THE CIRCULATION AND ENERGETICS OF THE SECHELT INLET SYSTEM, BRITISH COLUMBIA By Scott Wayne Tinis B. Sc. (Physics) University of Victoria, 1990 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES OCEANOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 1995 © Scott Wayne Tinis, 1995 _________________________ ____________________ In presenting this thesis in partial fulfilment of the requirements for an advanced shall make it degree at the University of British Columbia, I agree that the Library that permission for extensive freely available for reference and study. I further agree copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall riot be allowed without my written permission. (Signature) Department of The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract The sill at the entrance to Sechelt Inlet, 50 km northwest of Vancouver, is tuned almost perfectly to extract the maximum power from the barotropic tide. However, despite the enormous up-inlet energy flux from the barotropic tide (—‘42 MW), the diffusive processes in the deep-water of the inlet basin are weak, and the energy flux of the internal tide generated at the sill is relatively small (< 200 kW). The large tidal energy flux is almost completely dissipated at the sill, and most of the energy that manages to escape the sill region does so in the form of a turbulent jet that dissipates at mid-depth near the sill; very little energy is left over for mixing the deep-water. Using estimates of the change in potential energy of the water column by vertical diffusion, the mixing efficiency (flux Richardson Number) of the breaking internal tide is determined to be between 3 and 8%. Because the transfer of energy to diffusive processes is so inefficient, the vertical dif fusion of salt decreases the deep-water density by only —‘0.0l kg m3 per month. The decrease of the deep-water density conditions the inlet for eventual deep-water replace ment; however, hydrographic surveys in Sechelt Inlet suggest that while the mid-depth basin water is replaced once a year, the deep-water (below .--150 m) is replaced only about every five years. The wind has relatively little influence on the circulation. Much of the wind energy is contained in the diurnal seabreeze, and its effect on the overall baroclinic energy flux is estimated to be no more than 5%. The coherence of the wind to the currents in the lower frequency bands (f < 0.929 cpd) is small over most of the water column, with the frequency band between 0.2 f 0.66 cpd having the highest coherence. 11 Empirical orthogonal function (EOF) analysis also indicates that the wind is not primarily responsible for the low frequency variability: the EOF analysis could not con sistently identify the wind-driven mode as one that accounted for a significant percentage of the low frequency variance. The four-layer flow that was identified as the dominant mode of low frequency variability is also a persistent feature of the monthly mean cur rents, and is probably formed by density gradients created by the tidal mixing near the sill. The mean circulation is similar to that proposed in an earlier study of Sechelt Inlet by Lazier (1963). 111 1 7 8 12 14 18 19 20 17 Table of Contents Abstract U List of Tables vu List of Figures ix Acknowledgements xiv 1 Introduction 1 1.1 Fjord estuaries 1.2 Shallow-silled fjords 1.3 The oceanography of Sechelt Inlet 1.4 Motivation 2 Instrumentation and Data 13 2.0.1 Hydrographic surveys. 2.0.2 Current Meter Moorings 2.1 Data processing 2.1.1 Cyclesonde 2.1.2 Aanderaa RCM 2.1.3 InterOcean S4 2.1.4 Anemometers 2.1.5 Endeco oxygen meters 2.2 Data iv 2.2.1 Currents 21 2.2.2 Density 27 2.2.3 Harmonic Analysis 30 2.2.4 Wind 33 2.2.5 Runoff 34 2.2.6 Oxygen 36 3 Tidal Choking 39 3.1 Inviscid tidal choking 40 3.2 Choking with friction 44 3.3 Tidal Choking in Sechelt Inlet 46 4 Tidal Energy Partition 53 4.1 Energy Sinks 53 4.2 Barotropic Flux Model 54 4.21. Energy flux of the barotropic tide 55 4.3 Internal Tide 60 4.3.1 Theory of normal modes 64 4.3.2 Normal mode fitting 67 4.3.3 Energy flux of internal modes 79 4.4 Friction 84 4.4.1 Derivation of dissipation expression 84 4.5 Tidal Jet 88 4.6 The Energy Partition 92 5 Vertical Diffusion 93 5.1 Introduction 93 V 5.2 Vertical Diffusion 94 5.3 Mixing Efficiency in the Basin 101 6 Low Frequency Circulation 108 6.1 Filtering and spectral analysis 108 6.2 Wind 110 6.3 Runoff 127 6.4 Mean Circulation 131 6.5 Empirical orthogonal function analysis 136 6.6 Deep-Water Renewal 146 7 Conclusions 152 A Hourly Data Plots 157 vi List of Tables 2.1 Instrument uncertainties 16 2.2 The tidal constituents used for the harmonic analysis 31 4.1 M2 and K1 barotropic tidal parameters from the harmonic analysis of Egmont and Porpoise Bay, and barotropic energy fluxes . 