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    Location map. Moorings were deployed at locations noted by open circles, and the locations of anemometers are shown by solid circles. Wind measurements are available at La Laguna for 1 Dec 1997–15 Feb 1998 and at San Angel for Jun–Dec 1998. The grayscale for depth saturates at 10 m to emphasize the depth distribution in the northern part of the lagoon. The inset map shows the location of Laguna San Ignacio on the Baja California peninsula

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    (left) Wind- and (right) density-driven flow in a section near the center of a rectangular basin. The view is toward positive x, with positive wind stress and ρx. The contours and shading represent the axial velocity. Shaded areas correspond to negative axial flow: either upwind or downgradient. The contour interval is 0.1. The sense of the lateral circulation (Smith 1976) in the density-driven flow is represented by the heavy streamline

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    Axial currents at station 1 during July of 1998. The light lines represent the current at 5 depths; there is so little difference between currents measured at different depths that these lines can barely be distinguished. A positive current is toward the closed end. The heavy line represents minus the wind stress at San Angel. The sign of the wind stress is chosen to emphasize the correlation between negative wind stress and currents: the flow is upwind in this central part of the channel

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    Pressure differences (light line) between stations 1 and 2 (δp12) and stations 2 and 3 (δp23) in comparison with τs (heavy, top frame) and Ft, the index of tidal amplitude (heavy, bottom frame). The period for which current profile observations are available at stations 1 and 2 is indicated between the two frames

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    (top) Vertical structure of mean currents and of the principal EOF. (bottom) Time dependence of the principal EOF (solid) and of the axial pressure gradient (dashed)

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    (top) Vertical structure of mean currents and of the two largest EOFs. (bottom) Time dependence of the largest and second largest EOFs along with δp12

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    Vertical structure of the observed (left) wind-driven and (right) density-driven currents at (top) station 1 and (bottom) station 2. The profiles correspond to positive wind stress and density gradient

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    (left) Wind-driven and (right) density-driven streamline patterns from the solutions to Eqs. (A10) and (A13) in a basin with a parabolic bottom, with width equal to one-half of the length. The wind-driven solution is the same as given in Mathieu et al. (2002). The wind-driven flow is upwind in the center of the basin, and the density driven flow is downgradient in the center of the basin

  • View in gallery

    (left) Wind-driven and (right) density-driven streamline patterns for Laguna San Ignacio. The shading in the lagoon is related to depth; the darkest tone corresponds to a depth of 0.5 m, and the lightest tone corresponds to 10 m. Stations 1 and 2 are represented by the solid circles

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    A comparison of observed and modeled vertical structure of the (left) wind-driven and (right) density-driven currents at (top) station 1 (bottom) and station 2. The solid symbols refer to the northward flow, and the westward flow is shown by the open symbols

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Wind- and Density-Driven Circulation in a Well-Mixed Inverse Estuary

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  • 1 Unidad La Paz, Centro de Investigación Cientifica y de Educación Superior de Ensenada, La Paz, Mexico
  • | 2 Integrative Oceanography Division, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

Near the ocean, the residual circulation in Laguna San Ignacio, located on the Pacific coast of Baja California in Mexico, has been shown to be driven by tides. Here the subtidal circulation in the portion of the lagoon farther from the ocean is shown to be driven by the wind. The pressure difference between two stations, one near the closed end and the other midway along the central axis, is correlated well with the wind stress, in the sense that sea level rises downwind. Where the bathymetry is relatively simple, with a deep channel separating two shoal areas, the flow is upwind at the deepest part of the section, driven by the axial pressure gradient. In areas where the bathymetry is more complex, the direction of the observed flow is parallel neither to the local bathymetry nor to the applied wind stress. Linear theory qualitatively explains the major features of the wind-driven flow, including the relative strength of the pressure gradient to the wind stress, the direction of the flow, and the vertical structure, even in topographically complex areas. The residual circulation, after the wind-driven component has been removed, is assumed to be driven by the salinity gradient. That flow changes direction with depth. Where the bathymetry is simple, the near-bottom flow is toward relatively fresh water; flow is in the opposite direction closer to the surface. A linear model driven by a prescribed horizontal density gradient predicts downgradient flow at all depths near the deepest point of any section—a prediction that is qualitatively different from the observed flow.

