I CAUSES OP the CURRENT in LITTLE CURRENT CHANNEL OP
i
CAUSES OP THE CURRENT IN LITTLE CURRENT CHANNEL OP LAKE HURON
by
WARREN DAVID FORRESTER
B.A. The University of Toronto, 191+7
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF
THE REQUIREMENT S POR THE DEGREE OF
MASTER OF SCIENCE
in the Department of Physics
We accept this thesis as conforming to the required standard
THE UNIVERSITY OF BRITISH COLOMBIA
April," 1961 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my
Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
(W.D. Forrester)
Department of Physics The University of British Columbia, Vancouver 3, Canada.
Date April, 1961. ABb2ftACT
A current is observed to flow most of the time through
Little Current Channel, between North Channel of Lake Huron and
Georgian Bay. The current varies considerably in its speed, and frequently reverses its direction. Inconvenience is experienc• ed by ships wishing to pass through the narrow and shallow chann el at Little Current, as they must await an opportunity to do so at slack water or on an opposing current.
A field survey was carried out during the summer of 1959 in the vicinity of Little Current, Ontario, to determine the cau ses of this current and to ascertain whether or not predictions for the state of the current might be made sufficiently in ad• vance to be of assistance to shipping in the area. The field survey is described herein, and the analysis of the data is dis• cussed in detail.
The current in Little Current Channel is shown to be ess• entially a hydraulic flow, driven by differences in water level at the two ends of the channel. The differences in water level are attributed to the action of wind, atmospheric pressure, seiches, and lunar tides, in North Channel and Georgian Bay.
The actions in North Channel are considered to be greater than those in Georgian Bay, and are most fully treated.
It is concluded that the only contribution to the current at Little Current that could be predicted more than a day in ad• vance is that due to the lunar tide, and that to predict this would be of little value, since on many occasions the other in• fluences would distort and even conceal completely the tidal contribution. It i3 recommended, however, that a discussion of the causes of the current be incorporated into the Canadian
Hydrographic Service's publication, Great Lakes Pilot, as a matter of local interest, and as an aid to mariners wishing to make their own short-term forecast of the current. iv
TABLE OP CONTENTS
Page
ABSTRACT ii
LIST OF TABLES . iv
LIST OP ILLUSTRATIONS v
ACKNOWLEDGEMENTS vi
INTRODUCTION 1
METHOD 3
INSTRUMENTATION 8
RESULTS 13
DISCUSSION
General: 17
Effect of Tidesj Seiches, Wind and
Atmospheric Pressure: 21
(1) Tides: 21
(2) Seiches: 26
(3) Wind and Atmospheric Pressure:.. 32
CONCLUSIONS 38
LITERATURE CITED 1+1
LIST OP TABLES
Page
Table I: Preliminary Estimates of g and H of M2 23
Table II: Estimates of g and H of Tidal Constituents from Harmonic Analyses 2£ LIST OP ILLUSTRATIONS
Page
Pig. 1: Amplitude and Phase-lag of M£ at Gauging stations.. 1+2
Pig. 2: Observation stations on and around North Channel and northern Lake Huron 1+3
Pig. 3: Observation stations on and near Little Current
Channel 1+1+
Pig. k: Water Level Gauge, 1/12 Scale 1+5
Pig. 5: Gurley Current Meter, 1/1+ Scale 1+5
Pig. 6: Pendulum-type Current Direction Detector 1+6
Pig. 7: Wiring Diagram for Current Speed and Direction Recorder 1+6 Pig. 8: Currents in Little Current Channel (f t./sec.)...... 1+7 (a) for Current at Bridge flowing East at 2.0 ft./sec. (b) for Current at Bridge flowing West at 2.0 ft./sec.
Pig. 9: Water Temperature Lowering at Little Current,
associated with West-flowing Current 1+8
Pig. 10: Short-period Seiche action at Gore Bay 1+8
Pig. 11: Comparison of Current Speed with Water Level Difference along Little Current Channel 1+9 Pig. 12: Water Level Difference versus Square of Current Speed in Little Current Channel.. $0 Pig. 13: Priliminary Estimate of Lunar Tidal Effect in
North Channel 51
Pig. li+: Autocovariance Function 52
Fig. 15: Power Spectrum 52
Fig. 16: Smoothed Plots of Water Level, showing 5-hour Seich(from e hourlActioy n readingin Norts h ofChannel continuou. s records).. 53
Fig. 17: Plots of 5-h.our Running Means, showing 10-hour Seiche in North Channel 51+ Pig. 18: Plots of 10-hour Running Means, showing Wind and Pressure Effect in North Channel 51+ Pig. 19: Water Level Difference versus Square of Wind Speed in North Channel; 10-hour Means 55 vi
ACKNOWLEDGEMENT S
The author wishes to acknowledge the valuable advice and guidance received during this study from Drs. G.L. Pickard and
R.W. Burling of the Institute of Oceanography of the University of British Columbia; the aid of the Canadian Hydrographic Ser• vice of the Department of Mines and Technical Surveys in provid• ing personnel and facilities to help carry out the field work and certain of the calculations; the assistance of the Research
Branch of the Ontario Department of Lands and Forests in under• taking parts of the field operation; the cooperation of the Met• eorological Branch of the Canadian Department of Transport and the Weather Bureau of the United States Department of Commerce in providing meteorological data; and the assistance of the Com• puting Centre of the University of British Columbia in carrying out some of the lengthy digital computations. 1
INTRODUCTION
The masters of ships on the Great Lakes have reported be• ing inconvenienced by an apparently unpredictable current in the narrow channel at Little Current, Ontario, connecting Georgian
Bay with the North Channel of Lake Huron. A general chart of
Georgian Bay, Lake Huron, and North Channel is given in Fig. 1; a more detailed chart of North Channel is given in Fig. 2; and a further enlargement of the narrow channel at Little Current is given in Fig. 3, Although this narrow channel bears no name on charts of the Canadian Hydrographic Service, it is locally known as Little Current Channel, and will be so referred to herein.
Through Little Current Channel a current flows, sometimes from west to east and sometimes from east to west, sometimes in the direction of the local wind and sometimes in the opposite dir• ection. Ships passing through the narrow and shallow passage be• tween the north side of the Little Current swing bridge and the south shore of Goat Island must proceed slowly, but they must also maintain a speed of four or five knots through the water in order to retain steerage control. To attempt this passage with a following current greater than about one knot would apparently dangerously reduce control over the ship, since if sufficient speed for steerage were maintained, the speed relative to the bottom, the shore, and the bridge would allow insufficient man• oeuvring time. Consequently, it is customary for ships to an• chor outside Little Current Channel until they may make the pass• age in slack water, or, preferably in an opposing current. It had not been possible to foretell how long a ship might have to wait for a favourable current since on some occasions the water 2 flows fairly steadily in one direction for a full day or more, while on others it reverses direction again after less than an hour.
In 1959, the Canadian Hydrographic Service, the federal agency responsible for chart, water level, tidal, and current information in Canadian navigable waters, decided that an in• vestigation of this problem at Little Current should be under• taken. The object of the investigation was to obtain an under• standing of the origin of the flow, and, if possible, to develop a procedure by which it might be predicted. The author was priv ileged to carry out the necessary field work and the analysis of the results. METHOD
The factors that might contribute in varying degree to the phenomenon of the reversing flow at Little Current were consider• ed to be the following:
(a) Wind stress on the water surface in Little Current Channel
producing a direct wind current.
(b) Wind stress on the water surface of North Channel, Georg•
ian Bay, and Lake Huron, causing a tilt on the surface of
one or all of these basins and so producing a hydraulic
head at Little Current.
