Repiinled from:
ESTUAkmNE RSEXPCH. VOL. I1
G e o l o g y o n d Engineering
01975
ACADEMIC PRESS, I N C
New
York
S-n FronrLco
Londm
TIDE Ah?) FAIR-WEATHER WIND EFFECTS
IN A BAR-BUILT LOUISIANA ESTUARY
ABSTRACT
An in-depth, fair-weather, field study in July 1972 provided informtion
about the response of the water level of Caminada Bay, an extremely shallow,
bar-bullt Louisiana estuary. The water surface elevation was recorded at three
locations il the bay along the other parameters, an equipotentid surface was
established, and the time-dependent variations of a dope vector along the surface
gradient were computed. It was found that the instantaneous fair-weather wind
stress induced a slowly oscillating set-up around a time-averaged slope magnitude
of 1 . 5 ~ 1 0 rad.
- ~ This consrituted less than 50'70 of the measured time-averaged
slope. The remaining tirne-averaged dope is accounted for by tidal nonlinearities.
The instantaneous slope vector was found to rotate or oscillate in the horizontal
plane with a diurnal period. Tidal input through two entrances governed this
behavior, w h l e the wind stress and atmospheric pressure gradients served only to
modify the direction of the surface slope. In general, on the diurnal scale, tidal
rather than wind effects dominate the dynamics of Caminada Bay. However, the
mean water level responded to the wind direction on a time-scale longer than
one day. Winds p a r d e l rather than normal to the coast controlled the water
elevation, indicating an Ekman eifect.
INTRODUCTION
A series of papers in the 1950's by Pritchard ( l 7 , 1 8 , 19,201 and by Pritcha~d
1. Coasral Studies Institute, Louisiana State University, Baton Rouge, Louisiana 70803.
R m e n t nddrmr: Department of Geology, University of South Carolina, Columbia, South
Camha
BJORN K J E R F V E
and Kent (21) on coastal plain estuaries lsid the dynamical framework for
subsequent, intensive study efforts in various aspects of estuarine circulation and
dynamics. Sinularly, the study by LicAlister et. al. (15) and other investigations
pointed out the salient, dynamical features of fjord-type estuaries. However, the
bar-built estuary, the third major estuarinz type, has received virtually no
attention from the point of view of physical oceanography (3). The study by
Dyer and Rammoorthy (6) is a noteworthy exception rhou&. Apparently,
there is a need for a systematic investigation of the dynamics of bar-built
estuaries.
This study attempts t o illustrate the relative importance and effect of
astronomical tides and fair weather winds on the water surface behavior in a
representative, bar-built estuary, Caminada Bay, thus shedding light on the
dynamical structure of this type of coastal ernbayment. This is of special
interest, as Collier and Hedgpeth (4) and Copeland, Thompson, and Ogletree (5)
indicated that the wind effects outweighed tidal effects in controlling the surface
dynamics of Laguna hladre, Texas, a bar-built estuary similar to Canlinada Bay.
The water surface fluctuations are, of course, intimately tied to the estuaMe
velocity structure.
Both coastal plain and ijord estuaries are often successfully approximated by
a narrow channel, thus simplifying the analytical treatment by removing lateral
variations. As bar-built estuaries are often wide, in a relative sense, with more
than one opening to the ocean, the channel approximation is no longer valid.
Estuarine water surface slopes can be caused and maintained by a number of
different factors, t l e most obvious being atmospheric pressure gradient and wind
stress. Hellstrllm (lo), Haumitz (9), Keulegan (12), Van Dorn(25), and Kivisild
(13) studied wind-induced surface slopes on lakes. Van Dorn and Keulegan
indicated that the wind-induced slope should be given by a linear combination of
slopes produced by the surface wind shear and a wave effect. However, Saville's
(22) measurement of set-up on Lalle Okeechobee during storm conltions were
fully accounted for by the wind stress alone, in spite of waves 3 rn high. In view
of this result, wind waves were ignored in thls study. The effect of atmospheric
pressure gradients on the water surface was measured t o p e comparatively s m l l
and will be treated no further.