Corresponding author address: Clinton D. Winant, Integrative Oceanography Division, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0209. Email: cdw@coast.ucsd.edu

Abstract

Near the ocean, the residual circulation in Laguna San Ignacio, located on the Pacific coast of Baja California in Mexico, has been shown to be driven by tides. Here the subtidal circulation in the portion of the lagoon farther from the ocean is shown to be driven by the wind. The pressure difference between two stations, one near the closed end and the other midway along the central axis, is correlated well with the wind stress, in the sense that sea level rises downwind. Where the bathymetry is relatively simple, with a deep channel separating two shoal areas, the flow is upwind at the deepest part of the section, driven by the axial pressure gradient. In areas where the bathymetry is more complex, the direction of the observed flow is parallel neither to the local bathymetry nor to the applied wind stress. Linear theory qualitatively explains the major features of the wind-driven flow, including the relative strength of the pressure gradient to the wind stress, the direction of the flow, and the vertical structure, even in topographically complex areas. The residual circulation, after the wind-driven component has been removed, is assumed to be driven by the salinity gradient. That flow changes direction with depth. Where the bathymetry is simple, the near-bottom flow is toward relatively fresh water; flow is in the opposite direction closer to the surface. A linear model driven by a prescribed horizontal density gradient predicts downgradient flow at all depths near the deepest point of any section—a prediction that is qualitatively different from the observed flow.

Corresponding author address: Clinton D. Winant, Integrative Oceanography Division, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0209. Email: cdw@coast.ucsd.edu

1. Introduction

Laguna San Ignacio is a well-mixed evaporative lagoon located on the Pacific coast of the Baja California peninsula in Mexico (Fig. 1). General features are described by Winant and Gutiérrez de Velasco (2003). Tides, winds, and the baroclinic pressure gradients associated with axial density gradients combine to drive the residual circulation responsible for the exchange with the ocean. These forcing mechanisms vary in amplitude in different parts of the lagoon. Here we show that the circulation in the northern half of the lagoon (where the channel depth is about 5 m) is driven by the wind and hypothesize that, when the wind relaxes, the flow is forced by the near-permanent axial density gradient associated with evaporation. Winant and Gutiérrez de Velasco (2003) show that, in the southern extremity at tidal periods, pressure and axial current fluctuations are about one-quarter of a period out of phase, so that the tidal wave is near standing. The current amplitude is about 1 m s−1 in the channels (depths ranging between 10 and 25 m), and the residual circulation depends on the internal Froude number, a measure of the relative strength of tidal and buoyancy forcing. Most of the time, the tidal forcing dominates and the circulation is laterally variable, with residual flow away from the ocean in the deeper channels. During neap tides, the residual circulation in the southern part of the lagoon is vertically stratified, with a denser near-bottom flow toward the ocean and a relatively fresh influx near the surface.

The flow induced by wind stress acting parallel to the long axis of a barotropic, nonrotating basin was first described by Csanady (1973). The circulation develops as the result of the competition among the imposed wind stress, bottom friction, and the axial pressure gradient required to maintain no net flux across any section, as illustrated in Fig. 2. In shallow water, where the effect of the pressure gradient is relatively weak, the flow is downwind, and the corresponding bottom stress balances the imposed wind stress. In the deeper sections, the pressure gradient has a relatively larger influence and the flow is upwind in such a way that the bottom stress and the wind stress are together balanced by the pressure gradient. This basic circulation pattern remains qualitatively unchanged by more sophisticated parameterizations of the vertical eddy diffusivity K (Hunter and Hearn 1987; Friedrichs and Hamrick 1996; Wong 1994). Mathieu et al. (2002) extend the linear model to a closed rectangular basin. In that model, the circulation near the middle of the basin is the same as described by Csanady (1973). Near the ends, lateral pressure gradients are set up to make the flow turn to accommodate the closed end in areas of length comparable to the width of the basin. The observations described here support the Mathieu et al. (2002) model qualitatively, even in areas where the bathymetry is complex. It is straightforward to show that the rotation of the earth can be neglected as long as the characteristic depth of the basin h0 is smaller than the Ekman depth δ ≈ 10 m (Winant 2004).