(c) Atmospheric pressure differences, tilting one or all of
the surfaces of the three basins referred to in (b), and
similarly producing a hydraulic head at Little Current.
(d) Seiches, initiated by wind or atmospheric pressure changes
but continuing to oscillate at the natural periods of the
different water basins until finally damped out.
(e) Tides in Lake Huron and Georgian Bay, the presence of
which had already been detected although the amplitude
is very small.
(f) Fluctuation in the discharge of the Saint Marys River,
causing a corresponding fluctuation in the water level
of North Channel.
It was impossible in the two months available for the field op•
eration to install and operate sufficient meteorological and
hydrological monitoring equipment to permit an exhaustive study
of all the factors mentioned above. It was decided, therefore,
to rely on existing data gathering facilities around Georgian
Bay and the main body of Lake Huron, and to concentrate add- itional facilities around Little Current and North Channel. The
Canadian Hydrographic Service operates permanent water level gauges at G-oderich, Collingwood, and Thessalon, and the United
States Lake Survey operates similar gauges at Detour, Harbor
Beach, and Lakeport. Hourly water levels from each of these lo• cations are readily available from the respective operating ag• encies. The United States Weather Bureau operates a meteorolog• ical station at Sault Ste Marie , and the Meteorological Branch of the Department of Transport operates stations at Gore Bay and
Wiarton. Hourly readings of wind velocity and atmospheric press• ure are available from each of these stations. In addition, the
Fisheries Research Station of the Ontario Department of Lands and
Forests at South Baymouth records hourly wind velocities, but not atmospheric pressures. The locations mentioned above are all marked on Fig. 1. Values for the discharge from the Saint Marys
River can be obtained from the Water Resources Branch of the Dep• artment of Northern Affairs and National Resources only on the basis of monthly means, and it was not possible to supplement this information during the operation.
In the course of the survey, a temporary water level gauge was installed outside the westerly end of Little Current Channel, another temporary gauge was installed outside the easterly end of the channel, and a permanent gauge was installed on the channel itself. These three gauging sites will be referred to as Little
Current W., Little Current E., and Little Current respectively, and are marked on Fig. 3« A temporary water level gauge was also installed at Gore Bay for the latter part of the survey. The three gauges at and near Little Current were referred to a common level by means of spirit levelling between the stations. Agree• ment between the forward, levelling and the back levelling indic• ated that the gauge zeros were within 0.01 feet of the same lev• el surface, permitting the slope of the water in Little Current
Channel to be measured to this same accuracy. A water level transfer was computed between Thessalon and Little Current W. on the basis of lj? days' hourly water level readings to obtain a common reference level for these two gauges, and so to permit an assessment of the slope of the water surface in North Channel.
Such a water level transfer, of course, assumes that the mean water level was the same at the two places for the period of the transfer, and it is difficult to say in this case how nearly the assumption held true.
A station to record the current speed and direction in
Little Current Channel was set up on the southeasterly corner of the cribbing under the swing bridge at Little Current. This stat ion will be referred to as station Bridge in the remainder of the discussion. An automatic water temperature recorder was install• ed near the south shore of the channel and about 1000 feet west of the swing bridge to detect any correlation that might exist bet\*een the water temperature and the current in Little Current
Channel. Since it was not possible to obtain meteorological instruments in time to use them in this survey, the only met• eorological information that could be obtained in addition to that from the permanent weather stations was the visual record of the wind kept during the operation at Little Current.
Measurements of the current at several depths at station
Bridge indicated that the velocity is effectively constant over 6 the whole 20-foot depth except within a foot or two of the bott• om. For this reason, continuous records of the current velocity were taken only at the one depth of two feet below the surface.
The strongest current, and the current of most interest to shipp• ing in Little Current Channel, is that flowing under the swing bridge, and this was satisfactorily monitored by station Bridge.
To obtain a rough picture of the pattern of the current in the rest of Little Current Channel, velocity measurements were made at 16 locations in the channel while the current was toward the east, and at II4. locations in the channel while the current was toward the west. Measurements were made at depths of £ feet and
20 feet, but the velocity was about the same at both depths ex• cept when the deeper measurement was taken within a foot or two of the bottom. This operation was accomplished with the assist• ance of a small boat and several of the personnel from the Canad• ian Hydrographic Service launch CGL "Boulton". The stations occ• upied are shown in Fig. 8.
A 30-hour program of synoptic current measurements was carried out in an attempt to relate water movements in the pass• ages between Lake Huron and North Channel, and between Lake Hur• on and Georgian Bay, to the current through Little Current Chann• el. Both the Canadian Hydrographic Service launch CGL "Boulton" and the Ontario' Department of Lands and Forests ship RV "Porte
Dauphine" assisted in this program. "Porte Dauphine" placed two of her crew ashore at Mississagi Strait to observe the current direction as indicated by the drift of a tethered buoy, and then took up a position herself in False Detour Channel to measure the current velocity there. At the same time, current measure- 7 raent3 were made in Owen Channel by "Boulton" and at station
Bridge by observers working there. Measurements were made at each location every half hour for 30 hours except in Mississagi
Strait, where the tethered buoy broke loose after eight hours of observation. The observation positions in False Detour Chann• el, Mississagi Strait, and Owen Channel are marked on Fig. 2 by the letters D, M, and 0 respectively. 8
INSTRUMENTATION
The temporary water level gauges installed were standard
Ott portable gauges. In these, a flexible wire passes from a float, over a pulley, and back down to a counterweight (Fig. 1|).
The float contains lead shot, the amount of which must be adjust• ed to make the counterweight just balance the weight of the float when it is half immersed In the water. As the float rises or falls, the pulley is turned, and it in turn drives a chain through a series of gears, the ratio of which determines the scale of the record. Attached to the end of the chain is a pen carriage, which is thus moved up and down to make a trace of the water level on the chart paper. The chart paper is attached to a vertical rot• ating drum, which Is driven by an 8-day spring motor at a speed of one revolution per day. If the water level being recorded ex• hibits appreciable lunar tidal fluctuation, a full week of record without overlap may be obtained on one piece of chart paper and without adjustment of the pen height. Since only a small tide is present in the Great Lakes, it was necessary to raise the pen height by a tenth of a foot on the paper each day to avoid over• lap on the record; as the ratio of vertical pen travel to change in water level was 1:10, this corresponded to changing the datum to which the gauge was set by one foot each day. The paper then needed to be replaced only once each week. The temporary gauges were mounted inside small wooden weather-proof shelter houses set on top of stilling wells, the bottom of which extended below the level of lowest water. The purpose of a stilling well is to damp out rapid changes in water level, such as those due to waves or the wash from passing ships, which might otherwise clutter up the 9 record and even cause the float wire to slip on the pulley.
Wooden stilling wells were employed at Little Current E. and
Little Current W., and a galvanized metal stilling well was used
at Gore Bay. All three had an interior cross-section of about
100 square inches, to which the water had access only through a quarter-inch hole near the bottom. This limited water access provided the required damping of sudden water level changes.
Considerable difficulty was encountered as a result of the wooden
stilling wells becoming plugged by the growth of algae in the in•
let holes. This trouble did not occur in the galvanized metal well, and occurred in the wooden wells only after the water had warmed up from about I4.O degrees Fahrenheit in the middle of May
to about 60 degrees Fahrenheit in the middle of June. The prob•
lem was finally solved by the addition of a small amount of copp•
er sulphate into the bottom of the wells to discourage the growth
of the algae. The permanent gauge installed at Little Current is
one of the standard Canadian Hydrographic Service water level re•
cording gauges, which are similar in operation to the portable
gauges described above, but employ a strip chart instead of a
cylindrical chart. This installation remains at Little Current
as a permanent facility of the Canadian Hydrographic Service.