The tide is a long wave and will o f course cause a fall and rise in the water
level as well as instantaneous water surface slopes. However, the tide may also
maintain time-average surface slopes. Due to spatial variations in current
amplitude, C m e r o n and Pritchard (3) showed that a mean surface slope may
exist in the absence of wind shear stresses and density gradients. This effect
arises from the noulinear terms in the momentum equation. Unoki and IsozA5
(23, 21) used nonlinear current effects to explain the observed mean sea level in
Japanese ernbayments, and showed them to be similar to Longuet-Higgins' and
Stewart's (14) radiation stress. Qualitatively, the mean surface is raised in regions
E S T U A R I N E RESEARCH
of antinodes, usually at the head of a bay, and lowered at nodal points.
Density p d i e n t s (21) and f d i n g rain drops (2, 25) can both cause mean
surface slopes. The Caminada warer density was almost homogeneous and the
rain fnll was limited during the study period. Therefore, these effects warrant no
further discussion.
MEASUREMENTS AND DATA ANALYSIS
Study Awa.
Caminada Bay is a bar-built estuary, located along the Louisiana coast, 40 km
west of the active hlississippi River delta (Fig. 1). It is a portion of the Bxataria
basin, separating the ~ c t i v echannel-levee system of the Mississippi River from
the abandoned Bayou Lafouiche channel-levee system. The bay, representative
Figrue 1.
Study sitz: Cmninadi Bay, Louisum, withinstrument locations.
49
BJORN K J E R F V E
of the type of estusries found in Louisiana, m e x w e s some 14 by 6 km, and is
only on the order of one-meter deep. Surrounded by vast expanses of Sparrim
altemiflorn marsh, Caminada Bay is connected to ~djoinuigbays and the Gulf of
Mexico via 3 series of openings.
The Gulf Coast is a microtidal environment, usually experiencing low marine
energy conditions. Still, the land between the Mississippi and Bayou h f o u r c h e is
recedmg due to lack of an adequate sediment supply. The fresh-water runuff is
largely due to rain falling over the Barataria basin, and because of dry summers,
saline ocem waters encroach deep into the lower basin.
The Caminada and Gulf of Mexico tide is primarily of the diurnal kind, with a
weak semi-diurnal component. Furrhermore, the mean water level fluctuates on
a yearly basis with a September peak and a January low. The range of this
oscdlation is approximately 26 cm (16). The summer weather encountered in
the Caminada Bay area is dominared by the Bermuda High pressure system with
a superimposed sea-land breeze circulation and locally generated thunderstorm
winds. Hurricanes have struck the area occasionally. The latest direct hr on the
Baratalia basin was Hurricane Betsy in 1965.
Field Experiment.
The field experiment took place duiing a 20-day period in July, 1972,
preliminary measurements having been m d e during six days in A u p s t , 1971.
The study consisred of recordings of water surface elevation, wind speed and
direction, atmospheric pressure, and temperature, along with water temperature
and salinity measurements. The duration of the study was chosen to include at
least one full fortnightly tidal cycle with a tropic and an equatorial tide. To
facilitate presentation of the data, a time scale with ori& at 0000 on July 7,
1972, was defined. The study was concluded at 492 hrs or 1000 on July 27,
1972.
All data traces were &@tized wirh a sampling rate of 20 pts/hr and smoothed
with a binomial fiter. Stochastic analysis was performed.on the time series t o
detect and describe major data features. Auto- and cross-spectra were computed
for scalar and horizontal vector time series (81, using the Fast Fourier Transform
(1).
Water Level Maurements.
The water level was continuously recorded at three Caminada locations,
stations 1, 2, and 3 (Fig. I), using three capacitance water level gages. A
ESTUARINE RESEARCH
references datum was established by averaghg the water level records for each
station, assunling that the means define an equipotential surface. Rather than
using the over-all data traces to compute these means, it was convenient to base
the reference surface on the means for a three-day period during the equatorial
tide. Tidal nodineanties may then be assumed not to cause time-averaged
surface slopes because of the weak currents. The computed means were further
corrected for wind stress and pressure gradients. Considerations of gage response,
circuit linearity, and errors in the averagng process indcated that absolute
slopes greater than 1 . 0 ~ 1 0 - 6rad could accurately be assessed.
Wind Measurements and Stress Calculations.
The horizontal wind speed and direction were recorded continuously at
station 2, 6.77 m above the mean water surface. A supporting study in 1971
established a relationship between the wind speed and the surface shear stress. A
highly accurate, six-level anemometer system was then used to measure the wind
proffie at station 2. The number of 15-min averaged profiles measured was 386.
The extrapolated wind speed range at 6.77 m was from 0 to 10 m/sec. The
profdes fo!lowed the logarithmic law closeiy; more than 90% of the protlles had
a correlation coefficient in excess of 0.94.