For a prescribed density forcing, Fischer (1972) first described the equivalent solution to that proposed by Csanady (1973) for wind forcing. That and similar solutions (Hamrick 1979; Wong 1994), sketched in Fig. 2, describe a flow that is similar to the flow induced by wind stress. The circulation results from the competition between the depth-dependent axial pressure gradient induced by the prescribed density gradient and a barotropic pressure gradient, associated with a tilt in the sea level, required to bring the net transport through any section to zero. The flow is unidirectional and toward high density (upgradient) on the sides of the basin and unidirectional toward low density in the deeper sections. It is straightforward to extend, as we do here, the Mathieu et al. (2002) model to density forcing as long as the density field is prescribed. In concept, a major difference exists between forcing by wind and by density in a basin that is closed at one end, in that the strength of the wind is set by conditions that are independent of the circulation, whereas the density field is modified by the circulation through the transport equation. It is obvious that the flow described by Fischer (1972), acting on a prescribed axial density gradient, will immediately develop lateral density gradients; these gradients will induce a secondary circulation that will modify the density and velocity fields, as shown by Smith (1976). The lateral circulation is similar to the gravity-driven flow described by Linden and Simpson (1986) at low Reynolds number. In the steady vertically integrated transport equation, the axial buoyancy flux is always balanced by the lateral gradient of the lateral buoyancy flux, induced by the lateral flow. The sense of that circulation is sketched in Fig. 2. Here we show that the observed density-driven velocity changes direction with depth, unlike predictions of a linear model driven by a prescribed density gradient, and hypothesize that the difference is due to lateral advection.

2. Methods

a. Laguna San Ignacio

Laguna San Ignacio extends inland about 30 km from the Pacific Ocean (Fig. 1). The bathymetry of the southern half is described by Winant and Gutiérrez de Velasco (2003). A shallow (mean depth ≈ 1 m), almost circular, pool (El Remate) that is dry at low tide is located at the northernmost extremity. Just south of El Remate, a 5-m-deep channel of varying width separates two broad shallow areas with depths of order 1 m at low tide on either side. Two islands are located on the eastern shoal. Near the closed end, the channel is narrow (about 200 m wide). It widens toward the south, until it occupies the full width at a location just south of the islands. Even farther south, the channel subdivides into channels that are about 10 m deep.

The observational program extended from December of 1997 through December of 1998. It included quarterly surveys to determine the distribution of watermass properties as well as moored observations. Five 2-week-long field trips were conducted during the period, when the moored array was serviced and watermass properties were surveyed.

Station 1 is located 500 m south from the northern extremity of the channel, at the deepest point of that section. Station 2 is located just south of the islands, in an area where the sectional area of the lagoon changes rapidly. Station 3 is located in the topographically complex area north of Punta Piedras, near the bottom of the easternmost of three channels, in a depth of 11.5 m. The region of concern here extends from station 1 south to station 2.

b. Atmospheric forcing

The weather in the area surrounding Laguna San Ignacio varies between the two patterns that characterize the Eastern Pacific at midlatitudes. During late autumn and winter it is modulated by upper-level synoptic activity, consisting mostly of eastward-propagating cyclones and anticyclones. In spring and summer, the stationary North Pacific anticyclone and the thermal low pressure area over the Sonora Desert combine to produce an extended period of energetic winds directed toward the southeast. On the large scale, these winds are steered parallel to the coast by the mountain range (maximum elevations about 2000 m) that runs down the axis of the peninsula.