A wooden staff gauge, marked In tenths of feet, was fast•
ened to the jetty alongside each automatic gauge to provide a
check on the setting of the pens and to show up any clogging of
the inlets. Three brass benchmark plugs were set into bedrock or
concrete foundations at each location, and the zeros of the
gauges were referenced to them. Differential levelling was carr•
ied out at Little Current between all three gauges and their ref- 10 erence benchmarks, using a Zeiss "self-levelling" instrument.
In setting up such a level, it is necessary only to centre a rough circular bubble on the base of the instrument before ob• serving on the level rod; the interior optical arrangement com• pensates for any small lack of horizontality of the telescope.
The use of the "self-leveller" was found very convenient, since it increases the speed of levelling and reduces the sources of error for inexperienced observers.
Current speed at station Bridge was recorded by a Price pattern Gurley current meter through one pen of a recording chronograph, while the direction was recorded by a pendulum- type detector through the other pen of the chronograph. The
Gurley current meter (Pig. 5) "was chosen for its compact and re• liable design plus its ability to measure speeds up to five knots or more. It is provided with an array of six conical cups moun• ted on a vertical shaft, and as the cups and shaft rotate, an electrical contact is made either once for every revolution or once for every five revolutions, as desired. The circuit for one contact per. revolution is completed through a brush and a raised portion on the main impellor shaft. The circuit for one contact per five revolutions is completed through another brush and one of two raised portions on a secondary shaft, geared to rotate once for every ten revolutions of the main shaft. Since the chronograph could legibly record only as many as two pulses per minute, and since the Gurley impellor would turn at 22£ rpm in a
5-knot current, It was necessary to file off one of the raised portions on the secondary shaft and to place a 12:1 ratio step- down relay in the circuit between the current meter and the chron- 11 ograph. With this modification, one pulse was received by the speed-recording pen of the chronograph for every 120 revolutions of the current meter impellor, and a legible record could be ob• tained up to current speeds of five knots. The main source of difficulty in this arrangement was the electrical contact in the
G-urley meter, which burned down in as little as 12 hours, and never endured longer than 1+8 hours. This weakness resulted from the necessity to use 6 volts in series with the meter contact to operate the step-down relay, whereas the recommended voltage ac• ross the contact is 1.5 volts.
The pendulum-type direction detector, shown in Pig. 6, served admirably for the current at station Bridge, which flows either in one direction or the other. It consisted simply of a pole pivoted about a point above the water, with the lower end of the pole in the water and the upper end free to swing back and forth about two inches. A west-flowing current held the upp• er end of the pole against a microswitch, which closed a circuit in the chronograph and held the direction pen in its deflected position as long as the current flowed in this direction. A slack or east-flowing current released the microswitch and per• mitted the direction pen to return to its undeflected position.
The speed record served to distinguish between a slack and an east-flowing current. The chronograph used to record the speed and direction was a Priez Recorder, equipped with two separately actuated pen circuits, a 2i4.-b.our spring drive to turn the record• ing drum at two inches per hour, and paper charts that required to be changed every 21+ hours. Pig. 7 shows the wiring diagram for the current meter, relay, direction switch, and chronograph. 12
The recording thermometer installed at Little Current was
of the liquid-in-metal type. The sensing bulb was submerged on
a stand that held it about a foot above the bottom of the water,
and the capillary tube, l£0 feet in length, was passed through a protective neoprene hose on its way to the recorder. A Foxbor-
ough recorder was used, in which changes in the pressure of the
liquid in the sensing bulb were transmitted through a Bourdon
tube and a pen to a circular chart, calibrated to show temperat• ure in degrees Fahrenheit. The accuracy of the temperature rec•
ord was maintained to within a tenth of a degree by comparison
each day with the water temperature read from a standard mercury-
in-glass thermometer. 13
RESULTS
The data obtained and used in this study is too voluminous to be reproduced here, but the types of data and the intervals over which It was gathered are listed below, with reference to
samples of the data contained in certain of the figures. All dates referred to are in 195>9.
(a) Water levels at Little Current W. and Little Current E.
were continuously recorded from May 16 to June 9, and from
June 23 to July 3. In "the period from June 9 to June 23*
the records were frequently interrupted by clogging of the
inlet holes. Pigs. 11 and 16 show sample plots drawn from
half-hourly readings of these records. Pig. 17 shows a
plot of 5>-hourly running mean water levels at Little Curr-
ent WY as computed from hourly readings of the continuous
record.
(b) Water levels at Gore Bay were recorded continuously from
June 6 to July 3. Pig. 10 gives a reproduction of a small
part of the actual record, and Pig. 16 shows a sample plot
drawn from half-hourly readings of the record.
(c) Water levels at Little Current were continuously recorded
from June 9 until the end of the survey, and have been
continued thereafter by the Canadian Hydrographic Service.
(d) Hourly readings of the water levels at Lakeport, Harbor
Beach, Detour, Thessalon, Colllngwood, and Goderich were
obtained for the period of the survey from the agencies
operating the gauges at these locations. Sample plots
drawn from these readings for Thessalon and Detour are
shown in Pig. 16. (e) Current direction at station Bridge was recorded continu•
ously from May 15 to July 3. Current speed was measured
every half hour from 12:00 on May 18.to 18:00 on May 19,
and continuously, although with frequent interruptions,
from June 8 to July 2. Pigs. 9 and 11 show sample plots
drawn from half-hourly readings of this record.
(f) Current speed and direction were measured at one location
in False Detour Channel every half hour from 12:00 on May
18 to 18:00 on May 19, at depths of 10, 20, 30, ij.0, 50, 75*
and 100 feet. Current direction at the surface was ob•
served in Mississagi Strait every half hour from 12:00 to
20:00 on May 18, but the wind rendered these observations
meaningless.
(g) Current speed and direction were measured at one location
in Owen Channel every half hour from 12:00 on May 18 to
18:00 on May 19, at depths of 5, 35, and 55 feet.
(h) Water temperature in Little Current Channel was continu•
ously recorded from June 3 to July i+. Fig. 9 shows a
sample plot drawn from half-hourly readings of this re•
cord.
(i) Wind speed and direction were visually estimated and re•
corded three times each day at Little Current from May 15
to July 3. Hourly readings of wind speed and direction
arid of atmospheric pressure at Sault Ste Marie, Gore Bay,
and Wiarton, and hourly readings of wind speed and dir•
ection at South Baymouth were obtained for the period of
the survey from the agencies operating these weather
stations. 15
(j) Current speed and direction at 16 locations in Little
Current Channel were measured on June 12, with the current
at station Bridge flowing to the east, and were measured
again at llj. locations in the channel on June 16 and June
17, with the current at station Bridge flowing to the
west. Since about two hours was required to complete
measurements at all 11+ or 16 stations, conditions in the
channel did not remain constant; but, as a continuous re•
cord of the current at station Bridge was available, it
was possible to reduce the observations to a more synoptic
basis by multiplying each speed by a factor inversely pro•
portional to the current speed at station Bridge for the
same time. Currents were measured at depths of 5 and 20
feet, but the only significant differences observed be•
tween the two depths occurred when the lower measurement
was very near the bottom. The results of these synoptic
surveys are plotted as current vectors on two charts of
Little Current Channel in Pig. 8, (a) and (b). The aver•
age speed from the two depths has been shown except when
the lower depth was near the bottom, and then only the
measurement at 5 feet has been shown.