By performing linear regression of iogarithmic height above the water on wind
speed, the friction velocity, U,, (von &&n2s
constant &vided by the
regression coefficient) and the extrapolated wind speed, U, at 6.77 m were
computed for each proiile. Curvilinear regression of friction velocity on the 6.77
m wind speed yielded (Fig. 2)
where U, and U are measured in cmlsec and the linear correlation coefficient is
0.96 (1 1). The surface wind shear stress, 7 ,is related to the friction velocity via
where O is air density.
Slope Vector Calculations.
The set-up or difference in water surface elevation between any two points is
a time-dependent parameter of primary importance in this study. As Caminada
Bay cannot be assumed to be narrow, it is convenient to consider a
two-dimensionai slope vector along the water surface gadient rxther than the
scalar set-up.
F r i c f i o n Velocity
Figure 2.
"3.
Wind S p e e d
Curiliinea least squares fit betvieen friction veiocity, U,, and \ ~ n dspeed at
6.77 rn, U, based on 386 wind piofilcs with a conehtion p e f l i d e n t , I = 0.96.
Consider the Caminada water surface t o be a plane and choose a circle located
in this plane with its origin at the water surface at station 2. The magnitude of
the slope vector is the maximum slope of the water surface at any one time, i.e.,
a maximized, non-dimensional set-up. The direction of the slope vector is the
horizontal angle, counted clockwise from true north to the lowest elevation on
the circle periphery. By analyzing the slope vector magnitude and direction time
records, the three-dimensional behavior of the water surface can be induced. Of
course, the approximztion of the water surface by a plane is necessitated by the
use of only three tide gages.
RESULTS AND DISCUSSION
M a n Sea Level.
The smoothed water surface records indicate a greatly elevated mean water
ESTUARINE R E S E A R C H
level from 50 to 120 hrs and from 250 to 380 hrs at each of the three stations.
The record at sration I is presented in Figure 3. The mean water level was then 8
and 24 cm, respectively, above the fdtered value for other times. As the
predicted tide 3t Bayou Rigaud (Fig. 3) does not exhibit a sinular increase in the
mean elevation during these periods, meteoroiopid rather than astronomical
effects cause the surface rise.
F i g r e 3.
Cornp.uiron betivecn measured water level at station I and piedicted water level
at C ~ Y U R
U i p u d . A ? l - h r cqwII11y weighted running m a n filter has bcen used lo
caniputo the rime-avcmged water level. Thc liltcr tiequcncy response is such
t h ~ atn y osdUotion longei than 48 lus is reproduced accurately.
The alongshore component of the wind stress (Fig. 4) was most intense during
the periods of high mean water. The stress was then from the east, resulting in a
large alongshore (55-23S0T) component from a northeasterly direction, leading
at peak water level by approximately 20 111s.
+
21
Figure 4.
Y I H l l STRE55 ? R W 215
OZGREES TRUE
Mensllicd w h d stress and direction at station 2 as n function of time. The
battom g a p h shows the mess c o ~ n p o n e n t along the coastline. The
time-averaged m a p i r u d e and ciirection ii a vector average, using n 24-hr equally
weighted running m a n filter. The wind speed varied from 0 to Id rnlsec.
According to Ekman (7), the net transport in the wind-influenced surface
friction layer is in deep water 90° to the right of the down-wind direction in the
northern hemisphere. This resuit is modified in the presence of a coastline and in
shallow water with depth less t11m the friction layer. When the wind blows
pardlel to the coast with the coast t o the right of the downwind direction, a
two-layered circulation may develop perpendicuhr to the c o m , with
shore-directed flow in the surface layer and an equal return transport in the
bottom layer. Further, a wind regime of this kind will pile up water against the
coast, causing sea surface gadients away from the land mass. In Canlinada Bay,
ESTUARINE R E S E A R C H
the result is an elevated mean water surhce in response t o the intense
northeasterly wind stress and the coast31 surface gradients.
Consider an average rise of water levels at stations 1, 2, and 3 to be 24 cm in
100 llis (250-350 hrs). Take the surface area of the Bay to be 8 . 4 ~ 1 0m2.