The local wind is to the south, with typical speeds of order 10 m s−1. From December of 1997 to February of 1998, wind observations are available from La Laguna, on the eastern shore. The surface stress τs is estimated from wind speed and direction following the method proposed by Large and Pond (1981). The prevailing direction of the wind is from the north, with maximum stress values in excess of 0.1 Pa. No wind observations were made from March through May of 1998. From June through December of 1998, measurements were made at San Angel, located 10 km north of El Remate. Fluctuations in wind speed and direction are highly correlated between these sites, but the analysis presented here suggests that the San Angel observations somewhat underestimate the strength of the wind blowing over the lagoon.

c. Surveys

Seasonal hydrographic surveys were conducted during each field trip, during both spring and neap tides. A Sea-Bird Electronics, Inc., SBE-19 conductivity, temperature, and depth (CTD) sensor was cast from a small boat at about 50 stations on a regular grid extending over the entire lagoon. These surveys took about 10 h and were not synoptic relative to the tides. Highest salinities are observed near the closed end and vary seasonally (Winant and Gutiérrez de Velasco 2003). Minimum values, near 38 psu, occur in late winter, and maximum values, in excess of 40 psu, are observed in late August and September. For reference, the salinity in the adjacent ocean is 34 psu and varies little throughout the year (Lynn et al. 1982). Near the closed end, the water density exceeds that of the ocean by about 3 kg m−3, with little seasonal change because the effect of seasonally varying salinity is almost exactly compensated by seasonal changes in temperature.

d. Moorings

Low-profile frames were pinned to the bottom by long sections of pipe, jetted in by divers, at each station. Pressure (measured with the Paroscientific, Inc., 45 psia absolute pressure gauge) and temperature (measured with a YSI, Inc., model 44008 thermistor) were sampled on a 4-min interval for the entire observational period. An attempt was made to monitor salinity continuously, but the very high organic content of the rich lagoon waters limited the useful deployment of the salt sensors to little more than a week in each season. Because of the shallow water depth, the difference between surface and bottom pressure from density changes is small. We estimate the axial pressure gradient as the difference between bottom pressure at neighboring stations, divided by their separation. In the southern part of the lagoon, Winant and Gutiérrez de Velasco (2003) show that the residual circulation is forced by the tides: an index of the strength of the tidal forcing (Ft) is defined as the subtidal amplitude of the Hilbert transform of the pressure at station 3.

A single 1.2-MHz acoustic Doppler current profiler (ADCP) was used to measure currents. The instrument was mounted at the bottom at station 2 from 4 December 1997 to 20 February 1998, and at station 1 from 12 June to 31 August 1998. The ADCP measured horizontal currents at 0.5-m intervals, beginning 0.8 m above the bottom. Acoustic returns from the surface contaminate the ADCP to a depth of about 1 m. Tides change the position of the free surface by about 1 m relative to the bottom. As a result, reliable estimates of currents are available only to a depth of 2.2 m beneath mean sea level. Because the mean sea level is about 5 m at both stations, the current profiles have poor coverage of the near-surface flows. The ADCP returned observations every 10 min. Because the axis of the lagoon runs roughly parallel to north, and because the principal axes of the winds also coincide with north, we describe currents in terms of their x (positive toward the north) and y (positive toward the west) components; z is positive up from the surface. The current observations are subsampled at hourly intervals and are separated into tidal band and subtidal components by application of a filter whose cutoff frequency is set at 34 h.

3. Overview of the observations

Month-long time series of the axial component of the current measured at five depths at station 1 are illustrated in Fig. 3, along with the wind stress estimated from wind observations at San Angel. There is so little shear in the current field that the lines that represent the current at each depth are difficult to distinguish from each other. The current is made up of a tidal component, with amplitude of order 0.1 m s−1, and a low-frequency component of comparable amplitude. By plotting the negative of the wind stress over the currents, the figure makes clear that the low-frequency current is forced by the wind, in the sense that current is in the opposite direction from the wind.

