lower

masked layer

where

this

April

contributed

data

the

flows

is

analysed

estuarine

first

variance

representative

EOF

surface

unlikely.

in

separation

surface the

(with

in

wind-driven

to

and there

is

seaward

mode

the

in

April,

seen

the

estuarine

that

the

could

analysis.

Sechelt

(Tables

May

a

wind

in

water

mode

was

layer.

flow.

with

most

wind

may

zero

The

the

but

the

139

be

in

it

of a

Table

data

Chapter

were

6.3:

Depth

6.

not

268

238

208

170 The

160

180 150

140

130 120

100

90

80

70 45

60 40

50

35

30

20

9

6

4

2

Low

available.

(m)

first

Frequency

four

-0.10

-0.21

-0.26

-0.31 -0.27

-0.33 -0.20

-0.32

-0.11

-0.01

-0.04

-0.08

0.08

0.11

0.09 0.19

0.24

0.24 0.21

0.26

0.20

0.30

0.13

0.07

0.07

1

EOF

(52.1)

(16)

(15)

(29)

(16) (60)

(72) (56)

(77)

(52)

(68)

(89) (71)

(97)

(95) Circulation

(43)

(73)

(40)

(87)

(25) (19)

(

(

(

(

(

0)

3)

7)

6)

7)

eigenfunctions

Mode

-0.30

-0.23

-0.37

-0.32

-0.38

-0.02

-0.07

-0.06

-0.04

-0.07

-0.08

-0.14

0.14

0.24

0.21

0.19

0.20

0.26 0.27

0.25

0.05

0.06 0.12

0.12

0.04

2

(26.6)

(11) (35)

(36)

(23)

(25) (52)

(87)

(56)

(90) (21)

(51) (55)

(57)

( (

(

(

(1) (4) (

(

(

( (

(

(Percent

2)

0)

2) 6)

2)

9)

0)

3)

7)

8)

for

the

-0.30 -0.32

-0.01

-0.02

-0.13 -0.14

-0.12

-0.09

-0.03

-0.01

Variance)

-0.06

-0.08

-0.07

0.33 0.44

0.44

0.30

0.16

0.22

0.22

0.13

0.03 0.01

0.02

0.04 Basin

3

(13.0)

(64)

(80)

(50)

(91)

(30) (49)

(18)

(10)

(20)

( (

(

(

(5)

(

(

(0)

(1) (0)

(

(

(1) (

(1)

(1)

9)

0)

0)

5)

0)

3)

0) mooring

0)

0)

-0.00

-0.01

-0.06 -0.16

-0.07 -0.05

-0.08

-0.15

-0.15

0.36

0.50

0.45 0.37

0.08

0.04

0.22

0.02

0.12

0.20 0.13

0.20

0.14 0.05

0.09 0.03

in

4

January.

(4.8)

(51)

(31)

(26)

(17)

(

(1) (

(

(

(

( (1)

(

(1) ( (

( (

(

(

( (

(

(

(

0) 0)

4)

0)

2)

5)

3)

0)

0) 0) 0)

0)

0)

0) 2)

3)

3) 0)

Wind 140

data Table

Chapter

were

6.4:

Depth

6.

not

238

208

268

The

160

180

170

150

140

130

120 100

80

90

45

60

50

70 40

30

35

20

12

9

6 4

2

Low

available.

(m)

first

Frequency

four

-0.22

-0.29 -0.32

-0.26

-0.22

-0.14

-0.33

-0.06

-0.02

0.18

0.20 0.21

0.17

0.17

0.25 0.28

0.24

0.15

0.14

0.17

0.16

0.14

0.13

0.05

0.04

0.03

1

EOF

(38.8)

(52)

(42)

(44) (34)

(38)

(73)

(83) (60)

(25)

(48)

(63)

(54) (40)

(79)

(84)

(16)

Circulation

(22)

(41) (28)

(21)

(18)

(

(2)

(1)

(

(

3)

0)

2)

eigenfunctions

-0.25

-0.33 -0.37

Mode

-0.36

-0.06 -0.38

-0.24

-0.02 -0.10

-0.01

-0.02 -0.03

-0.02

0.18

0.24 0.22

0.02

0.12 0.23

0.06

0.24

0.04 0.04 0.26

0.05

0.12

2

(35.3)

(30)

(33)

(41) (46)

(77)

(93)

(97) (94)

( (55)

( (18)

(

(19)

(52)

( (57)

(1) ( (66)

(

( (1)

(

(

(

(Percent

0) 0)

3)

3)

0)

0)

0)

3)

9)

0)

for

the

-0.27 -0.37

-0.37

-0.18

-0.12

-0.08

-0.04

-0.01

-0.06

-0.11 Variance)

-0.06

0.18

0.33 0.34

0.34

0.29

Basin

0.19

0.12

0.08

0.16

0.15

0.09

0.03

0.05

0.06

0.06

3

(16.5)

(22)

(51)

(48) (55)

(46)

(30)

(65) (78)

(14)

(12)

(12)

( (

(

(1)

(

(

( (

(1)

( (

(

(1)

(1)

(1)

mooring

3)

7)

8)

0)

7)

2) 0)

0)

5)

2)

-0.09

-0.03

-0.09

-0.09

-0.25 -0.28

-0.31

-0.24

-0.21

-0.19

-0.24 -0.14 -0.04

-0.10

-0.02 -0.10

-0.03

-0.05

0.39

0.35

0.24

0.35

0.15

0.01

0.17

0.07

in

4

February.