~ This
implies that 56 m3 of water was on the average added each second, most likely
through Caminada Pass, as water flowing through Barataria Pass must primarily
fill Barataria Bay. Caminada Pass has a 3 x 1 0 ~m2 cross-section, implying a
cross-sectionally averaged net inflow of 1.9 cm/sec during the rise fof the water
surface. Similarly, the level feu 16 cm in the next 30 111s in response to the
decreasing ~Vmdstreess. This corresplnds to a 4.3 crnlsec spatially averaged net
outflow through Caminada Pass. Both velocities are of reasonable magnitude and
compare well wit11 time-averaged current measurements made in Caminada Pass
during a 1971 study (26).
Water Surface Slopes.
The surface slope of Caminada Bay changes both in magnigude and
orientation as a function of time. The measured slope vectors are presented for a
few days during one equatorial (Fig. 5) and one tropic (Fig. 6) tide.
The surface slope gradient rorated anticlockviise 36O0 in 24 hrs during the
equatorial tide, whereas it oscillated diurnally 60° to either side of the
vectoridy, time-averaged value (180") during the tropic tide. However, both
direction records show similar steplke appearances, indicating long periods of
constant slope direction followed by rapid direction changes. The two
magnitude records are quire similar with pronounced 12-hr oscillations
(recitified wavesj, indicating a diurnal period of the slope mapitude. This was
supported by diurnal peaks in the power spectra, which were computed for
vector time series (1 1).
At this point, it became desirable to sinwlate the obsened slope vector
behavior with an appropriate analytical model. The momentum equation was
integrated vertically, the coriolis and nonlinear field accderation terms were
argued to be small in comparison to the retained terms. density was taken to be
constant, and the bottom friction was made linear. The resulting set of linear
partial differential equations was broken down into two sets of equations: one
representing wind response and one governing tide effects. To facilitate the
analytical treatment, Cminada Bay was approximted by a rectangular basin,
14x6 krn, with the long axis oriented from southeast to northwest, with a
uniform still-water level of 1 m.
The horizontal momentum component equations were balanced by an
unsteady current term, a slope term, and the wind stress, which was assumed to
be much greater than the portion of the bottom friction corresponding to the
wind-induced current. As the wind stress was from the southeast (Fig. 4) during
LW
H R G N i l U O E OF S E T - U P
cc ~.
, h 0 0
ib8.00
*bo.OD
?;..DO
?i..OO
?...OO
HOUR3
Figures.
!vleasuied direction and r n a ~ i t u d eof slope vector, 1000 July 14-0113 July 17,
1972, during a n equatorid tide. Tho smooth lines we vectanally :~vernged,2 C h r
equally weighted running mcnns.
both the tropic and equatorial tides shown in F i s r e s 5 and 6, the stress
direction was assumed t o be constant. The spectrum of the stress magnitude
indicated a dominant 24-hr peak, which appears as a regular stress oscillation in
the record (Fig. 4). The wind stress was therefore simulated, assuming a linear
ESTUARINE RESEARCH
5.m
"
J
123.00
'IJS.ilD
~h5.00
~k4.00
V63.00
Y?S.OO
185.00
~ k . 0 0
rkao
&s.ao
ub5.o~
HOURS
g
flRGNITUOE OF SET-UP
LW
So3.m
R g u e 6.
.
r k m
.koo
ukoo
uis.co
HOUR3
HW
&=.on..
I m s u i e d dlreczion and mgnitude of slope vscror, 2 1 0 0 July 23-0900 July 27,
1972, d k n g r tropic tidc. The srnoorh lincs sre vecroridly averaged, 24-hr
c q u d l y weighted running means.
combination of a mean (synoptic) and a sinusoiddly varying (sea-land
breeze)srress. The mean was 0.18 and 0.11 dyne/crnZ for the e q w t o r i d and
tropic tide periods. respectively. The r.m.s. stress was chosen as the amplitude of
the oscillatory term. Its value was 0.09 and 0.08 dyne/cmZ for the equatorial
and tropic tides, respectively. When combining the horizontal momentum
component balancce with the hydrostratic equation and an appropriate mass
conservation equation, it was found that the maximum wind-induced volume
transporr h g e d 6 111s behind the peak wind stress. Also, as can be expected, the
wind-controilcd w ~ t e rsurface maintained a mean slope correspondmg to the
m c m stress and oscillated diurnally in response to the sea-land breeze stress.
