The vertical structure of coastal currents

Deep-SeaResearch.1976,Vol. 23, pp. 925 to 936, PergamonPress. Printedin Great Britain.

The vertical structure of coastal currents C L I N T O N D . W I N A N T * a n d JACK R . OLSON'~

{Received 29 August 1975; in revisedJbrm 29 December 1975; accepted 21 February 1976) Abstract--A vertical array of four equidistant current meters was used to measure horizontal currents in 18m of water. The instruments resolved frequencies up to 15cph for a period of 33 days in late s u m m e r 1974. Onshore (EW) and longshore INS) currents were essentially uncorrelated at all depths. Longshore currents exhibit significant coherence with the surface tide but not at frequencies higher than the tidal frequencies. The effect of a southerly wind lasting over 3 days was evident as a northbound current that was most intense near the surface. The spectrum of onshore currents exhibits a peak at the semidiurnal frequency corresponding to internal tides, and there is a second lower, but broader, peak at frequencies between 1 cph and the buoyancy frequency. Onshore current amplitudes corresponding to the internal tides are on the order of 2 0 c m s - k while the higher frequency fluctuations have amplitudes on the order of 3 cm s - ~. There is significant coherence between all measurements of onshore current with a phase shift of n between surface and bottom currents. The onshore current measurements are consistent with the mode 1 oscillations of a three-layer model consisting of homogeneous surface and bottom layers separated by a layer having constant buoyancy frequency. INTRODUCTION

the United States have been described by SMITH systems in and HOPKINS (1972) and HARLETT and KULM shallow coastal water has not kept pace with (1973). Beyond these, measurements of currents theoretical and experimental advances in coastal in shallow coastal waters and their relation to and nearshore processes (INMAN and BRUSH, physical processes (surface tides, internal tides, 1973). This is particularly true with regards to wind stress and internal waves) are generally current fluctuations in the frequency band be- lacking although observations of currents over tween I cycle per day (cpd) and 1 cycle per the shelf break reported by WUNSCH and HENDRY minute Icpm), which includes tidal energy as well (1972) demonstrate that baroclinic fluctuations at as internal wave energy. the semidiurnal frequency are enhanced with deCurrent fluctuations of frequency less than creasing depth. Current measurements at tidal 1 cpd associated with coastal upwelling have been frequencies in 4 km of water off the California documented on the west coast of the United shelf reveal that onshore currents are strongly States (e.g. SMITH, 1974; HUYER, SMITH and affected by baroclinic 'noise' (MuNK, SNODGRASS PILLSBURY, 1974) and the west coast of Africa and WIMBUSH, 1970), while even the longshore (e.g. TOMCZAK, 1973; BANG, 1973). Fluctuations component of current is at times intermittently in the band of frequencies greater than 1 cpm swamped by internal tides. associated with surface waves have been reported Current measurements in shallow waters have by THORNTON and KRAPHOL (1974) as well as not been directly related to internal tides although Krauss (personal communication). there is a substantial body of evidence in the In the frequency band 1 cph to 1 cpm K. W. form of temperature measurements (e.g. CAIRNS, Nelson and J. R. Olson (personal communication) have measured the currents associated with in* Scripps Institution of Oceanography, University of Caliternal waves with periods on the order of a few fornia, La Jolla, California 92093, U.S.A. minutes. The effects of tidal currents on the sedi+Naval Undersea Center, San Diego, California 92132, mentary morphology of the northwestern shelf of U.S.A. 925 THE

UNDERSTANDING

of

current

926

CLINTON D. WINANT and JACK R. OLSON

1967; CAIRNS and NELSON,1970; WINANT,1974) that points to onshore currents of the order of 20 cm s- 1 associated with internal tides. Currents associated with tidal displacements of the thermocline should be out of phase by rc across the thermocline (at least in the case of the lowest mode of oscillation). A question with perhaps more than purely physical significance in this regard is whether there may be sufficient shear across the water column to overcome the stabilizing influence of the thermocline and thus enhance the vertical mixing.