(3.3)

(11)

(1) ( (10) (19)

( (11)

(

(

( (

(

(

(

(

(1) (

(

( (

(

(

(

(1)

(

(

0)

0)

0) 4)

8)

6) 7)

5) 5)

3)

0)

0)

0) 0)

0)

0)

0)

2)

0)

Wind 141

Chapter

Table

Depth

6.

Wind

268 238

208

170

180 160 150

140

130

120

100

90

80

40

50

60 45

35

70 30

25

20

12

6.5:

1.5

9

4

2

6

Low

(m)

The

Frequency

first

-0.17

-0.11 -0.08

-0.18

-0.06

-0.23

-0.27

-0.29

-0.29

-0.27

-0.21

-0.06

0.12

0.14

0.08 0.13

0.24

0.18

0.16

0.26

0.27

0.24 0.17

0.23 0.21

0.06

0.10

0.01

0.03

1

four

(70.3)

(37)

(62)

(62) (46)

(23) (35) (52)

(18)

(90) (16)

(72) (93)

(98)

(88) (98)

(94)

(73)

(54)

(91) (84)

(95)

(70)

(84)

(83) (18) Circulation

(41)

(

(1)

(

0)

9)

EOF

eigenfunctions

-0.26

-0.25

-0.26

-0.18

-0.19

-0.21 Mode

-0.00

-0.07

-0.14

-0.06

-0.01

-0.05

-0.07

-0.14

0.14

0.27

0.35 0.18

0.31

0.35

0.20

0.17

0.26

0.04 0.13

0.08

0.03

0.01

0.05

2

(14.1)

(27)

(41) (26)

(17) (59)

(35)

(19)

(56)

(77)

(27)

(14)

(12)

(43)

(13)

(11)

(

(1) ( (1)

( ( (4)

(1)

(

(

(

(

( (

(Percent

0)

8) 0)

0)

0)

0) 2)

2)

0)

7)

for

-0.25

-0.19

-0.20 -0.18

-0.18

-0.08

-0.05 -0.05

-0.16

-0.17

-0.07

-0.16

Variance)

0.36

0.31

0.23

0.33

0.34

0.15

0.14

0.17

0.16

0.11

0.10

0.11

0.00

0.21

0.14 0.02

0.03

the

3

(8.2)

(52)

(56)

(20)

(13)

(10)

(29)

(40)

(11)

(15) Basin

( (18)

(

(

(

(1) (

(1)

( (

( (4) (1)

(

(

(

(

(

(

(5)

4)

8) 6)

0)

2)

7) 2)

0)

5) 0)

7) 0)

2)

0)

mooring

-0.43

-0.41

-0.43

-0.14

-0.23 -0.12

-0.03

-0.16

-0.25 -0.04

-0.10

-0.13

-0.05

-0.04

-0.26

0.10

0.10

0.15

0.04

0.09 0.21

0.19

0.01

0.02

0.01

0.04 0.08

0.10

0.21

4

(3.2)

(35)

(30)

(42)

(1) (

(1)

(1) ( (

(1)

(1) (

(

( (

( (

(1) ( in

( (

(

(

(

( ( (

(

(

3)

8) 0) 5)

5)

0)

6) 0)

0) 0)

0) 0)

0)

2)

0)

0)

0)

2) 6)

0)

April. 142

Chapter

Table

Depth

6.

Wind

268

238 208

180

160

170 150

140

130

120

100

90

80

60

6.6:

50 40

70 45

35

30

25 20

Low

15

12

9

4

2

(m)

The

Frequency

first

-0.19

-0.05

-0.22

-0.14

-0.24

-0.26

-0.27 -0.27

-0.19

-0.26

-0.11

-0.01

0.08

0.12

0.16

0.23

0.22

0.22 0.20

0.07

0.15

0.25

0.26

0.27

0.22

0.04

0.05

0.03

1

four

(79.2)

(32)

(88)

(90)

(13)

(52) (61)

(89)

(87)

(85)

(87)

(16)

(64)

(91)

(95)

(97)

(76)

(96)

(93) (95)

(67)

(96) (89)

(97)

(51)

Circulation

(

(

(

(

5)

0)

9)

5)

EOF

eigenfunctions

-0.35

-0.42

-0.20

-0.35

-0.11

-0.10

Mode

-0.23

-0.04

0.14 -0.04

-0.08

0.15 -0.09

0.34

0.26 -0.09

0.16

0.19

0.18

0.10

0.13

0.10

0.09 0.11

0.17

0.09

0.16 0.01

2

(9.8)

(15)

(19)

(36)

(28)

(66)

(30)

(75) (65)

(

(

(35)

( (

(

(

(0) (

(

(1)

(1)

( (

( (

(

(1)