Extreme values for some of the data obtained at Little
Current are given here to present some picture of the character of the fluctuations that the current and water levels are sub• ject to, but it must be remembered that these are extreme values from only about a month of records. The current in Little Curr• ent Channel was observed to flow toward the east for as long a time as 31+ hours, and for as short a time as 0.5 hours. It was 16 observed to flow toward the west for as long a time as 22 hours, and for as short a time as one hour. The highest current speeds recorded were 5.4 feet per second toward the east, and 3.6 feet per second toward the west. The water level at Little Current ¥. was observed to be as much as 0.56 feet above that at Little Curr• ent E., and as much as 0.52 feet below it. 17
DISCUSSION
General:
An examination of the data from the simultaneous current surveys in False Detour Channel, Mississagi Strait, Owen Channel and Little Current Channel yielded no conclusive results. At
False Detour Channel and Owen Channel, current speeds up to one foot per second were measured, but the direction varied greatly with depth. No correlation could be found between the water movements in the various channels sampled. Possibly a more com• plete cross-sectional coverage of the channels would have shown up some correlation, but equipment and personnel for such an extensive undertaking were not available.
An interesting feature appeared in the June water temper• atures at Little Current on plotting them alongside the currents at station Bridge. The temperature was observed to drop by as much as two Fahrenheit degrees after the current direction had reversed from east to west, and then to rise again after the
current had returned to the east. The temperature changes lagge the current changes by one to three hours, depending on the
strength of the current. The temperature lowering was credited to the influence of colder water from Georgian Bay, which would be brought into and through Little Current Channel by a west
current. Warmer water from North Channel would eventually dis• place this colder water as the current turned to flow again to the east. The sample current and temperature records reproduced
in Fig. 9 illustrate the temperature lowering associated with a west-flowing current. It should be cautioned that since this re lation between current and temperature results from the temper- 18 ature difference between the water of Georgian Bay and that of
North Channel, it may manifest Itself differently at different seasons. It is quite probable that by late autumn the water in
North Channel would be colder than that in Georgian Bay, and if so, a temperature rise would then be associated with a west-flow• ing current.
An excellent example of short-period seiche action was provided In the water level records obtained at Gore Bay, a sam• ple of which is reproduced in Pig. 10. Gore Bay, on which the town of Gore Bay is situated, has an effective length, L, of ab• out 12,000 feet, and an average depth, h, of about 72 feet. If it is hypothesized that a resonant oscillation is set up in Gore
Bay in the form of a standing wave with a node at the entrance and an antinode at the head of the bay, then the period of the oscillation should approximately be given by Merian's formula
(Proudman, 1953. p. 232) as
T = ijX = 1,000 seconds = 17 minutes, •pgh in which g = the acceleration due to gravity = 32 feet per second per second. The period obtained for the seiche in Gore Bay by counting the number of oscillations in a 10-hour period was 11+ minutes, in good agreement with theoretical value. In Pig. 10, a rather rapid rise in water level may be seen to have occurred
between 05:30 and 06:30 on June 26. This disturbance appears to have set up seiche action in Gore Bay of larger amplitude than usual. By 09:30, the amplitude had decayed to about its average value of 0.05 feet. During the three weeks of record obtained at
Gore Bay, seiche action of this period was continuously present, 19 varying in amplitude from 0,01 feet to 0.2 feet.
It became apparent early in the investigation that there was almost complete correlation between the current flowing In
Little Current Channel and the difference in water level between
Little Current W. and Little Current E. In Pig. 11, plots of
four days' records of water levels at Little Current W. and Litt•
le Current E. are shown, along with plots of the water level
difference and the recorded current at station Bridge for the
same period (all plots are drawn from half-hourly readings). The
close correlation between the current and water level difference
evident in this figure is equally apparent in all the records ob•
tained. The current in Little Current Channel must mainly be
caused by the water level difference between the two ends of the
channel plus the effect of the wind stress acting directly on the water surface of the channel. If the influence of the water lev•
el difference is predominant, it may be shown from dynamic prin•
ciples that the square of the current is proportional to the wat•
er level difference. A. plot was made of the square of the curr•
ent speed versus the difference in water level between Little
Current ¥. and Little Current E. , and is reproduced in Pig. 12.
Points marked by square crosses represent observations made when
the water level difference was increasing at a rate greater than
0.05 feet per hour, points marked by open circles represent ob•
servations made when the water level difference was decreasing
at a rate greater than 0.05 feet per hour, and points marked by
closed circles represent observations made when the water level
difference was increasing or decreasing at a rate less than 0.05
feet per hour. The line drawn through the points was located by 20 visual inspection. The apparent change in the slope of the line near the origin is believed to have been caused by a slight shel• tering effect of the bridge cribbing at the location of the curr• ent meter while the current flowed toward the west (Pig. 3 shows location). The meter had been suspended from the end of a 10- foot boom to escape the effect of eddies that formed along the southerly side of the cribbing in a west-flowing current, but apparently some effect was still felt. The tendency for the square crosses to lie above the line and for the open circles to lie below the line in the plot indicates that a good deal of the scatter in the points is due to the presence of a time lag be• tween the water level difference and the current. Some scatter must also have been caused by the direct effect of the surface stress of the wind blowing along Little Current Channel in ass• istance or opposition to the current. The conclusion drawn from the above comparisons was that the current in Little Current
Channel is essentially a hydraulic flow, driven by the difference in water level at the two ends of the channel, and that to ex• plain this difference In water level would be to explain the current. It was an advantage in this study to be able to deal with the water levels rather than the current, because about 750 hours of water level records had been obtained as opposed to only about lj.00 hours of current record, and, although the water level records had suffered one lengthy interruption in the middle, the current record had been briefly interrupted almost every day.
Further, the water level record from Little Current ¥. could be expected to indicate effects arising in North Channel or Lake
Huron, and the Little Current E. record to indicate effects aris- 21
Ing in Georgian Bay, while the current record by itself could be expected to indicate only the combined result.
Effect of Tides, Seiches, Wind and Atmospheric Pressure;
The major influences contributing to the water level diff• erence at the two ends of Little Current Channel, and hence to the current through the channel, were found to be lunar tide, seiches, wind, and atmospheric pressure. Each of these is dis• cussed in detail below.
(1) Tides:
The following discussion of the effect of tides in the
Great Lakes has been given (Ontario, Legislative Assembly, 1953):
"Tides are the most important factor affecting the levels of seas and oceans, but on the Great Lakes, due to their relat• ively small range, they are not significant. However, of all the factors creating fluctuations , those caused by lunar influences are the only ones which are constant even if they are small. "Because the range of tides in the Great Lakes are small they are easily hidden by short period surface disturbances of wind and barometric pressures. Pour years of continuous records by the Canadian Hydrographic Service at each of the stations men• tioned in Table No. 11 were necessary to establish the following average tidal ranges.
Table No. 11
Lake Gauging Station Spring Tide Neap Tide Superior Port Arthur o.oa ft. 0.03 ft. Michipicoten 0.12 ft. 0.06 ft.
Huron Thessalon 0.16 ft. 0.08 ft. Collingwood 0.13 ft. 0.06 ft. Goderich 0.09 ft. 0.01+ ft. Erie Port Stanley 0.06 ft. 0.05 ft. Port Colborne 0.11 ft. ft. 0.05 Ontario Port Dalhousie 0.06 ft. 0.03 ft. Toronto 0.05 ft. 0.03 ft. Kingston 0.05 ft. 0.05 ft. "The spring tides occur during the period of new and full moon, the neap tides on the waxing and waning quarters of the moon. Prom the table it will be observed that the range of spring tides is approximately twice that of the neap tides and 22 that the tidal effect on the larger and deeper lakes of Super• ior and Huron is almost twice that of Lakes Erie and Ontario."
Young (1929) reported on observations he made of the water levels at Little Current, but, as were many of the early tidal studies on the Great Lakes, his investigation was too superfic• ial to reveal much of the true picture. Hutchinson (1957) writes in his discussion of tides in the Great Lakes (p. 333) the foll• owing comments on Young's work.