the mean lower low water depth is 17m. The coordinate system used to describe the measurements has the x-axis running eastward onshore, the y-axis longshore positive to the north, and the z-axis vertical with its origin at the bottom. The current meters, numbered 1 through 4 with increasing distance from the bottom, were equidistant with a separation of 4 m; the lowest meter was 4 m from the bottom. The instruments were mounted on a taut wire midway between the tower pilings and oriented to measure horizontal currents. The current meters (Fig. 2) are described in

The field observations A vertical array of four electromagnetic current meters was installed from the Naval Undersea Center (NUC) tower for a period from 17 August to 25 September 1974, resulting in approximately 33 days of nearly continuous measurements (two interruptions in the operation of the array took place between 30 August and 2 September and 7 to 9 September). The tower (Fig. 1)is off Mission Beach in San Diego, where

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detail by OLSON (1972). They are sensitive to two components of current in a plane perpendicular to the axis of the instrument. Two-section low pass RC filters were used to remove high frequency current fluctuations due to surface waves, so that the effective cutoff frequency of these measurements is 15 cph. In a characteristic section of the measurements (Fig. 3), the onshore fluctuations suggest semidiurnal variations with amplitudes on the order of 20 cm s- 1, as well as higher frequency, but smaller amplitude fluctuations. The semidiurnal frequency oscillations seem coherent with the surface

The vertical structure of coastal currents

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Fig. 3. Current and tidal fluctuations, 9 to 25 September 1974. The bottom four traces represent the longshore currents, the next four traces represent the onshore currents, while the top trace is a prediction of tidal elevation for La Jolla, California.

tidal displacement over periods of a few days. However, when examined for periods of over a week the phase relationship between the surface tidal displacement and the onshore current does not remain constant. For example, while eastward flow was taking place at the bottom during periods of high tide on 9 to 11 September, western flow took place at high tide on 16 to 17 September. This apparent lack of coherence is borne out by the spectral analyses presented later. Onshore currents are further characterized by a phase difference of x between bottom and surface currents, so that a shoreward flow at the bottom corresponds to a seaward flow of surface water. As a result, large values of shear, up to 50 cm s- 1, are developed across the 12-m span of the instrumentation. The obvious question of whether such large shear values lead to instabilities and'turbulence is reserved for later discussion. Onshore current reversals appear suddenly and are generally consistent with the motion of internal bores described by CAXRNS (1967) and WINANT (1974). Short term (6 to 8 h) simultaneous

temperature profiles are available and show the onshore velocity to be highly coherent with the temperature structure. It is therefore concluded that the semidiurnal onshore fluctuations are caused by the internal tide, which, upon reaching such shallow waters, often manifests itself by surges of either cold water near the bottom or warm water near the surface. Longshore currents also show evidence of strong semidiurnal periodicity. In this case, however, there is no phase difference across the water column, and the fluctuations, which also have amplitudes on the order of 10 cm s-1, seem to retain an approximately constant phase relation to the surface tide displacement. Thus, alongshore semidiurnal current fluctuations may be ascribed directly to the surface tides. The energy distribution A convenient method for analyzing current meter records has been proposed by GONELLA (1972). In the present case, however, the longshore and onshore current records show no signi-

928

CLINTON D. WINANT and JACK R. OLSON 1 DAY

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Fig. 4. Spectral density estimates of the onshore (S=) and longshore (S~) current components measured 4 m off the bottom.

Fig. 5. Spectral density estimates of the onshore (S~) and longshore (S~) current components measured 16m off the bottom.