Statistics of the observed currents, summarized in Table 1 for both stations, document the different response of the currents between sites that are located in relatively simple and in complex bathymetry. Near the closed end, at station 1, the direction of the time-averaged currents coincides closely with the direction of the major axis of both the residual and tidal-band currents. That direction is very close to the local direction of the axis of the channel. The mean current is positive, in the opposite direction from the mean wind stress. Fluctuating currents are highly polarized in the same direction. The amplitude of the tidal current changes little with depth. The subtidal currents are largest near the bottom. At station 2, the behavior of the tidal-band currents is similar to station 1, but the mean and subtidal currents are different. The mean flow and the amplitude of the major-axis fluctuations are about one-fifth times those at station 1. The mean is oriented almost at right angles to the axis of the channel and the wind (measured less than 1 km away). The ratio of major to minor axes of the subtidal flow is much smaller than at station 1, and the orientation of the major axis varies considerably with depth and is never close to the local orientation of the channel. The structure of the subtidal flow is the subject of the remainder of this paper.

4. The subtidal circulation

The forcing imposed by wind stress, buoyancy, or tides in a closed or semienclosed basin determines pressure gradients and the circulation. Because the pressure gradient varies according to the forcing, fluctuations in the pressure gradient on basin scales can be used to identify the dominant forcing. The axial pressure gradients acting on the northern and southern portions of the lagoon (δp12) and (δp23), estimated as differences in pressure between adjacent stations divided by their separation, are illustrated in Fig. 4. Between stations 1 and 2, δp12 is visibly correlated with τs. Between stations 2 and 3, δp23 is highly correlated with Ft, the index of tidal amplitude. Winant and Gutiérrez de Velasco (2003) have shown that, when the residual circulation is driven by tidal processes, the axial pressure gradient fluctuates with the spring–neap cycle, and we conclude that the residual circulation south of station 2 is mostly driven by the tides, although strong wind events, such as those that took place in December of 1997, can also affect δp23 and the residual circulation south of station 2.

These relationships are quantified in Table 2. The correlations with wind stress are computed for separate periods, corresponding to different locations of the anemometer and ADCP. The first is the period during which the ADCP was installed at station 2 and the wind observations were taken at La Laguna. The wind stress is significantly correlated both with pressure gradient estimates and with the major-axis current fluctuations at station 2. These are directed nearly at right angle to the wind (Table 1). The difference in the regression coefficient for each estimate of δp is consistent with the channel depths in the northern part of the lagoon being roughly one-half as deep as in the south.

For the second period, when the ADCP was installed at station 1 and wind observations were made at San Angel, the correlation between δp12 and τs/h0 is very high, but the regression coefficient is 2 times that during the first period. Because the La Laguna site is located on the shore of the lagoon, and because we show in section 5 that the regression coefficient computed during the first period is very close to the prediction of linear theory, we conclude that the San Angel wind observations accurately represent the time dependence but underestimate the amplitude of the wind over the lagoon, leading to the larger value of the regression coefficient. The correlation with δp23 is much less during this period, probably because of the lack of very large wind events such as took place during the first period. The correlation between wind stress and major-axis vertically integrated subtidal current is very large, and the signs of the correlation and regression coefficients are in the expected sense. Only δp23 is significantly correlated with Ft, confirming the hypothesis that tidal forcing has little effect on the residual circulation in the northern lagoon.

The vertical structure of time-averaged currents at station 1 is illustrated in Fig. 5. The mean subtidal axial flow is toward the closed end, with typical amplitudes of 0.05 m s−1. The lateral flow is very weak. The mean value of the wind stress is not zero, and we conclude that the mean currents owe their structure to the wind stress, with a small contribution from the buoyancy-driven flow. Empirical orthogonal functions (EOFs; Emery and Thomson 2001) provide a convenient way to describe the vertical structure of the circulation. At station 1, 98% of the variance in the combined axial and lateral currents is accounted for by the first EOF. The time dependence of that EOF is compared in Fig. 5 with δp12. The correlation between the two series is 0.96. When the wind blows toward the Pacific (negative τs), pressure is higher at station 2 (downwind) and the time dependence of the EOF is negative. The vertical structure of this EOF is illustrated in Fig. 5. The axial component is negative because the sign has been chosen to emphasize the visual correspondence with δp12. The negative values correspond to current fluctuations in the opposite direction from the wind: strong wind stress toward the Pacific corresponds to strong current toward the closed end. This is the expected direction at the deepest point in the channel (Csanady 1973; Hunter and Hearn 1987; Mathieu et al. 2002; Wong 1994).