(1)

(

(Percent

3)

2)

5)

8)

7) 2)

3)

4)

1) 0)

7)

2)

0)

4)

for

-0.20

-0.08

-0.01

-0.00 -0.39

-0.32

-0.10

-0.10

-0.05 -0.09

-0.21

-0.18 -0.04

-0.15

-0.14

-0.14

0.29 -0.18

Variance)

0.22

0.20

0.34

0.38

0.07

0.13

0.03

0.04

0.13

0.17

the

3

(4.1)

(26)

(13)

(10)

(13)

(13)

(22)

( (

(

( (44)

(

(1) (21)

(

(

(

(

(

(3)

(1) (

(

(1)

(

(1)

(1) (

Basin

0)

0) 0)

0)

0)

0)

0)

5)

3)

0)

0)

0)

2)

3)

mooring

-0.48

-0.31

-0.04

-0.01

-0.28

-0.11

-0.13 -0.25

-0.21

-0.12

-0.16 -0.17

-0.08

-0.02 -0.21

-0.06

0.31

0.33

0.17

0.03

0.09

0.03

0.00

0.08

0.15

0.10 0.11

0.18

4

(2.6)

(14)

(48)

(12)

(13)

(

( (

(1) (

(

(

(

( (

(

(

(

(1) (1)

(

(

(

( (

(

(

(

(

in

5)

0)

4) 0)

0) 0)

2)

4)

0)

0)

0)

0)

0)

0) 0)

2)

0) 0)

2) 4)

0)

May. 143

Chapter

Table

Table

6.8:

Depth 6.

Depth

6.7:

Wind

Wind

12

12

Low

9

4

6

4

2 9

6

2

The

The

(m)

(m)

Frequency

first

first

four

0.36

0.58

0.56 -0.48

-0.54

-0.42

0.45 -0.55

four

0.08

0.13 -0.02

0.05

1

1

(57.7)

(72.8)

EOF

(41)

(97)

(88) (66)

EOF

Circulation

(

(

(96)

(97) (73)

(87)

(

(

2)

9)

0)

1)

eigenfunctions

eigenfunctions

-0.63 Mode

-0.53

-0.29

Mode

-0.09

0.25

0.41 -0.31 -0.18

0.45

0.70 0.41

0.14

2

2

(35.4)

(19.2)

(56)

(10)

(92) (32)

(31)

(

(22)

(88) (37)

(Percent

(

( (

(Percent

1)

2)

9)

1)

for

for

the

the

-0.31 -0.16

-0.02

-0.02 -0.02

-0.09

-0.24

0.94 -0.27

Variance)

Variance)

0.91

0.07

0.17

3

Salmon

3

Salmon

(6.4)

(6.4)

(58)

(

( (

( (

(62)

(

( (

(

(

4) 0)

0)

0)

0)

0)

0)

0) 4)

2)

mooring

mooring

-0.04

-0.47 -0.63

-0.15

-0.50 -0.25

-0.65

0.04 0.60

0.33 0.40

0.06

4

4

(0.4)

(1.5)

in

(

( (

( (

(

in

(

( (

( (

(

0)

0) 0)

0)

0)

0)

0)

0)

6)

0)

1)

1)

February.

January. 144 Chapter 6. Low Frequency Circulation 145

Table 6.9: The first four EOF eigenfunctions for the Salmon mooring in April.

Mode (Percent Variance)

Depth (m) 1 (78.7) 2 (18.1) 3 (2.0) 4 (1.1)

Wind 0.38 (76) -0.40 (18) -0.23 ( 0) -0.76 ( 4) 2 -0.23 (36) 0.56 (52) -0.78 (10) -0.17 ( 0) 4 -0.48 (93) 0.21 ( 4) 0.37 ( 1) -0.24 ( 0) 6 -0.51 (98) -0.02 ( 0) 0.22 ( 0) -0.44 ( 0) 9 -0.45 (83) -0.41 (15) -0.17 ( 0) -0.08 ( 0) 12 -0.33 (59) -0.55 (37) -0.37 ( 1) 0.36 ( 0)

Table 6.10: The first four EOF eigenfunctions for the Salmon mooring in May.

Mode (Percent Variance)

Depth (m) 1 (67.3) 2 (26.5) 3 (4.4) 4 (1.6)