"Young (1929) reported larger tides in the north channel of Lake.Huron; although the mean interval in the strongly marked oscillation that he observed was 12.14. hours, the luni-tidal in• terval recorded was somewhat irregular. The range, up to about 10 cm., seems very large. The oscillation may be a seiche, poss• ibly forced by the tide. Young rejected the idea of a seiche, as the period seemed too long."
Whether or not tides contribute to the current in Little
Current Channel depends upon the difference in water level that they may produce between the two ends of the channel, and this
in turn depends upon the difference in phase lags of the tides at the two ends, as well as upon their amplitudes*. If tides of the magnitude quoted in the above table for Lake Huron were to be 180 degrees out of phase at the two ends of the channel, they would produce a maximum water level difference of the order of a tenth of a foot, which, by Pig. 12, would give rise to a current of about 2.5 feet per second, or 1.5 knots.
A preliminary estimate of the phase lag, g, and amplitude,
H, of the principal semidiurnal lunar tidal constituent, M2, at
Little Current E., Little Current W., Gore Bay, Thessalon, and
Detour was made by averaging out all fluctuations other than those with a period of 12.5 hours. A description of the aver• aging procedure and plots of the results are given in Pig. 13.
* "Amplitude" is half of the "range". 23
It is apparent that the phase lag of M2 changes only slightly in the length of North Channel, with most of the change occurring
between Gore Bay and Little Current W. M2 at Little Current W. ,
however, lags behind M2 at Little Current E. by about four hours, which is sufficient to cause a water level difference of as much as 0.1 feet. The phase lag, g, of a tidal constituent is so de• fined that the observations can be related to any specified time meridian, and analysed as though they had been taken at Green• wich. Thus, g may be estimated from Pig. 13 by subtracting the
Greenwich Mean Time of upper meridian transit of the moon for
June 6 (12:01 G.M.T.) from the observed Eastern Standard Time of high water on June 6', and multiplying this difference by the
"speed" of the constituent, which is 29 degrees per mean solar
hour for M2, The amplitude, H, of M2 may be read directly from
Pig. 13 as the maximum height above or below the axis. Values of
g and H estimated in this manner for M2 are given below in Tab• le I.
Table I
Preliminary Estimates of g and H of M2
Gauging Station g of M2 H of M2
Detour 203 degrees 0.05 feet Thessalon 217 " 0.06 " Gore Bay 208 " 0.10 " Little Current M. 230 " 0.10 " Little Current E. 125 " 0.05 . "
The verification that tides do play an important role in causing the current in Little Current Channel pointed out the
need to examine tidal constituents other than just M2. Conse• quently, harmonic analyses were made of the water level records 24 for all the gauging sites on Lake Huron and Georgian Bay, using the method of analysis described by Doodson and Warburg (193&,
PP. ij.3-66). Analyses were made from hourly readings of 29 days of record at each station except Little Current W., Little Curr• ent E., and Gore Bay, where shortages of record permitted only
15 days to be employed. In addition, a second analysis was made for the permanent gauge at Little Current, to provide some indic• ation of which results were actually significant. The harmonic analysis produces values of g and H for the following nine con• stituents :
M2: the principal lunar semidiurnal constituent,
S2: the principal solar semidiurnal constituent,
N2: the larger lunar elliptic semidiurnal constituent,
K£i the luni-solar declinational semidiurnal constituent,
K-j_: the luni-solar declinational diurnal constituent,
0-j_: a lunar declinational diurnal constituent,
P]_: the solar declinational diurnal constituent,
M^_: a shallow-water quarter-diurnal constituent,
MS[^: a shallow-water quarter-diurnal constituent.
Table II gives the results of the harmonic analyses, and values
of g and H for M2 have been marked on the map in Pig. 1. There is seen to be good agreement between the preliminary estimates
for M2 given In Table I and the values obtained from the harmonic analyses.
In the case of the constituents with very small amplitudes it was difficult to decide whether or not the numbers had any signif• icance at all. Fortunately, for the purpose of this study, it was necessary to make such a decision only at Little Current W. Table II
Estimates of g and H of Tidal Constituents from Harmonic Analyses Station
M2 S2 N2 (Record used) K2 Kl 01 Pi 3^ Lakeport H ft. .031 .016 .008 .001+ .008 .010 .003 .002 .001 (June 1-29) g° 009 349 301 31+9 029 171+ 029 128 359 Goderich H ft. .022 .021+ .007 .006 .003 .001+ .001 .006 .005 (May 1-29) g° 31+6 015 358 015 188 171 188 062 353 Harbor Beach H ft. .016 .003 .007 .001 .011 .005 .007 .001 .001+ (June 1-29) g° 31+6 317 268 317 121+ 225 121+ 121 066
Detour H ft. .01+3 .013 .009 .001+ .016 .009 .005 .002 .002 (June 1-29) g° 201+ 237 21+1 237 081 121+ 081 003 208 Thessalon H ft. .073 .021+ .007 .006 .020 .035 .007 .001+ .011 (May 1-29) g° 211 232 171+ 232 086 131 086 208 280 Gore Bay H ft. .096 .009 .013 .002 .025 .027 .008 .002 .003 (June 7-21) g° 211+ 11+1+ 238 11+1+ 085 071 085 212 317 Little Current W. H ft. .087 .011+ .001+ .023 .021+ .008 .001 .006 (May 17-3D g° 226 233 233 098 330 098 185 170 Little Current H ft. .0k3 .015 .023 .001+ .020 .011 .007 .008 .001}. (July 1-29) g° 228 153 206 153 059 157 059 31+2 298 Little Current H ft. .052 .021 .018 .006 .022 .019 .007 .006 .011 (Aug. 1-29) g° 221 222 201 222 123 231+ 123 272 156
Little Current E. H ft. .01+5 .010 .018 .003 .019 .011+ .006 .010 .010 (May 17-3D g° 103 116 101 116 061+ 009 061+ 056 039 Collingwood H ft. .014.1 .013 .017 .001+ .011+ .020 .001+ .007 .001+ (June 1-29) g° 030 086 031 086 339 21+0 339 331+ 329 26 and Little Current E. The phase lag would not be expected to change appreciably between Little Current W. and Little Current, but, since Little Current is located on the slope of the channel, the amplitude might be expected to be somewhat less at Little
Current than at Little Current ¥. This reasoning seems to be roughly borne out in the the results of the analyses. It was de• cided to accept as legitimate tidal constituents at Little Current
¥. those constituents with an indicated amplitude greater than
0.01 feet, provided that the three phase lag values calculated for Little Current and Little Current ¥. covered a spread no greater than 70 degrees. This rather arbitrary criterion reject•
ed all constituents except M2, N2, and Kl. The same three con• stituents were also accepted as constituting the tide at Little
Current E. It must be admitted that S2 could also be a legit• imate contributor to the tides, since it fell just outside the limit of rejection.
On the basis of the three constituents retained, the tides at Little Current ¥. and Little Current E. were predicted at hourly intervals for the period of the survey, employing a tide- predicting machine of the Canadian Hydrographic Service. This made it possible to remove most of the tidal effect from the water level records and to study other influences more easily.
The tide predictions indicated that the tides alone could pro• duce a water level difference along Little Current Channel as great as 0.18 feet, which, by Pig. 12, corresponds to a current speed of about three feet per second at station Bridge.