The horizontal momentum component equation for the tide effect were
balanced by an unsteady, a slope, and a bottom-friction term. As a first
approximation, it was assumed that two two-dimensional tidal waves enter and
progress through Caminada Bay at right angles along the long and short w e s of
the estuary and reflect perfectly at the inside banks. Physically, the two waves
may be thought of as the ridd input t h o u g h Caminada and Barataria passes,
respectively. Thc theoretical tidal surface elevations at the three stations were
computed by assuming reasonable values for tidal amplitudes at the passes and a
phase angle between the two waves. In general, the model was insensitive ro the
choice of reasonoble phase anzle.
The solutions of surface elevation due to wind and tide effects were added to
yield a theoretical distribution of water level in space and time. A simulnted
surface slope vector time series was computed for an equatorial (Fig. 7) and a
tropic (Fig. 8 ) tide in the same manner that the slopes were computed from the
measured surface elevations. The qualitative agreement between the measured
and simulated slope vector time series is outstanding for both equatorial (Figs. 5
and 7) and tropic (Figs. 6 and 8) conditions.
"7,
J,
w-
e
U
w
-8
%.oa
a. oo
is.oo
ru.m
a2.m
u0.m
us.m
HOUR3
b
Figure 7.
SETUP H R G N I I U O E
Simulated slope dircction and magnitude for the equatorid tide, 1000 July
1 4 4 1 1 3 July 17, 1972.
A compnrison between the measured and sin~uhtedinstantaneous direction
series shows excellent agreement with respect to: (a) 24-hr periodicity; (b)
steplke dircction changes every 12 hrs; and (c) general appearance of time series,
i.e., one anticlockwise rotation of thc slope vector every 24 lus during the
equatorial tide and a 14 hr oscillation in direction during the tropic tide. On the
ESTUARINE RESEARCH
Figure 8.
Sirnuiated slope vector diiection and magmitude for the tropic tide, 2100 July
23-0900 July 27, 1972.
negative side, the analytical model does not reproduce the time-averaged slope
direction weil. This is probably due t o omission of n o d n e a r effects or the
coriolis acceleration (1 i).
The ageement between the measured and simulated instantaneous slope
magnitudes is also amazing, consideling the simplicity of the model. A 24-hr and
a 12-hr period are apparent (visually and in the spectrum) in measured as well as
simulated records. T i e measured instantaneous rnagiitude is approximately a
factor of 4 greater than the simulated slope. Also, the measured time-averaged
slope, 4 x 1 0 . ~ rad, is underestimated by a factor of 4 in the model. This
discrepancy may be explained in terms of slopes induced by the neglected
nonlinear terms in the momentum equation (3, 11).
CONCLUSIONS
This study considers the response of the water elevation in a shallow bar-built
Louisiana estuary t o tidal and fair-weather wind effects. d s o , water surface
slopes were measured and are presented in a novel fashion as a vector time series.
I t was found that:
(a) Tidal effects dominate the dynamics (rise and fall of the water surface;
currents) on the d u r n d time s a l e .
(b) F z k v e a t h e r wind effects can cause considerable changes in mean water
elevation through an Ekman mechanism on a time scale greater than the diurnal;
W O R N KJERFVE
winds parallel rather than normal to the coast controlled the mean water level in
Caminada Bay.
(c) Measured absolute water surface slopes in this microtidal bar-built estuary
reached a maximum of 3 x 1 0 . ~rad with 3 mean of 4 x 1 0 . ~rad for the described
fair-weather synoptic wind conditions with a superimposed sedand breeze
circulation
(d) Time series of water surface dopes can be simulated extremely well, using
a linear three-dimensional analytical model.
(e) The nonlinear field acceleration terms seem to maintain surface slopes
greater than wind-induced slopes.
(0To model a "wide" estuary, e.g., Caminada Bay, which h3s two major tidal
entrances, it is necessary t o allow for lateral mriations; a channel approximation
does not produce useful results.
ACKNOWLEDGMENT
Financial support for this study was provided by the Coastal Studies Insritute,
Louisiana
State
University,
Baton
Rouse,
under
contract
N00014-69-A-0211-0003, Project NR 388 002, with geography programs of the
Office of Naval Research.
This research was part of a doctoral dissertation in the Department of Marine
Sciences at Louisiana State University. The author is thankful to Drs. S. P.
Murray, C. J. Sonu, S. A. Hsu, and to the teclmicims of the Coastal Studies
Institute and the Department of Marine Sciences.
B e n h t , J. S. and Piersol, A. G.
1971
Random Data:
Anxlysis and hleasurement Pmcedures.
Wiley-Intcrscience. 390 p.