Wind 0.38 (69) -0.25 (11) -0.70 (15) -0.53 ( 3) 2 -0.30 (43) 0.52 (50) 0.23 ( 1) -0.66 ( 4) 4 -0.48 (83) 0.29 (11) -0.41 ( 3) -0.10 ( 0) 6 -0.51 (93) -0.03 ( 0) -0.48 ( 5) 0.34 ( 0) 9 -0.44 (67) -0.48 (32) 0.10 ( 0) -0.02 ( 0) 12 -0.28 (35) -0.59 (60) 0.24 ( 1) -0.41 ( 1) indication 200 every renewals is runoff for measurements during 1957, the turnover but disappointing 1957 the main The at deep Because 6.6 Inlet Chapter much the Previous good From basin new m. mid-depth new sill to is March sill year Deep-Water main is years very There less 1993 at of water measurements of 6. (1962 low at January water water in from the the the Skookumchuck sill Low frequent: the infrequent. 1962, studies where (as are from is at connecting reaching to bottom intrusions strong then is it temperature the an proposed Frequency shown 100 so 1990 1964 January is the the increase 100 vigorous, passes to Renewal (e.g. and mixing relatively to water; replace. and point of bottom The depths m in April of the 200 channel Lazier, 1986, by Narrows data through Fig. 1990 Circulation in water renewing or of at however, the vertical m Lazier oxygen 1992 the of water view in high the and 6.20. in to density between 1963) 100 were winter, salinity a Sechelt before 1992) sill, there August of oxygen shallow (1963)). diffusion was water Mid-depth to levels the measuring seen replacement were of 150 was there entering replaced. when Jervis records relative Inlet the 1993. must at in levels basin m. fortunate no The of inflow 200 the is the from Inlet bottom heat The intrusions enter at no During quiescence the the (> (75 renewal m late renewing Temperature, 200 of indication must and UBC and in lack hydrographic 2.5 m) main the the enough winter m water 1990, several ml the between salt. that of inlet deep be hydrographic cycle of basin. of 1_i) bottom entrance water significantly water renewal but of it the of to first basin surveys of is were 1990 renewal salinity have the because Because deep-water due parameters is the over are replacement water densest first to in and seen to measurements between bottom seen Sechelt surveys Sechelt a an and at denser sill there 30 the 1991, in in intrusion or to and to and allowed August oxygen Sechelt mixing during below water occur Inlet, these Inlet. 40 is from than with was the 146 the no m Chapter 6. Low Frequency Circulation 147

of new water, the gradual increase in oxygen (see Fig. 6.20) is probably due to downward diffusion of oxygen from the mid-depth replacement, rather than from replacement of the deep-water itself. It is tempting to say that, based on the hydrographic surveys, bottom water renewal occurs with a period of approximately 5 years. However, the one survey in 1981 suggests that there was no renewal in the previous winter, and that the existing basin water had been resident a long time. At best, the bottom water renewal in Sechelt can be said to be infrequent, with the average residence time of the basin water below

150 m being probably five years or more.

Since oxygen is a good tracer of new water, changes in oxygen at depth’ usually indicate the presence of new water. Normally, an increase in oxygen is accompanied by an increase in density, because the replacement water is likely to have a density greater than the resident basin water. However, the background rate of density change in the deep-water is about 0.01 kg 3m per month, and will tend to deepen the isopycnals over time, even if the water remains undisturbed. Contours of oxygen and density are shown in Figs. 6.21 and 6.22, from hydrographic surveys before and after mid-depth renewal in

1990 and 1991. In 1990, mid-depth renewal took place between February and March. The oxygen contours suggest that the new water penetrated to just below 150 m, displacing the resi dent basin water towards the head. An oxygen minimum occurs at 50 m as the relatively oxygen-rich plume appears to push under the surface layer. The oxygen isopleths at station 8, near the head of Salmon Inlet, are noticeably displaced upwards. The 24.4 at contour deepens between February and March 1990, due to vertical diffusion, but the 22.2 and 22.0 isopycnals are displaced upwards, indicating an increase in the mid-depth densities associated with the renewal. There is also an increase in the tilt of the 22.2 and

22.0 isopycnals between the sill and station 3, and, to a lesser extent, in the 22.4 contour line. 1957 1961 1962 1963 1964 1981 1985 1986 1990 1991 1992 1993 9.4 9.4 (9.77)j (Io.o8 (9.98) 9.2• :: A 9.2 1 ‘ 9.0 :: I j 9.0 c-) ‘/ 8.8. ::i°°1 8.8 8.6 I :: .‘ 8.6 0 8.4. 8.4 200 m 8.2 8.2 8.0 8.0 7.8 7.8 29.0 29.0 I 28.8 o (7.61r •.. o 28.8 • (7.44) 28.6 • 28.6 0 lOOm 28.4 28.4 I ; I 28.2 28.2 0• I 28.0 I 28.0 I / I 27.8 I 27.8 I I ,. 27.6 27.6 - 4 • 4 o 1oom :: Is 3 II 2 \\ 0.. 2 200 m’%, 0 1957 1961 1962 1963 1964 1981 1985 1986 1990 1991 1992 1993

Figure 6.20: Temperature, salinity and dissolved oxygen at 100 and 200 m in Sechelt Inlet from 1957 to 1993. Significant gaps in time have been removed from the plot, and data values which exceed the bounds of the plot are indicated by (). In years with only one survey, individual data points are indicated by (Q) at 100 m and (D) at 200 m. Chapter 6. Low Frequency Circulation 149

In 1991, mid-depth renewal also took place between February and March, but to a lesser degree than in 1990. An oxygen-rich plume can be seen penetrating to about

100 m, causing an oxygen minimum at 50 m at station 3. The response of the isopycnals in 1991 is shallower than in 1990; The effect of the inflow is seen only at depths shallower than 100 m. The 22.0, 22.2 and 22.3 o isopycnals all deepen slightly; the 21.5 isopycnal, however, becomes shallower with the inflowing dense water. In February, the isopycnals are actually tilted towards the head. This behaviour could be in response to the large discharge of water from the Clowhom River Dam in February: as the surface pressure gradient increases (tilts seaward) from the discharge, the isopycnals lower in the water column will tilt towards the head to compensate. The isopycnals at station 8 become elevated in March, as in 1990.