ficant coherence at any depth. A physical interpretation of this is that onshore currents result primarily from the incidence of internal modes that are in shoal water at the depth of the measurements, thereby directing their energy towards the shoreline; longshore currents, on the other hand, are related to processes such as wind stress and the tides, which are independent of the internal modes. For this reason a natural set of principal axes arises as the on-offshore and longshore direction. This choice is supported by the lack of any significant coherence between onshore and longshore currents at any depth in the bandwidth resolved by the measurements as well as by the local topography, characterized by bottom contours which are mostly parallel to the local coastline. Spectral density estimates of the onshore (S,) currents and the longshore (S~) currents were computed for each current meter. Results for current meter no. 1 (closest to the bottom) are shown in Fig. 4, and for current meter no. 4 (closest to

the surface) in Fig. 5. Results for the two other instruments do not vary significantly in their qualitative aspects. Spectra of both onshore and longshore currents at all depths exhibit a maximum on the order of 10 3 (cms-1) 2 (cph) - t at the semidiurnal frequency, along with a lower peak at the diurnal frequency. For frequencies f increasing to 1 cph, the spectral estimates decay as f - 2 and are generally similar to the power density spectra of currents measured on the continental slope off Cape Cod in the same season by WUNSCH and H E N D R Y (1972). Between 1 and 15 cph the onshore spectra and, to a lesser extent, the longshore spectra show a second broad peak with maximum values on the order of 2 (cm s - 1 ) 2 (cph)- 1 falling off rapidly as the frequency approaches the buoyancy frequency N (during the experiment N varied over a wide range up to a maximum on the order of 30 cph). This second lower peak corresponds to the energy associated with internal waves, which

929

The vertical structure of coastal currents

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are observed to run on the thermocline in coastal waters (LAFOND, 1962) and which are generally directed onshore. In view of these results, it is convenient to think of the energy as being generally partitioned into two bands, one roughly centered on the semidiurnal frequency with 0.015 cph < f < 1 cph and another high frequency band corresponding to internal waves with 1 cph < f < 15cph. The vertical variation of onshore and longshore energy in both bands is shown in Fig. 6. Maximum energy in the low frequency band is associated with the onshore energy profile, which shows a minimum near the center of the water (,olumn and maxima at the edges. The distribution of onshore energy in the high frequency band shows the same dependence in depth, and it is noteworthy that this depth dependence is inconsistent with what would be expected from a simple twolayer model in which maximum energies ought to be concentrated at the interface, or near the center of the water column. In contrast the longshore energy shows no similar behavior, although currents near the surface seem slightly more energetic than at the bottom. Energies in both the longshore and offshore direction are roughly an order of magnitude larger in the low frequency band than in the high frequency band. An alternative method of investigating the variation in depth of currents as well as the relative

coherence between onshore and longshore-currents involves using a spatial correlation matrix A whose elements are made up of correlations between the velocity components u and v at each depth. The eigenfunctions of the matrix A are termed empirical eigenfunctions of the data set and offer a natural set of normal modes that are weighted in proportion to the amount of variance within the data which is represented by each eigenvector. The method has recently received application in geophysics and has been presented in some detail by WINANT, INMAN and NORDSTROM (1975). If the nt samples of longshore velocity measured at current meter n are denoted by U,(t) and the nt samples of onshore velocity are denoted by V.(t), we define a data matrix U with elements U., = U , ( t ) - 0, n=l,4 U,+4,, = V,(t)- U.. Rows 1 through 4 of U correspond to the onshore currents, from which the mean t?, has been subtracted, while rows 5 through 8 of U correspond to the longshore currents minus the mean 9".. A symmetric correlation matrix A is defined with elements AiJ = nt t~l U " U ~t•

930

CLINTON D. WINANT and JACK R. OLSON 20

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Fig. 7. Dependence on depth of the onshore eigenfunction (a) and the longshore mode (b).

The trace of A is equal to the total variance in the data set, and each eigenvalue and corresponding eigenvector of A can be associated with a certain proportion of the total variance. The correlation matrix A has been computed using filtered time series resampled at intervals of 1 sample h - 1 partly to maintain the level of computations reasonable and also because the lower frequency motions (1 cpd to 1 cph) are most energetic. The eigenvalues of A are distributed such that two eigenvalues represent 35 and 30~o of the variance in the data, with the remaining variance distributed among six other eigenvalues. For reasons that will become shortly apparent the largest eigenvalue is associated with an onshore mode, while the next highest eigenvalue is associated with a longshore mode. The onshore and longshore eigenvectors are shown in Fig. 7. The onshore eigenvector elements that correspond to longshore currents are all negligibly small with amplitudes of order i0 -z. The onshore elements, however, describe an almost finear dependence of velocity with depth with a current reversal occurring near the middle of the water column. This is consistent with the energy distribution portrayed (Fig. 6) along with the phase reversal across the water column (Fig. 3) and suggests the onshore current distribution is corn-