(2) Seiches:
An example of a short-period seiche at Gore Bay has been 27 shown in Fig. 10, and discussed earlier. Such seiche action is often found in well-defined hays, but its effect is limited to
Only a small area outside the bay itself. The seiche actions that were of most interest at Little Current were the oscillat•
ions that could be set up in the larger water bodies of Lake Hu• ron, Georgian Bay, and North Channel. Approximate periods for
lengthwise uninodal seiches were computed for these three bodies
of water by Merian's formula for closed basins (Proudman, 1953*
P. 225),
T = 2L , 7gh" where T = the period in seconds,
L = the effective length of the body of water in feet,
g = the acceleration due to gravity = 32 ft./sec./sec.,
h = the average depth of the body of water in feet.
The periods thus indicated were 6.3 hours for Lake Huron, i+,3
hours for Georgian Bay, and la.,5 hours for North Channel. Multi-
nodal seiches should also be possible in these basins, their per•
iods being the appropriate fractions of the periods of the corr•
esponding uninodal seiches. If the bodies of water should osc•
illate in the manner of open-ended basins, with a node at the
entrance and an antinode at the closed end, then periods of twice
those of the closed-basin uninodal seiches would be encountered.
A seiche of this nature in North Channel would be expected to
have a period of about nine hours.
To estimate the importance of seiche action in North
Channel, a power spectrum analysis was made of thirty days of
water level record from Little Current ¥. The advantage of power
spectrum analysis over harmonic analysis in detecting seiches is 28 that the power spectrum method does not require that the oscill• ations be free from random phase shifts. Blackman and Tukey
(19^8) give a detailed discussion and development of the theory of power spectrum analysis, and MacMillan (1959) gives an out• line of the essentials needed to program such an analysis for digital computation. By analogy with electrical measurements, the term "power" has been used to refer to the square of the amp• litude of fluctuations per unit frequency band. The steps foll• owed in arriving at the power spectrum for Little Current W. were as follows:
(a) The total record of thirty days' water levels was read at
half-hourly intervals. Readings were averaged through a
"window" 0.75 hours wide to filter out frequencies greater
than one cycle per hour. This was necessary to prevent pow•
er which might be present at these higher frequencies from
masquerading as power in the lower frequency range being
dealt with.
(b) The predicted tidal height was subtracted from each of the
readings.
(c) The value of the autocovariance function for each of 37 time
lags, equally spaced from 0 to 18 hours, was computed on the
Alwac Ill-E digital computer at the University of British
Columbia, using a program prepared by Proese and Duffus
(1959). The plotted function is shown in Pig. 11]..
(d.) 37 equally-spaced point estimates on the two-sided power
spectrum between frequencies of zero and one cycle per hour
were calculated by numerical integration of the Fourier trans•
form of the autocovariance function. Application of the 29
statistical theory discussed by Blackman and Tukey to this
calculation indicated the standard deviation of each spect•
ral estimate to be 1^ per cent at the 80 per cent confidence
level.
(e) A smoothing formula was applied to the spectral estimates
obtained in step (d).
(f) Each of the smoothed spectral estimates was multiplied by a
frequency factor to correct for the effect at that frequency
of the averaging carried out in step (a). To convert the
two-sided spectrum to a one-sided spectrum, these values
were then multiplied by a factor of two, providing the fin•
al estimates from which the power spectrum, as shown in Pig.
15, was drawn.
The spectrum indicates that almost all the power at Little
Current W. is concentrated into three frequency bands. The band at zero frequency is, of necessity, high in power, since it must
contain contributions from all frequencies less than one cycle in thirty-six hours. Although they are not truly periodic, such variable influences on the water level as wind, atmospheric press• ure, precipitation, evaporation, and run-off may all contribute to the power near zero frequency. The band of power centred ab• out 0.1 cycles per hour (period of 10 hours) may consist of con• tributions from wind and atmospheric pressure effects, which can possess some semidiurnal periodicity; from the solar semidiurnal tidal constituent S^, which was omitted from the tidal predict• ions; and from portions of the other semidiurnal tidal constitu• ents, for which under-correction or over-correction may have been made. Most of the power in this band is, however, believed to be 30 caused by oscillation of North. Channel as a basin open at the west end to Lake Huron. The band of power centred about the frequency 0.2 cycles per hour (period of 5 hours) is believed to be entirely due to the uninodal oscillation of North Channel as a closed basin.
Seiche action with a 5-hour period is visually apparent in the water level records on five or six occasions during the month in which observations were made, each occurrence lasting from 30 to 70 hours before disappearing. In Pig. 16 are repro• duced smoothed plots drawn from hourly readings of the water lev•
els at Little Current ¥., Gore Bay, Thessalon, and Detour, for
one occasion on which the 5-hour seiche in North Channel was app•
arent. The seiche action at Thessalon and Detour is clearly 180 degrees out of phase with, that at Little Current W. , at the other
end of the channel. Since the water is shallower at the eastern
end, the node is probably slightly east of mid-way in the chann•
el. At Gore Bay, which must be quite near the node, the seiche
action is not readily apparent. This 5-hour seiche may be the
same one that Young (1929) has attributed to an oscillation In
Georgian Bay, but it is not possible to be sure, since Young
does not specify at which end of Little Current Channel he placed
his water level gauge.
In order to isolate the 10-hour seiche, 5-hour running means of the water level at Little Current W. were computed to
eliminate most of the clutter caused by the 5-hour seiche.
Plots of these running means are reproduced in Pig. 17, both for
the levels as recorded and for the levels as corrected for the predicted tide. An oscillation of 10-hour period stands out 31 clearly in the levels corrected for the tide, but appears in the uncorrected levels only as a distortion in the tidal frequency and amplitude. It is believed to have been the constructive in• terference of this seiche with the true tide that led Young to estimate the amplitude of the tide in North Channel at such a large value.
The area contained under the power spectrum curve in a particular frequency band gives an estimate of the mean square
amplitude of oscillations in that frequency range. Attributing
all power in the frequency band between 0,17 and 0.22 cycles per
hour to the $-hour seiche gives it a mean square amplitude of
0.0016 feet squared, or a root mean square amplitude of O.OI4.
feet, for the complete duration of the record. The 3>-hour
seiche was apparent to the eye during approximately half of the
record, with a maximum amplitude of about 0.2 feet and an aver•
age amplitude of about 0.1 feet. Thus, a visual estimate of the
average amplitude over the whole record gives 0.05 feet, in good
agreement with the estimate from the power spectrum.
Attributing all power in the frequency band of the power
spectrum between 0.07 and 0.13 cycles per hour to the 10-hour
seiche gives it a mean square amplitude of O.OO36 feet squared,
or a root mean square amplitude of 0.06 feet, for the complete
duration of the record. Allowing for a factor of 0,7, by which
the employment of 5-hour means decreases amplitudes at this fre•
quency, the average amplitude of the 10-hour seiche for the 13-
day interval shown in Pig, 17 was visually estimated as about 0,1
feet. Comparison of this value with the root mean square ampl•
itude of 0.06 feet indicated by the power spectrum suggests that 32 the 10-hour seiche was quite prominent in most of the record ob• tained. However, only the portion of the record shown in Pig. 17 was plotted on the basis of 5-hour running means with the tide removed to make the seiche visually apparent.
A power spectrum of the water levels at Little Current E. was not calculated because the water level fluctuations at this
station did not exhibit as great a range as those at Little Curr•
ent W#, and because time available for the study was limited.
Several slight indications of possible seiche action of about a
5-hour period appeared in the record at Little Current E., but no indication could be found in the Collingwood record of simil•
ar out-of-phase oscillations at the other end of Georgian Bay.
The fact that much greater seiche activity seems to occur in
North Channel than in Georgian Bay is probably because the axis
of North Channel runs east and west, and most winds and atmos•
pheric pressure disturbances, which may initiate seiches, move
along this axis or nearly parallel to it.