One of the potential problems associated with renewal of the deep-water is the upward displacement of the resident low oxygen basin water. In 1962, the oxygen at station 8 dropped to below 1 ml 1_i at 10 m, and remained very low until 150 m, where it increased to 4 ml 1_i. Even in Porpoise Bay (station 6), where oxygen values are normally well above 2 ml 1’ down to 75 m, oxygen values fell below 2 ml M at 20 m. Although the upwelling of deep-water is visible during mid-depth replacement, it is not as severe as during a replacement of the bottom water. The 1962 event demonstrates that it is possible for displaced bottom water to reach Porpoise Bay, and that may have implications on disposal of waste in the inlet. The upwelling of basin water will need to be considered when determining the assimilative capacity of Sechelt Inlet for pollution. It could also have a deleterious effect on salmon farming. ______

Chapter 6. Low Frequency Circulation 150

1 21.5 2 3 4 7 8 22— 224

100 )222 j

200 - - I! -I--—.

300- (a) .... Dt (as) (kg )3ni I I I I 40 30 20 10 0 Distance from the head (km)

0- 1 2 3 4 7 8

• .. ‘S - *—- -— — ,. . —r - :• • ‘“-•—--- : ,— : 4 - 2• . 3 - / / : > 100 : • — : ..; : : ‘ - “ 7 ;___._._- .——r’—’1 E . : - • -— - .—.-— •

• •—.—-. _•.,— 200’ 1.5 _._....;-...— —--— : - / ::: 300- (b) Oxygen (ml 1)

I I I I 40 30 20 10 0 Distance from the head (km)

Figure 6.21: Along-channel section contours of (a) density (kg 3m and (b) oxygen 1_i), ) (ml for February (solid) and March (dashed) 1990.

20O

::

Figure

(ml

300-

ioo

300-

Chapter

0

1_i),

6.22:

(a)

(b)

for

6.

5

I

r

February

40

Low

40 Along-channel

I

I

1

:

1

/

Frequency

21 (solid)

—

2

_4:—

2

section

Circulation

and

30

30

I

Distance

Distance

March

3

3

contours

from

from (dashed)

__

:

4

4

the

the

of

20

20

I

I

(a)

head

4

head

1991.

density

Density

(km)

(km)

7

7 I

___

Oxygen

(kg

10

10

I

I

(as)

m 3 )

S

8

:j

(kg

(ml

and

n1 3 )

1)

(b)

0

0

I

oxygen

I 151

a

sinks.

and

turbulent

dissipated

the tides

sill

progressive

dissipation

order

provide

the

robust

1980) the

inflow

at

The

small

the

The

computed

estimates

surface

K 1

barotropic

circulation

to

of

and

The

enough

sill.

analytical

fraction

constituents

three

an

the

magnitude

tidal

close

average

energy

over

Because

internal

tide.

vertical

5

main

from

in

jet.

MW

to

tide.

of

to,

the

in

chapter

model

significantly

Some

flux

that

up-inlet

The sinks

the

but

Sechelt

larger

sill,

through

was

tide.

the

diffusive

The

of

theory

of

not

up-inlet

(b)

narrow

energy

between

was

of

4,

barotropic

high

the

than

The

energy

the

Inlet

directly the

which

Burrard

derived

processes

internal

presented

reduce

frequency

tidal

apparent

those

kinetic

constriction

(about

flux

is

0.1

flux

accounts

weak,

over

energy

of

tidal

and

in

Conclusions

Inlet

of

the

tide

Chapter

of

energy

the

order

5% is

in

inefficiency

0.2

the

about

internal

152

tidal

flux

explained

despite

4

and

(de

internal

chapter

flux

that

MW

for

at

MW,

sill,

to

flux

into

Young

Indian

Skookumchuck

amplitudes

42

were

nearly

7

better

of

through

in

waves

the

and

MW,

of

Sechelt

4.

tide

direct

Knight

by

of

identified

the

and

Arm

The

highly

is

all

estimate

the

the

based

based

was

by

turbulent

the

Pond,

frictional

of

fluxes

Inlet landward

(de

transfer

frictional

Inlet

far

not

the

energetic

kinetic

on

on

to

Narrows

Young

the

the

is

measured,

1989).