patible with the mode i oscillations of a constant buoyancy water column. The longshore eigenvector elements that correspond to onshore currents are small with one negligible exception. The distribution of longshore elements shows an essentially even velocity profile as expected from the data of Fig. 3. The longshore currents To investigate the coherence between the longshore currents and the surface tides, a time series with hourly samples of sea surface displacement was generated, using the seven largest harmonic constituents as listed in the International Hydrographic Bureau sheets for La Jolla, California. The time series of longshore currents was filtered and resampled at hourly intervals and coherence estimates were computed for the two series. The result is shown in Fig. 8 along with the distribution of relative phase with frequency. Significant coherence exists at both the diurnal and semidiurnal frequencies, around which the harmonic constituents are grouped, and the phase lag is nearly zero at frequencies surrounding the semidiurnal frequency. Ideally, one would expect surface displacement and longshore currents to be in phase for a wave traveling north along the coast. However, measurements of tides off the shelf of California ( M U N K , SNODGRASSand WIM-

931

The vertical structure of coastal currents

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BUSH, 1970) have shown less than maximum coherence between surface displacement and longshore currents, as well as some variable phase lag between the two records. Coherence estimates (with 66 degrees of freeDAY

I HOUR

dom) and corresponding phase angles between longshore currents are shown in Fig. 9. These results are typical of those obtained for all pairs of longshore current measurements. They show significant coherence only for frequencies less than or equal to the semidiurnal frequency. Where the coherence is significant, the motion is in phase through the water column, and the coherence estimates decrease in proportion to the separation between instruments. An analysis similar to that establishing the coherence between longshore currents and surface tides was used to investigate coherence between longshore, as well as onshore winds and currents. Hourly measurements of wind speed and direction made at Lindbergh Field in San Diego by the National Weather Service and at Scripps Pier in La JoUa were used. There is no significant difference between these wind measurements on time scales of 1 day or longer, and there is no significant coherence between either of the longshore or offshore winds and the measured currents over the 33 days the currents were measured. Nonetheless, during the period 18 to 21 August a steady wind blew from the south over Southern California, which significantly affected the long-

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Fig. 9. Coherence estimators and corresponding phase between pairs of longshore current measurements. (a) corresponds to the current meters closest to the surface and the bottom, while (b) corresponds to the current meters closest to the bottom.

CLINTOND. WINANTand JACKR. OLSON

932

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rents showed no unusual behavior during the period). The largest longshore currents recorded during the experiment took place at this time with velocities just exceeding 40 cm s- 1. The effects of wind stress decay with depth, inducing a mean shear through the water column.