59 4.2 Modal fits to the velocity and perturbation density profiles of the M2 tide for January 74 4.3 Modal fits to the velocity and perturbation density profiles of the K1 tide for January 74 4.4 Modal fits (amplitude and phase) for the M2 tide 80 4.5 Modal fits (amplitude and phase) for the K1 tide 81 4.6 Net up-inlet baroclinic tidal energy flux at station 3 (MW) for (a) M2 and (b) K1 constituents in January, February, April and May 83 5.1 Summary of diffusion calculations for K,, = 96 5.2 Modal energy fluxes for the first four modes of the M2 and K1 constituents. 103 6.1 Mean monthly discharge from the Clowhom River dam for January to May 1991 130 6.2 Mean velocities and net volume fluxes at the Basin mooring 135 6.3 The first four EOF eigenfunctions for the Basin mooring in January. 140 6.4 The first four EOF eigenfunctions for the Basin mooring in February. 141 6.5 The first four EOF eigenfunctions for the Basin mooring in April 142 vii 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” List of Figures 1.1 Southern British Columbia and Vancouver Island 2 1.2 The Sechelt Inlet system 3 1.3 Lazier’s proposed circulation for inlets with shallow sills 10 1.4 Temperature, salinity and oxygen for Sechelt (100 and 200 m) and Narrows Inlet (75 m) 11 2.1 Moorings deployed during the Sechelt Inlet experiment 15 2.2 Along-channel Basin currents at selected depths for January 23 2.3 Along-channel Salmon currents in the surface layer for January 24 2.4 Power spectra of the along-channel Basin currents for January 25 2.5 Power spectra of the along-channel Salmon currents for January 26 2.6 Basin densities () at selected depths for January 28 2.7 Salmon densities (as) in the surface layer for January 29 2.8 Sea-level spectra from the pressure records of the Basin cyclesonde . 32 2.9 Wind record from Salmon Inlet for January 34 2.10 Estimated monthly runoff from: (a) all sources (Trites, 1955), and (b) the Clowhom River dam (from daily discharge rates from 1985 to 1990). 35 2.11 Oxygen values (ml 1_i) from the moored Endeco oxygen meters 37 2.12 Power spectra of Egmont oxygen time-series 38 3.1 Choking of flow through a constriction 40 3.2 Relation between amplitude reduction and phase shift of the surface tide across a sill 41 ix 3.3 Choking coefficient, cos , versus topography-tide factor, 44 3.4 Skookumchuck Narrows 47 3.5 Tidal amplitudes at Boom Islet (solid line) and Rapid Islet (dotted line), from January 31 to February 10, 1984 48 3.6 Tidal currents versus hydraulic head across Skookumchuck Narrows. 50 3.7 Velocity measurements in Skookurnchuck Narrows for July 9 and 10, 1983 52 4.1 Model for the generalized phase analysis 56 4.2 Analysis of the modified barotropic tidal flux model 60 4.3 Profiles of Basin along-channel velocity and perturbation density from the M2 constituent for January 62 4.4 Profiles of Basin along-channel velocity and perturbation density from the Is constituent for January 63 4.5 TS diagrams for January, February, April and May 68 4.6 Log Brunt-Vãisãlä frequency profiles for January, February, April and May 69 4.7 Vertical velocity modes (w(z)) for January 70 4.8 Horizontal velocity modes (u(z)) for January 71 4.9 Perturbation density modes (p(z)) for January 72 4.10 In-phase (a.) and in-quadrature (b) velocity profiles of the M2 tide for January 76 4.11 In-phase (a.) and in-quadrature (b) perturbation density profiles of the M2 tide for January 77 4.12 Net up-inlet baroclinic tidal energy flux (MW) for (a) M2 and (b) K1 constituents in January, February, April and May 85 4.13 Schematic of a single channel inlet showing the coordinate system used in the derivation of frictional power loss 86 x 4.14 Frictional dissipation rate computed using the one dimensional sill model versus estimated power loss from the modified barotropic tidal flux model 89 4.15 Along channel velocity profile of the tidal jet during flood tide 90 4.16 Kinetic energy flux of the turbulent jet entering Sechelt Inlet versus total barotropic tidal flux 91 5.1 Eddy diffusion coefficients for December1990 to January 1991 (125-215 m).