(Farmer

tide

in

the

be

power

very

tidal

smallest

Sechelt

of

dissipation)

loss

(a)

analysis

of

energy

dissipation

gauge

and

energy

tidal

chokes

The

direct large: the

jet,

extracted

of

and

Pond,

energy

but

of

Inlet

records

sill,

and

dissipation

flux

interaction

of

Freeland,

the

frictional

from

the

the

may

the

a

(c)

is

at

are

of

1987).

three

more

from

tides

from

tidal

also

and

the

the

M 2 the

the

be an

work

Inlet, found

0.002

For finds

the

diffusion

(1989), which

Stigebrandt narrow-band

q

single

a

by

work

where

only

the

Arm). vertical of

the

Chapter

broad-band

the

Comparing

the

Vertical

vertical

transfer

Sechelt

breaking

1.33

that

was about

of

±

and

by

frequency.

tend

0.5

tidal

source

an

0.001

Gargett

When

diffusion

±

of

Stigebrandt

7.

attributed

they

indeed

0.13

estimate

to

salt 0.01

diffusion

diffusivity

jet

Inlet,

and

of

Conclusions

limit

q of

MW.

internal

have

of

the

not

are

mechanical

based is

and

the

and

kg

Aure,

the

(Stigebrandt,

other

responsible

For

1.0,

set

0.03

estimated

positively

disturbed

The

q m 3

internal

Holloway

for

by

heat

in

and

internal

by

on

Sechelt K,

and

1989).

wave

Sechelt

Stigebrandt

inlets,

the

flux

1.5

per

Gargett

changes

Aure

(see

Rf

and

a 0

energy

flux

(e.g.

tide

gain

Richardson

month.

spectrum,

correlated.

by

for

(1984).

waves

is

Inlet,

chapter

it

Inlet

the

for

1976;

a

has

Richardson

deep-water

may

forming

and

in

0.08,

in

Gade

site-specific Brunt-Väisälä

“well-behaved

in

potential

and is

temperature.

q

which

been

A

Stacey,

Gargett

Holloway

weak

also

the

5)

with

power

and

and

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Aure

number

with

1.05

the

suggested

internal

be

provide

compared

Edwards,

q

an

intrusions,

number 1984).

energy

middle

and

to

due

± law

=

the

constant.

(1984),

estimated

for

0.08

wind-generated

wave

frequency,

1.0

These Holloway

the

relationship

to

energy

tide

the

Sechelt

of

as

density

when

(mixing

the

to

based

analysis

1980;

basins”.

the

than

the

energy

the

to

neighbouring

estimates

The

dissipation

flux

basin

background

primary

vertical

the

suggested

N,

Inlet

those

on

de basin

layer

efficiency)

range

of

of

was

for

following

Young

The

internal

changes

waters

mixing,

Stigebrandt

agrees

the

found

of

density

(20

mixing:

established

source

diffusive

background

of

q

of

that

internal

inlets

and

to

are

rate through

q

high

with

in

waves

in

the

but

was

is

150

K,,

of

decreases

closer

other

Pond,

salinity

q

(e.g.

determined

of

theoretical

in

frequency processes.

energy

the

found and =

=

m),

tide,

are

work

between

vertical

Sechelt

a 0 N,

rate

0.5

fjords,

Indian

to

range

1988;

Aure

while

of

and

one

the

153

for

for

for

by

of

of a

seiche

in

several of

16 seiching.

coherence

Inlet rents

between

winds the

coherent herent

200

ences

0.929

likely

Sensitivity to

the

depth internal

Chapter

Salmon

water

cm

measure,

In

The

The

surface

wind

m,

causes

is

cpd)

s 1 well

could

change

Salmon

are

where

were

days

generally

peak

wind

coherence

the

waves

response

at

7.

energy

A

spatially

between

Inlet

above

was studies

layer,

the

explain

high

wind

since

typically

of

strong

Conclusions

their

coherences

the

appears

Inlet,

oscillation

which

would

generally

beginning

is

spatial

the

54

high

baroclinic

and

and

suggests

the

frequency

of

of

the

in

correlated,

outflow

the

cm

there

the

95%

the

the

wind-generated

the 0.2 to

may

have

propagate

(Baker

wind

s

phase

variability have

of

wind

baroclinic

low,

diurnal

currents

with

noise

also

that

of

also

a

estimated

0.4

tidal

wind

f

and

approaches

phase

February

relatively

but

and

response

and

to

appeared

a

cause

the

to

level

the

away

energy

period

0.66

seabreeze,

the

at

it

is

Pond,

0.7

the

low

speed

in

energy

in

was

currents.

the

(0.31)

some

currents

flow

from

the

cpd

were

from

coherence

contrast

frequency

from

to

little

flux the

of

higher

to

end

1995).

of

wind,

the

and

flux

(or

approximately

a deep

found.

and

be

were

about

the

Brunt-Väisälä

influence

simple

by

the

of

wind

in

1.5

the

a

showed

to

in

no

The

which

its

January sill

baroclinic

the

between

low

wind

found

Clowhom

Knight

to

Salmon

23

diurnal

more

effect

The

in

two-layer

and

more

lower

frequency

5

cm

on

Salmon

variations

may

that

days

only

frequency

break

than

s’,

the

and

on

Inlet,

the

two

complex Inlet

tides

frequency

response.

frequency

River

be

the

the

period).

shallower

circulation.

which

model.

wind

a

5%.