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It has been mentioned that onshore currents show no significant coherence with either the surface tide or the wind stress. Coherence estimates .SLamong four various pairs of onshore current LONGSHORE 20 C U ~ meters are shown in Fig. 11, along with the re16 E lative phase. Figure 11 compares current meters 1 -2 ~ and 4, across the water column, with the greatest separation. The coherence is high at all energetic ~-2 e frequencies and the phase is constant and equal ; 20r .k^.,~j ~ =o to n. The coherences among the adjacent pairs -20 of onshore current measurement (Fig. 11) show the unusual result that the coherence between "J - "¢~"~'.-4t'k ,.a- 4 adjacent pairs is in all cases lower than the co|7 18 19 20 21 22 herence between the measurements at the bounAUGUST, 1974 daries of the water column, which are separated Fig. i0. Longshore current, wind and tidal fluctuations, 17 by three times the distance between adjacent pairs. to 22 August 1974. The bottom four traces represent the The coherence is significant between all pairs at longshore current. The next trace represents the longshore the energetic frequencies, with a phase difference component of wind, the sixth trace represents the onshore wind, the seventh trace corresponds to barometric pressure of n between the measurements at meters 2 and 3 fluctuations and the top trace is a tidal prediction for La and no phase lag between instrument 1 and 2 Jolla, California. and instruments 3 and 4. This unusual result, with higher coherence between measurements that are shore currents. In the absence of any pressure further separated, can be explained by considering systems aloft this unusual occurrence is ascribed the mechanics of the stratified water column. The to extremely warm temperatures that persisted horizontal velocities associated with the mode 1 over the desert to the east of Southern California oscillation of a stratified fluid undergo a phase at the time (J. Namias, personal communication). change with depth. Exactly where the phase In Fig. 10 the longshore current components at change takes place depends on the exact thermoall depths, along with longshore and onshore wind cline position as well as its thickness. If the uncomponents, the barometric pressure, and tide certainty associated with these parameters is of prediction are shown for 17 to 22 August. The the order of the separation between two current southerly wind, with speeds to 6 m s- 1, is apparent meters, the phase difference cannot always be on the fifth trace from the bottom. Correspond- expected to occur between those current meters. ingly, a low is observed in the barometric pressure Another way of understanding this is to realize (the semidiurnal periodicity in the pressure is due that although the thermocline was almost always to atmospheric tides), and the usual daily sea contained between current meters 1 and 4, it was breeze from the west is suppressed. The effects of less often between current meters 2 and 3, because this applied wind stress were most strongly felt it may wander down between meters 1 and 2 or in the surface longshore currents (onshore cur- wander up between meters 3 and 4. The result of LONGSHORE WN I OS

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933

The vertical structure of coastal currents 1 HOUR

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the variable vertical thermocline position is to allow for the phase difference between meters 2 and 3 to be less consistent than for meters 1 and 4. This results in lower estimates of coherence for the shorter separation, although the motion of the water column is just as organized on both scales. Although continuous temperature measurements were not made simultaneously with the measurements reported on here, short records (6 to 8 h) of isotherm position in the water column were obtained from vertical arrays of thermistors (with spacing of 1 m). Two arrays, C and D, were located on an east-west line 130 m south of the tower, separated by 45 m. A typical record from

these arrays is shown in Fig. 12 along with the simultaneous measurements of onshore current. The high degree of correlation between currents and temperature is obvious. It is particularly noteworthy that the water column is sheared at all times during this period with either cold water moving east at the bottom (0900 to 1300) or, after the occurrence of a surge or event (WINANT,1974) which took place at 1305, warm water moving towards shore at the surface. Isotherms did not spread significantly during the period. The only noticeable variation in the thermocline structure took place between 0830 and 1030, when the thickness of the thermocline

934

CLINTON D. WINANT a n d JACK R. OLSON

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Fig. 12. Temperature structure and onshore currents on 21 August 1974. The top and bottom panels represent isotherm heights as a function of time as interpolated from measurements taken with vertical thermistor arrays located west (12a) and east (12c) of the current meter array. The thermistor arrays are 4 5 m apart and aligned 130m south of the current meter array.

was reduced. The overall structure of the thermocline thus reflects a lack of mixing during the period. If mixing had occurred, thermal diffusion would have spread the isotherms apart. The stability of a stratified water column to shear is measured by the Richardson number Ri = N2/u '2, where u' is the vertical gradient of velocity. MUNK (1966)demonstrated that if h is the vertical dimension over which p and u vary, then Ri increases with h, so that a sharper thermocline is more susceptible to shear instability. For the data of Fig. 12, N is approximately constant and equal to 0.05 s-1. Maximum shear during the passage of a packet of waves at 1130 is u' = 0.0133 s- ~, which gives Ri = 16. A theoretical criterion for stability (MILES, 1963) is that the distribution of Ri should be nowhere less than 1/4. Experiments have shown turbulence to occur for values o f R i > 1/4, but in general it is not likely for instabilities to set in for Ri > 1. In the presence of the warm surge at 1305 the Richardson number has a minimum value of less than 1. The fine scale perturbation in the isotherm records between 1320 and 1330 may then have resulted