Cadwell, D. R. and Eilioit, W. P.
L(2):
Surface rtiesses produced by rainfall. J o u . Phys. Oe-.,
1971
145-148.
Clrncron, W. hi. and Pritcimd, D. W.
1963
Estuaries. In nio Sea. V d . 11, p. 306-324. (ed. Hill, hl. N.)
Intcislience Publishers.
Collier, A. and IIedppcrh, I. W.
1950
An introduction to the lrydropaphy of ti& vaters of Texas.
Publ. Inst. Marine Science., I(?). Udv. Texas: 125.194.
Copciand, U. I.
Thompson,
,
J. H., Jr., and Ogletice, W. B.
n?ccffects of wind on watcr levels i n t h e Texas L:~gona Mudre.
1968
Toxu lour. Science., 20(2): 196-199.
Dyer, K. R. and Ramamoorthy, R.
1969
S;iiiniry and watcr circulation in the Vcll3i estuary. Limol.
Ownog., 14(1): 4-15.
ESTUARINE fiESEARCH
On the inilucnce of the earth's rotadon an ocean-currents. h k i v
f& Maternatik, Asmmomi och Fysik., 2(11): 1-53.
A rotzly component rnmhod for a d y r i n g meteorological and
oceanogsphic vector time series. DeepSea Res., 19(12):
833-846.
The slope of hire surfaces undcr variable wind Beach Erosion
Board Tech. Mem, 25. 23 p.
Wind effect on lake; and rivers. Ingeniiirwetenskap&ademins
Handlinw, 158.191 p.
Dynamics of the water surface in a bar-built estuary Doctoral
dissertation. Department of M a k e S c i m m , Louisiana State
UrUv. 9 1 p.
$Find tides in m a i l dosed channels. Jour. Res. Nat. B. Stand.,
46(5j: 358-381.
Wind effect a n s k l l o u . bodies of ii8arer with speciil reference to
Lake Okcechobee. gun& Tekn. ~ 6 ~ l ; o i a Handtingar,
ns
83. 146
P.
Longuet-Hil,ni, 11. S. and Stcwart, R. W.
1964
Radiation suesses in water wavcs: 3 p h y s i d discussion, with
applications. Deepsea Res., 1 l ( 4 ) : 529.562.
\I;AEster, W. B., Rzttray, )I., Jr., and B m m , C. A.
1959
The d y n n n i a of a ijord estuary: Silver Bxy, Alaska. Tcch. Rep.
62. Oceanogaphy. Univ. Wxhington. 70 p.
Mac&, J. G. and Hopkins, S. I<.
Studies on oyster mortdiliry in relariun to n a t m d eenvironmenrr
1961
and to oil f i c l b i n Louisiznrr. PubL Inst. Marine Science. 7. Univ.
Tcras: 1-131.
Pritchard. D. V.
1952
Salinity distribution and circulation in thc Clieiapcakc Dny
estulirine system. Jour. M u . R e s , 11: 106-123.
Pritchard, D. V.
1954
h study of :he salt bsllrnce in a coastal plain cstuary. Jour. Liar.
Res.. 1 3 : 133-144.
Pritchard, D. V.
1955
Fstuarinc circulation patterns. Proceedings o f ASCE, 81.
71711-717/11.
Pritchard, D. V.
15: 3 3 4 2 .
Piitchard, D. V. a n d K m t , R. E
1956
A method for detcrmirlinr mean longitudind velocities in a
coasrai &plaincstuary. Jour. hlm. Res. 1 5 : 81-91.
Savillc, T., 31.
Wind set-up and waves in shallow water. B a c h Erosjon Board
Tech. Mem., 27. 36 p.
Unoki, S. and Isouki, I.
Mean sea level in tays, with specid reference ro the mean slope
1965
of sw surface due to the standing o s d a t i a n of tide. 0-ogr.
Mag, 17(%): 11-35.
Unoki, S. and Isoraki, I.
A possibility of generndon of surf beats. Proceedings of 10th
1966
Conf. Coastd Eng. (Tokyo)., 1: 207-216.
Van Doin, W. G.
1953
Wind m e s s an an artifitid p o n d Jour. Mar. R e s , 12(3):
249-276.
Waiters, C.D., Jr. and Hornandez-Anla, hl.
1971
Some physiwi observations in C;imimda Pars channel. 1 2 p.
(Unpublished data.)
1952
23.
24.
25.
26.