Inlet,

days.

responsible

when

where

response

diurnal

than

could

sudden

circulation

have

dam

bands

and

geometry

falls

where

The

An

(Pond

The they

in

bands

the

The

some

not

than

was

seabreeze

the

Sechelt.

large

in

internal

reminiscent

A

low

along-channel

existence

that

be

for

approach

depth

the

the

large

influence was

followed

surface

et

(lower

9

separated.

in

coherence

discharge

the

m;

al,

currents were

range

difficult

Sechelt

Coher

part

seiche

of

would

1995).

below

lower

than

cur

of

the

154

the

co

by

on

of

of

of a

and event

The

has

Salmon renewal

water

no

the

taken

by

Salmon

up-inlet

circulation the

while currents,

surface),

at

not

percentage frequently

is

Chapter

not

the

bottom

the

The

The

Empirical

sill.

deep-water

been

health

low

consistently

in

since water

(below

Basin

primarily

mid-depth

diffusion

vertical

in

Inlet

oxygen The

Inlet

1963,

counterfiow

was

demonstrated 7.

and

Sechelt

water

problems

appear

proposed

of

1957

in

water

station.

Conclusions

150

seemed

identified

during

upwelling

orthogonal

the

is

the

for

levels

displacement

probably

suggest of

responsible

replacement

m) identify

low

intrusion

Inlet

to

mass

surface

heat

eventual

is

if

is

by

mid-depth

lead

The

to

in

frequency

replaced

contaminated

produced

as

by are

of

and

Lazier

formed

this

be

that

the

function

four-layer

formed

the

low and the

the

of

not

sensitive

salt

renewal.

displaced

for

the

wind-driven

during

of

wind.

water

dominant

oxygen

lower

(1963).

consistent

only

by

known.

replacements.

decreases

variance.

the

existing

underneath.

mid-depth

by

the

(EOF)

flow

once

in low

by

layers

the

to

density

Hydrographic

water

water

tidal

The

February.

the

bacteria.

mode,

is

frequency

1991

deep-water

approximately

tilting

the

analysis

Instead,

mode

also

moves

jet

lower

modulation

was

water

can

gradients

deep-water

study,

The

pushes

accounting

a

During

seen

threaten

as

of

persistent

layer

It

seaward

is

supports

empirical a

variability.

one

the

is

surveys

the

four-layer

by

replaced

as

mid-depth

conceivable

is

created

one

oxygen

every

far

that

of

intrusions

exact

blocked

density

fish

to

for

the

as

feature

particularly

the

in

modes

accounted

compensate,

stocks

once

five

station

35

conditions

low

flow

by

The

the

isopleths

assertion

water

over

by

to

years.

that

the

of

a

frequency

of

Sechelt

(with

both

EOF

85%

and

the

year,

new,

6 time,

the

tidal

towards

pollutants

in

for

sill,

Since

cause strong

of

at

for

in

monthly

outflow

analysis

Porpoise

that

but

similar

denser

conditioning

Inlet

the

a

mixing

the

Sechelt

and

deep-water

variability

significant

there

the

aesthetic

the

the

variance

renewal

head

system

a

which

to

at

water

deep-

mean

could

weak

head

wind

Bay.

near

was

and

the

the

155 of

strong monitored,

dormant

as

accumulate

Chapter

Porpoise

deep-water

7.

and

wastes

in

Conclusions

Bay

unoxidized

the

during

intrusion.

that

deep-water

appear

times

for

several

could

to

of

be

bottom

years,

be

assimilated

pumped

water

only

to

flushing.

in

back

be

the

forced

up

deep-water

near

If

to

pollution

the

the

of

surface,

surface

the

is

inlet

not

even

again

carefully

may

as

by

156

lay

far a

to

Basin

Figs.

the

This

A.12.

Basin

months

appendix

A.4

densities

Note

velocities

to

of

A.6;

the

February,

contains

are

positive

change

shown

are

shown

the

April

in

in

flow

along-channel

scale

Figs.

and

in

is

seaward.

Hourly

Figs.

between

A.7

May.

Appendix

to

A.1

A.9;

157

Data

the

Densities

velocity

to

Salmon

2

A.3

Plots

to

A

and

12

and

are

m

densities

density

Salmon

given

data

and

as

are

plots

velocities

o

the shown

=

of

p deeper

—

hourly

in

1000

are

Figs.

depths.

shown

data

kg

m 3 .

A.10

for in

currents

Figure Appendix -10 t10 -1o 410 2-io 10 Q U) c c..J -i0

CD 2

CN

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2

E E E -30 -30 30 30 -30 -10 30 r. -30 -10 -30 30 10 30 30 10 30 10

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Along-channel

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3/1/91

3/1/91 3/1/91

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1991.

Positive 158

currents

Figure Appendix -10 ‘10 -10 10 2-io -10 10 ‘10 U) c.J -10 cD10 C%J

E E

2 2 E -30 -30 -30 -30 -10 -30 -10 30

30 .qri -30 30 30 -30 -10 30

30 4/23/91 30 10 10 30

30 4/23/91 10 10

10

4/23/91

A.2:

indicate A.