from turbulence induced by the surge. Experimental investigations of the mixing that accompanies internal surges (c.f. SIMPSON, 1972; and the review of MAXWORTHYand BROWAND, 1975) all indicate that turbulent mixing occurs near the front of a surge, although the turbulence decays some distance from the front as the stabilizing effects of the stratification become dominant. Thus, even in spite of the large values of shear that characterize the onshore motion, turbulent mixing seems to occur during relatively short periods, accompanying the fronts of the internal tidal surges. A packet of several internal waves moving toward shore is evident in the middle of the record, which appears highly coherent both between the temperature records and the current records. The temperature gradient thickness is on the order of 4 m, roughly a fourth of the water column, and current velocities associated with the packet are out of phase between the central current meters with the largest velocities occurring at the extreme meters. Internal waves of this kind have often been reported (e.g, LAFOND, 1962) and usually

935

The vertical structure of coastal currents

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the middle of the stratified layer). Solid top and bottom boundaries at z = + H are assumed to simplify the problem, because the inclusion of a free surface boundary condition would only add a surface mode, in which we are not interested. The equations of motion consist of Laplace's equation for a velocity potential in the top and bottom layer while the usual equation for w2, the z dependence of the vertical velocity in the middle layer, is ~2W2

~ ~z

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N

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1

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(c) Fig~ 13. Three-layer model of the thermal structure in coastal waters. (a) represents the lowest mode of oscillation with maximum shear at the center of stratified layer and oscillation of the boundaries are in phase. (b) represents the next mode of oscillation with a jet-like flow in the stratified layer that is opposed to the motion in the homogeneous layers. (c) shows the dispersion relation for the lowest four modes in the case where kH is very large.

described using a two-layer model. As previously mentioned such a model is inconsistent with the current measurements because onshore amplitudes are not maximal in the center of the water column. Because salinity variations in the area are not sufficient to affect density to the extent that the 5 °C temperature gradient through the period does, it seems worthwhile to consider a three-layer model (Fig. 13) as an alternative simple representation. This consists of homogeneous surface and bottom layers separated by a finite thickness (2h) interfacial layer in which the density p varies continuously as a function of the depth z (which is measured positively upwards from an origin in

tan h [k(tt- h)

for odd modes in which the boundaries of the stratified layer oscillates in phase as in Fig. 13a, and m

tan mh = ~ tan h [k(H-h)] for even modes as in Fig. 13b. The dispersion relation for the four lowest modes is given in Fig. 13c. The frequency of the waves in the wave packet near the center of Fig. 12 is approximately 0.012 s- 1. The corresponding phase speed for the first mode predicted by the three-layer model is 18cms -1, which is in close agreement to the measured phase speed of 19 cm s- 1, in view of the large amplitude of the disturbance (the product of the wave number multiplied by the amplitude is approximately one). CONCLUSIONS

Measurements of the vertical structure of currents in shallow coastal water during the summer reveal that onshore and longshore currents are essentially uncoupled through the water column. The longshore currents appear to be primarily barotropic, with most energy resulting from the

936

CLINTON D. WINANT and JACK R. OLSON

direct action of tidal forces, for frequencies greater than 1 cpd. Sustained longshore winds can induce substantial longshore currents, although the data are insufficient to establish any statistically significant facts about motions with frequency less than 1 cpd. The onshore currents are more energetic than the longshore currents, with a vertical structure phase shifted by rc across the water column. This phase shift points to the onshore motion being baroclinic at all frequencies in the band resolved by this investigation. Energy in the band 0.015 to I cph is associated with internal tides, which often appear in the form of bores or surges. Energy in the band 1 to 15 cph is associated with internal waves. These can be simply approximated using a three-layer linearized model. The shear associated with the onshore motion is not generally large enough to overcome the stabilizing effect of the stratification. There is little evidence of turbulence and horizontal mixing in the frequency band resolved here, although patches of turbulence may be associated with the arrival of internal surges. The measurements reported here can only be thought of as characteristic of the current systems that prevail during the summer season. Clearly it is to be expected that the weaker stratification characteristic of other seasons will modify the structure presented, if only quantitatively. These measurements are thus inadequate to allow a precise determination of dissipation rates in shallow water, although they are consistent with the estimates of WUNSCH and HENDRY (1972) and WINANT (1974). Acknowledgements--Current measurements described here were acquired during the Advanced Research Projects Agency sponsored Ocean Waves Experiment. Analysis of the data was sponsored by the Geography Programs of the Office of Naval Research. Thanks are due to R. S. ARTHUR. REFERENCES BANG N. D. (1973) Characteristics of an intense ocean frontal system in the upwell regime west of Cape Town. Tellus, 25, 256-265. CAIRNS J. t . (1967) Asymmetry of internal tidal waves in shallow coastal waters. Journal of Geophysical Research, 72, 3563-3565.