At station 2 the structure of currents is different from station 1. Lateral currents are comparable to axial currents at all depths (Fig. 6), and there is significant shear throughout the water column: the mean lateral current changes sign from top to bottom. Two EOFs account for 89% of the variance. Only the largest EOF is significantly correlated (0.78) with τs and with δp12 (0.61). The second EOF is not significantly correlated with τs, δp12, or Ft. The lateral component of the largest EOF changes little with depth. Because the time dependence of the largest EOF is positively correlated with τs, the lateral component is toward the west for a positive wind stress. The axial component is in the same direction as τs near the surface and reverses direction near the bottom. We show in the following section that this structure is consistent with linear theory in an area where the depth contours (and the flow direction) change with axial position.

Linear theory, as described in the appendix, predicts similar vertical structures for the current response to wind and buoyancy forcing (Fig. 2), and, as a result, EOF analysis does not isolate the two different responses. These forcing mechanisms have different temporal behavior in the lagoon: to the best of our knowledge, the axial density gradient is steady while the wind stress fluctuates and even changes sign. Here we define the density-driven response to be the average of current observations at times when the wind stress is weak (|τs| < 0.01 Pa). We note that this condition occurs infrequently (Fig. 4). During the first period, when the ADCP was at station 2, the condition was met four times, and during the second period it was met five times. The statistical reliability of these estimated density-driven flows is not very high.

The wind-driven current is estimated as the difference between the observed current and the density-driven flow, as just defined. This wind-driven signal is correlated with δp12. At each location, the amplitude of the response to wind stress is then defined to be the product of the slope of the linear regression (Emery and Thomson 2001) between the wind-driven current and the wind stress and the standard deviation of the wind stress.

The vertical structure of the so-defined wind- and density-driven flows, at stations 1 and 2, is illustrated in Fig. 7. At station 1, the wind-driven current is unidirectional, aligned with the axis of the channel and in opposite direction from the wind stress, as expected, because linear theory predicts downwind flow over the shoals and upwind flow in the deeper areas. The vertical structure of the wind-driven response at station 2 is remarkably different. The north component of current reverses sign at middepth. It is directed downwind at the surface and upwind at depth. The lateral component is unidirectional, to the west for a positive wind stress. The density-driven flow at station 1 is aligned with the axis of the channel and reverses sign with depth: near the surface, the current flows toward the area of higher density. This behavior is in contrast with linear theories of density-driven circulation (Fischer 1972; Wong 1994) that predict a unidirectional flow away from the region of high density in the deeper channels. At station 2, the northward component of the density-driven flow is similar to what is observed at station 1, and the westward component is unidirectional (toward the west) and of a magnitude comparable to the other component. Although the observed response at station 1 is broadly compatible with theory, the remarkable feature at station 2 is the substantial unidirectional westward component of flow.

5. Linear theory

Following Mathieu et al. (2002), an equation for the transport streamfunction can be derived for wind- and density-driven flow, as shown in the appendix. The wind-driven solution (ψτ) given by Mathieu et al. (2002) for a basin that is one-half as wide as it is long and where the depth profile is parabolic is reproduced in Fig. 8. Near the central section of the basin (x = 0), the solution is as given by Csanady (1973) for an infinite-length basin: the flow is downwind on the shallow sides and upwind near the center (y = 0). The presence of closed boundaries at either end forces the flow to turn. The turning areas have lengths comparable to the width of the basin. Solutions for ψρ in the same basin are also illustrated in Fig. 8. The streamline pattern is qualitatively similar to the solution for wind-driven flow, with a tendency for streamlines to be closer near the center of the basin. That difference is related to the forcing by wind stress in Eq. (A8) being proportional to h−1 while the forcing by buoyancy is proportional to h. The length of the turning areas for the density-driven solution is the same as for the wind-driven flow.