The limited record available does not permit an estimate
to be made of the maximum water level difference that might arise
at Little Current because of seiches alone, other than that it
could be at least as great as O.I4. feet. Even this conservative
estimate is twice the difference that could be produced by tides
alone, although the corresponding current would be only l.lj. times
as great.
(3) Wind and Atmospheric Pressure:
Wind and pressure effects are here discussed together be•
cause it was found difficult to separate their effects complete•
ly. Occasions on which significant atmospheric pressure variat- 33
ions occurred were also occasions on which the wind was strong.
Insufficient meteorological coverage around Georgian Bay and the main body of Lake Huron, as well as the restricted time avail•
able, forced the study of wind and pressure effects on the water
levels to be limited to North Channel. Hourly records of the wind were available for this vicinity from Sault Ste Marie, Gore
Bay, and South Baymouth. A comparison of the three stations' wind records, however, showed too much inconsistency to justify
averaging all three, and it was decided to use just the record
from Gore Bay, the only station actually located on North Chann•
el. As a measure of the atmospheric pressure difference along
the channel, there was no choice but to use the hourly records
available from Sault Ste Marie and Gore Bay. The water level
records from Little Current W. and Thessalon were employed to
assess the slope of the water surface in North Channel.
The computed harmonic tidal constants for Little Current
W. and Thessalon (Table II) were felt to be similar enough to
justify the expectation that tidal effects would almost cancel
out from the differences in water level between the two places.
This saved the trouble of calculating hourly tidal predictions
for Thessalon. To remove contributions from seiche action, 10-
hour running means were computed from hourly values of the water
level difference for the 13-day interval from May 16 to May 29.
Sverdrup, Johnson, and Fleming (191+2, pp. i4.89-l4.9i) and Hutchin• son (1957, pp. 270-286) discuss theoretical and empirical eval• uations that have been made of the effect of wind in producing a
tilt on the surface of a body of water. Keulegan (195D » foll•
owing the work of Ekman and others, shows that for a long narrow 3h channel the difference in water level between the two ends, pro• duced by a wind blowing along the axis of the channel, should approximately be proportional to the square of the wind speed.
Gillies (1959) obtained reasonably good confirmation of this re• lation in applying it to a study of wind effects on Lake Erie.
Since it seemed that North Channel should fit the conditions of
Keulegan's theory as well as Lake Erie, 10-hour running means of the east-west component of the square of the wind speed as re• corded at Gore Bay were prepared for the same 13-day period as for the water level difference along the channel. Plots of the mean water level difference and the mean component of the square of the wind speed are reproduced in Fig. 18, along with a plot of 10-hour running means of the difference in atmospheric press• ure between Sault Ste Marie and Gore Bay. It would be expected that an atmospheric pressure gradient along the channel would affect the water slope directly by what is often referred to as the "inverted barometer effect". In addition, an atmospheric pressure gradient would be expected to give rise to wind, which would also affect the slope of the water in the channel through the wind stress on the surface. This expected complicity between cause and effect is borne out by the strong correlation visually apparent between all three plots in Fig. 18.
An attempt was made to isolate the effect of wind stress on the slope of the water surface in North Channel by correcting the water level differences between Little Current ¥. and Thess• alon for the inverted barometer effect. To do this, it was nec• essary to assume that the pressure difference between Sault Ste
Marie and Gore Bay was the same as that between Thessalon and 35
Little Current W., and that the pressure changes occurred slow• ly enough to permit the slope of the water surface to adjust it• self to them on the basis of 0.1 feet of water being equivalent to 3 millibars of pressure. 10-hour mean water level differen• ces, corrected for pressure effect, were taken at intervals of five hours from May 16 to May 29 and plotted against the corr• esponding 10-hour means of the east-west component of the square of the wind speed at Gore Bay. Two least-squares regression lines were computed for these points, one for the wind from the west, and one for the wind from the east. The plot is repro• duced in Fig. 19, along with the regression lines. The linear relation between the two quantities is well supported by the high correlation coefficient of 0.80 obtained for the west wind points. The east wind points are too few in number to lend much significance to their low correlation coefficient of 0.23. Part of the scatter in the points may possibly be due to tidal influ• ence not completely removed by cancellation, to gradual changes
In Lake Huron level extending over longer than ten hours, or, possibly, to variations in the discharge from the Saint Marys
River at the head of North Channel (Fig. 1). Most of the scatter, however, must be due to the attempt to represent the wind stress over the whole of North Channel from measurements of the wind at only one shore station,, and to the fact that the wind changed too frequently for the water slope to be expected to have come to complete equilibrium with the wind stress. Nine points were rejected from the regression calculation, and are not shown in
Fig. 19. In each of the nine cases, the point lay on the steep slope of one of the humps in the wind profile shown in Fig. 18. 36
At these points it could not be expected that the slope of the water would have reached an equilibrium with the rapidly chang• ing wind velocity. Lack of data concerning fluctuations in the discharge of the Saint Marys River prevented any direct assess• ment of the effect this may have had on the scatter of points in
Pig. 19. However, it was reasoned that the effect could not be great, because if the Saint Marys River were making its presence felt at Little Current, then the mean water level at Little Curr• ent W. would be expected to be higher than that at Little Current
E. , and this did not appear to be so. The mean water level at
Little Current W. was actually found to be the same as that at
Little Current E. to within plus or minus 0.01 feet for the 30- day period covered by the survey.
Atmospheric pressure and wind appear to be the only two agencies to account for the fact that the current in Little Curr• ent Channel may flow for a day or more in the same direction, with only slight variations in speed. If either or both of these agencies imposes a fairly long-term level difference at Little
Current Channel, then the shorter-term tides and seiches will not produce as great variations in current speed as usual, since the current speed varies only as the square root of the differ• ence in water level. Although it is not much more than a guess, it may be supposed that the extreme atmospheric pressure differ• ence between the two ends of North Channel would not exceed 9 millibars, corresponding to a water level difference of 0.3 feet between the two ends, or a difference in water level of 0.15 feet between Little Current W. and Little Current E. It would also seem reasonable to assume that a wind speed of as high as 37
5>0 miles per hour could, on occasion, be maintained over North
Channel for long enough to permit the water slope to reach equ• ilibrium with the wind stress. Under such a condition, and if it is assumed that extrapolation may be carried to this point from Pig. 19, the corresponding water level difference between the two ends of North Channel would be 6 feet, or 3 feet between the two ends of Little Current Channel. The difference at Litt• le Current Channel might be even greater than 3 feet, because the same wind might also impose a slope on the water in Georgian
Bay. Extrapolation from Pig. 12 indicates that a 3-foot level difference would cause a current of about 12 feet per second, or
7 knots, in Little Current Channel. Several residents who had lived most of their lives in Little Current told of occasions on which they had observed extremely high current speeds in Little
Current Channel. Their estimates of the maximum speed varied between 7 and 13 knots, but none of the estimates were the re• sult of actual measurement. Since visual estimates of the speed of flowing water tend usually to be high, it is felt that 7 knots is a reasonable estimate for the maximum current speed that would be encountered in Little Current Channel. It was un• fortunate that higher wind speeds did not occur during the sur• vey. . 38
CONCLUSIONS
It is concluded from the study that the current in Little
Current Channel is caused mainly by the variable hydraulie head produced between the two ends of the channel by fluctuations in the slope of the water in North Channel and Georgian Bay. The fluctuations in North Channel seem to be much greater than those
In Georgian Bay, and were the only ones studied in detail.