CAIRNS J. L. and K. W. NELSON (1970) A description of the seasonal thermocline cycle in shallow coastal water. Journal of Geophysical Research, 75, 1127-1131. GONELLAJ. (1972) A rotary-component method for analyzing meteorological and oceanographic vector time series. Deep-Sea Research, 19, 833-846. HARLE'YI"J. C. and I. D. KULM (1973) Suspended sediment transport on the northern Oregon continental shelf. Bulletin of the Geological Society of America, 84, 3815 3826. HUYER A., R. L. SMITH and R. D. PILLSBURY (1974) Observations in a coastal upwelling region during a period of variable winds (Oregon coast, July 1972). Tethys, 6, 391404. INMAN D. L. and B. M. BRUSH (1973) The coastal challenge. Science, 181, 20-32. LAFOND E. C. (1962) Internal waves, part 1. In: The sea, Vol. 1, Physical oceanography, Interscience, pp. 731 751. MAXWORTHY T. and F. K. BROWAND(1975) Experiments in rotating and stratified flows: oceanographic application. In: Annual Review of Fluid Mechanics, Vol. 7, Annual Reviews, pp. 273-305. MILES J. W. (1963) On the stability of heterogeneous shear flows, part 2. Journal of Fluid Mechanics, 16, 209-227. MUNK W. H. (1966) Abyssal recipes. Deep-Sea Research, 13, 707 730. MUNK W. H., F. SNODGRASSand M. WIMBUSH(1970) Tides offshore: transition from California coast to deep sea waters. Geophysical Fluid Dynamics, 1, 161-236. OLSON J. R. (1972) Two component electromagnetic flow meter. Marine Technolo#y Society Journal, 6, 19-24. SIMPSON J. E. (1972) Effects of the lower boundary on the head of a gravity current. Journal of Fluid Mechanics, 33, 759-768. SMITH J. D. and T. S. HOPKINS (1972) Sediment transport on the continental shelf off Washington and Oregon in light of recent current measurements. In: Shelf sediment transport, process and pattern, D. J. T. SWIFT, D. B. DUANE and O. H. PILKEY, editors, Dowden, Hutchinson & Ross, pp. 143-180. SMITH R. L. (1974) A description of current, wind and sea level variations during coastal upwelling off the Oregon coast, July August 1972. Journal of Geophysical Research, 79, 435-443. THORNTON E. B. and R. J. KRAPHOL (1974) Water particle velocities measured under ocean waves. Journal of Geophysical Research, 79, 847-852. TOMCZAI~ M., JR. (1973) An investigation into the occurrence and development of cold water patches in the upwelling region off NW Africa (Rossbreiten-Expedition 1970). Meteor Forschun.qser#ebnisse. A, No. 13, 42 pp. WlNANT C. D. (1974) Internal surges in coastal waters. Journal of Geophysical Research, 79, 4523-4526. WINANT C. D., D. L. INMAN and C. E. NORDSTROM (1975) Description of seasonal beach changes using empirical eigenfunctions. Journal of Geophysical Research, 80, 1979-1986. WUNSCH C. ~tnd R. HENDRY (1972) Array measurements of the bottom boundary layer and the internal wave field on the continental slope. Geophysical Fluid Dynamics, 4, 101-146.