4

Along-channel VAvr\r

\f’N Hourly

WhJ flow -

v\fJ,

VVAr’

towards

Data

5/1/91

5/1/91

5/1/91

Basin

Plots

the currents

“ sill

U (units

V

5/8/91

5/8/91 5/8/91 V

‘1

in are

V the

V cm

• surface

•

s’).

5/15/91

5/15/91

v-- 5/15/91 layer J

W for

U

5/23/91

5/23/91

5/23/91

I”if’

v April

yl.(V y- ‘

A”V-w, 1991.

‘r

r’ 1 ‘r N

,IJ

Positive 159 Appendix A. Hourly Data Plots 160

6/1/91 6/8/91 6/15/91 6/23/91 30 10 E M ..A i . %. 1, .. Ih(%. — . A & n r ri.. -10 ••r’ v -30

30 E 10 co10 -30

30 E 10 -10 iJv1rvlfl\1vPAe&fy1v/Al 6/1/91 6/8/91 6/15/91 6/23/91

30 2 10 c’4-10 -30

30 2 10 A LI) -10 fiJA[fAf -30 30 ri 10 -10 Wt jANA -30

30

10 ,A, AA.rAv A, 2-io i,—- V ‘‘-‘ -30

30

30 ‘10 -10 &J’rr\t vVV”j -30 6/1/91 6/8/91 6/15/91 6/23/91

Figure A.3: Along-channel Basin currents in the surface layer for May 1991. Positive currents indicate flow towards the sill (units are cm s’). Appendix A. Hourly Data Plots 161 I 2/23/91/‘wvW’N3/1/91 3/8/91 3/15/91 3/23/91 40

0

40 2/23/91 3/1/91 3/8/91 3/15/91 3/23/91

Figure A.4: Along-channel Salmon currents in the surface layer for February 1991. Pos itive currents indicate flow towards the sill (units are cm s’).

4/23/91 5/1/91 5/8/91 5/15/91 5/23/91

qg•rwvvwfJ\-4%6 4/23/91 5/1/91 5/8/91 5/15/91 5/23/91

Figure A.5: Along-channel Salmon currents in the surface layer for April 1991. Positive currents indicate flow towards the sill (units are cm s’). ______--

Appendix A. Hourly Data Plots 162

6/1/91 6/8/91 6/15/91 6/23/91 40 20 -20 \f\A/JV71V4VA -40 1VfV’J 40 20 .. .Afl/i iA fl -20 VV -40

40 20 A i,A - - .4 I . A Co20 -20 -Jvwvvv VVVVVVVWVJ VVYflfWW -40

40

20 4 I - A. cj02 vvq — -20 \MiVVV 6/1/91 6/8/91 6/15/91 6/23/91

Figure A.6: Along-channel Salmon currents in the surface layer for May 1991. Positive currents indicate flow towards the sill (units are cm

Appendix

21

21

°

0

0

0

E

o 0

14

E

°

E

E

E18

20

22

20

20

21

22

20

22

21

20

21

22

22

22

10

18

10

14

A. 2/23/91

—

2/23/91

2123/91

Hourly

Figure

Data

3/1/91

3/1/91

3/1/91

A.7:

Plots

Basin

densities

3/8/91

3/8/9

3/8/91

1

(o)

for

3/15/91

3/15/91

3/15/91

February

1991.

3/23/91

3/23/9

3/23/91

1 163 Appendix A. Hourly Data Plots 164

4/23/91 5/1/91 5/8/91 5/15/91 5/23/91

CD 14 10

22 142 18 10 4/23/91 5/1/91 5/8/91 5/15/91 5/23/91

222 to 21 20

222 ° 21 20 2 22 ------21 20

222 21 20

222 21 20. 4/23/91 5/1/91 5/8/91 5/15/91 5/23/91

Figure A.8: Basin densities (Jt) for April 1991. Appendix A. Hourly Data Plots 165

6/1/91 6/8/91 6/15/91 6123/91

E 18 14 10

22 14E 18 10 6/1/91 6/8/91 6/15/91 6/23/91 E22

E 22 21 20

= 22 Q LO 21 20

21 20

21 20 6/1/91 6/8/91 6/15/91 6/23/91

Figure A.9: Basin densities (a) for May 1991. Appendix 14 CD E 14 E18 CD • E

E 4/23/91 22 10 18

10 14 4/23/91 22 22 10 18 10 14 18 14

10

Figure

2/23/91

2/23/91

Figure A.

______

A.1O:

Hourly

A.11:

Salmon

3/1/91

3/1/91

Salmon

Data

5/1/91 5/1/91

______

Plots

densities

densities

3/8/91

3/8/91

(o)

5/8/91

5/8/91

(oj)

in

in

the

the

surface

3/15/91

3/15/91

surface

5/15/91

5/15/91

layer

layer

for

for

February

3/23/91

5/23/91

3/23/91

5/23/91

April

1991.

1991. 166 Appendix 14

CD 2 2 22 10 18 14 18

10

Figure

A.

Hourly

A.12:

Data

Salmon

6/1/91

6/1/91

Plots

densities

6/8/91

(o’)

6/8/91

in

the

surface

6/15/91

6/15/91

layer

for

May

1991.

6/23/91

6/23/91 167

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