Tides and seiches are responsible for the rhythmic reversal of
current observed in Little Current Channel on occasions when met•
eorological disturbances are slight. The main tidal contribut•
ion arises from the difference in phase lag of the principal lun•
ar semidiurnal tidal constituent in North Channel at the west
end of Little Current Channel and that in Georgian Bay at the
east end. Tides alone can produce a hydraulic head at Little
Current as great as 0.2 feet. North Channel was observed to
oscillate in the principal mode both as a closed basin and as an
open-ended basin, giving rise to seiche periods of both five and
ten hours. These two seiches appeared to be present most of the
time, each with an average amplitude of about 0.1 feet and a maximum amplitude of about 0.2 feet. Unlike the tides, seiches
are generally a result of meteorological disturbances which occ• ur irregularly, and cannot be predicted far in advance. Wind
stress along the axis of North Channel, and atmospheric pressure
difference between the two ends of the channel may be taken to
account for the currents that flow fairly steadily in the same
direction at Little Current for a day or more. It is likely
that wind and pressure disturbances that raise the water level
at the west end of Little Current Channel, by their action on 39
North. Channel, would tend also to lower the water level at the east end of Little Current Channel, by their action on Georgian
Bay, and similarly, that disturbances that lower the water level at the west end would tend to raise the water level at the east end. Such effects, however, were not studied in Georgian Bay, other than to notice that they appeared much less marked than in
North Channel. Over the 13-day interval in which the atmospher• ic effects were studied, it seemed that the wind and pressure influences tended to augment each other. This would be of no great significance at times of very high winds, however, because the wind stress effect on the water slope must then overshadow all other influences, being proportional to the square of the wind speed. It is felt that a current speed as high as 7 knots might at times be generated in Little Current Channel, mostly by the wind.
The tidal contribution to the current at Little Current
could easily be predicted on a basis valid in the absence of other disturbances. However, since seiches would greatly dis• tort the picture most of the time, and in a manner unpredictable more than a day in advance, and since wind stress and pressure effects would completely mask the tidal contribution on many occ• asions , in a manner also unpredictable more than a day in ad• vance , it would seem that such tidal predictions might be no more than a source of further frustation to shipping navigating
Little Current Channel. Nevertheless, it is thought that a brief elaboration of the various causes of the current, as dis•
cussed above , might advantageously be incorporated into the Can• adian Hydrographic Service's publication, Great Lakes Pilot, partly as a matter of local Interest, and partly as a basis on which mariners might make their own short-term forecast of the current in Little Current Channel from a knowledge of weather conditions prevailing at the time. 41 LITERATURE CITED
Blackraan, R.B. , and Tukey, J.W., 1958. The Measurement of Power Spectra. "New York, Dover Publications, Inc.
Doodson, A.T., and Warburg, H.D. , 1936. The Admiralty Tide Tables, Part III. London, H.M.S.O. (Hydrographic Dep• artment of the Admiralty).
Froese, C., and Duffus, H.J., 1959. Programming the Alwac III-E Digital Computer for Geomagnetic Data. Ottawa, Defence Research Board (Pacific Naval Laboratory, Esquimalt, B.C., Technical Memorandum 59-1+).
Gillies, D.K.A. , 1959. Winds and Water Levels on Lake Erie. Royal Meteorological Society, Canadian Branch, Publication 9(1): 12-21}.. .
Hutchinson, G.E. , 1957. A Treatise on Limnology, Vol. I. New York, John Wiley and Sons, Inc.
Keulegan, G.H., 1951- Wind Tides in Small Closed Channels. Journal of Research of the National Bureau of Standards, 1^6:358-381.
MacMillan, L.W., 1959. Digital Calculation of Power Spectra. Esquimalt, B.C., Defence Research Board (Pacific Naval Laboratory Note 59-12). Unpublished Manuscript for Internal Use.
Ontario, Legislative Assembly, 1953. Select Committee of the Ontario Legislature on Lake Levels of the Great Lakes, Report.
Proudman, J., 1953. Dynamical Oceanography. London, Methuen and Co. Ltd.
Sverdrup, H.U., Johnson, M.W. , and Fleming, R.H. , 191+2. The Oceans. Englewood Cliffs, N,J. , Prentice-Hall, Inc.
Young, R.K,, 1929. Tides and Seiches on Lake Huron. Journal of the Royal Astronomical Society of Canada, 23:Uli5-ll55. Fig„ 1: Amplitude and Phase-lag of M2 at Gauging stations.,
Fig. 3: Observation stations on and near Little Current Channel. SUSPENSION CABLE
SPRING WIND RECORDER
SHELTER «-HOUSE
J -
STILLING I—WELL COUNTER• WEIGHT
FLOAT
15-POUND LEAD WEIGHT
Fig. 4: Water Level Gauge, 1/12 Scale,, Fig. 5: Gurley Current Meter, 1/4 Scale. 4=- VJ1 1+6
MICROSWITCH
"7* PIVOT BOLT
Fig, 6: Pendulum-type Current Direction Detector.
RECORDING DRUM / STEP- DOWN RELAY -• •- \****** 4 MICROSWITCH DIRECTIO SPEED PEN PEN
FRIEZ RECORDER
CURRENT METER
Fig. 7: Wiring Diagram for Current Speed and Direction Recorder. kl
Fig. 8: Currents in Little Current Channel (ft0/sec.)
(a) for Current at Bridge flowing East at 2o0 ft„/sec.
(b) for Current at Bridge flowing West at 2„0 ft<,/sec0 Fig. 9: Water Temperature Lowering at Little Current, associated with West-flowing Current, JUNE 28 JUNE 29 JUNE 30 00 0 0 HRS. 00
UJ a. in - 2 /j A z :L \ A/^ Oft./sec. ui cc cc \j - 2 O LITTLE CURRENT o BRIDGE
Fig» 11: Comparison of Current Speed with Water Level Difference along Little Current Channel,, 10 ° 0 (ft/sec)2 10 20 West flowing | East flowing
Figo 12: Water Level Difference versus Square of Current Speed in Little Current Channel. 51 co r LLI M
TIME (E.S.T.)AT WHICH EACH GROUP IS CENTRED
Each water level plotted above is the mean of a group of 25 recorded water levels, taken at time intervals of 12,,5 hours„ The time at which the water level is plotted refers to the time of the central member of the group.
An interval of 12.5 hours was chosen because it is close to the 12„4-hour period of the principal lunar semidiurnal tidal constituent, and because the records had already been read at each hour and half hour,,
The same method of group averaging applied to intervals of 12 hours and 13 hours gave curves of the same shape as those above, but of amplitude only about half as large. This decrease in amplitude for intervals on either side of 12.5 hours indicates that the period concerned is indeed that of the principal lunar semidiurnal tidal constituent,, The amplitude may be read directly from the plot, and the phase-lag may be obtained from the upper meridian transit of the moon at Greenwich (12:01) on June 6„
F.igo 13: Preliminary Estimate of Lunar Tidal Effect in North Channel.
Fig. 16: Smoothed Plots of Water Level, showing 5-hour Se iche Action in North Channel. (from hourly readings of continuous records) MAY 18 20 22 24 26 28
Fig. 17: Plots of 5-hour Running Means, showing 10-hour Seiche in North Channel.
Fig. 18: Plots of 10-hour Running Means, showing Wind and Pressure Effect in North Channel. ^ 0.6
0.4
0 2
Oft. y = 0.0023 X + 0.02 (WIND WEST Correl'n Coeff. = 0.80
y = 0.0026 X + 0.01 (WIND EAST
-0.2 — Correl'n Coeff. = 0.23
•0.4 100 (FROM EAST) 0 (m.p.h.) 100 (FROM WEST) 200
EAST-WEST COMPONENT OF (WIND SPEED) AT GORE BAY ig„ 19: Water Level Difference versus Square of Wind Speed in North Channel; 10-hour Means.