Solutions for Laguna San Ignacio are computed by numerically solving Eq. (A8) in a closed rectangular basin using Gauss–Seidell iteration (Fausett 1999). One-half of the basin is assigned the depth distribution of the lagoon, and the other one-half is the mirror image. The streamfunction is set to zero at grid points on the edge or outside of the actual lagoon and at island locations. Experiments were carried out to determine how far south from station 2 the lagoon bathymetry needed to be replicated. We found that as long as the domain extended at least one basin width south of that station, there was no appreciable change in the computed ψ at or north of station 2. The solutions for ψτ and ψρ are illustrated in Fig. 9. Just as for the rectangular basin described above, the streamline patterns for wind- and density-driven flows are qualitatively similar in the lagoon geometry, although for density-driven flow the streamlines are concentrated in the areas of greater depth. Although station 2 is located close to the axis of the deepest channel, the direction of the vertically integrated flow is nearly along the east-to-west axis, in close agreement with the direction of the observed current at that station, as described in the previous section.

Given the transport streamfunction, the sea level η can be computed by integrating Eq. (A7). The ratio of the average pressure gradient ρgηx between stations 1 and 2 and τs/h0 can then be determined. The value given by the linear solution is 1.85, in remarkably close agreement with the regression coefficient for the period during which the ADCP was installed at station 2 (Table 2). Whereas predictions of velocities based on the linear theory require a priori knowledge of the vertical eddy diffusivity, the ratio of the pressure gradient to τs/h0 does not.

With ψ and η, the velocity u can be evaluated from either Eq. (A12) or Eq. (A15). The results are compared with the observations in Fig. 10. The reference depth h0 for the velocities is taken as the maximum depth in the model bathymetry (10 m), and we take K to be 10−3 m s−1, in the middle of the range suggested by Friedrichs and Hamrick (1996). At station 1, the wind-driven current is unidirectional, aligned with the axis of the channel and in opposite direction from the wind stress. The amplitudes of the observed and modeled currents are remarkably similar, the only discrepancy having to do with the thickness of the bottom boundary layer, which is less than 0.8 m (the height over the bottom of the lowest ADCP bin) in the observations. In the model, the shear is spread over the entire water column as is expected for a fully developed laminar flow. The modeled structure of the wind-driven current at station 2 is different from that at station 1, as in the observations. The westward component is unidirectional, and the northward component reverses, with the near-surface flow in the same direction as the wind stress. The structures of the modeled and observed currents are similar. In the model, the variable topography induces lateral pressure gradients that drive a net flow to the west (for a positive wind stress). Near the surface, the northward flow is in the same direction as the wind stress, and it reverses near the bottom. The modeled amplitude at station 2 is several times as large as that in the observations. This difference could be related to our choice of K, but a lower value would make for poorer agreement near station 1. Nonlinear effects associated with the turning and acceleration of the flow in this area could also explain the discrepancy.

The modeled density-driven flow at station 1 is unidirectional and almost aligned with the axis of the channel. This result is consistent with the analyses of Fischer (1972), Hamrick (1979), and Wong (1994) but is in marked contrast with the observations, in which the density-driven flow reverses direction at middepth. At station 2, the predicted density-driven current is also unidirectional while the observations show that the flow changes direction at middepth. Although the wind-driven linear model qualitatively reproduces the observed structure of the flow, the observed density-driven flow always reverses direction with depth whereas the modeled flow does not. This point is addressed further in the following section.

6. Discussion

The linear model [Eq. (A1)] ignores time-dependent and advective terms. Two intrinsic time scales characterize this problem: a frictional time Tf = h20/K that is about 7 h (with K = 10−3 m s−1) and the semidiurnal period of nearly 12 h. Because the wind stress typically persists over periods that are considerably longer than either of these times, the neglect of the unsteady term seems reasonable.

The relative importance of advection to friction is given by uh20/KL, where L is a representative length. With u ≈ |τs|h0/4ρK and with L = 10 km, the ratio is 0.25. We conclude that advection should not have much influence over the pressure difference between these stations or the velocity at station 1. In the wind-forced linear solution, near station 2 (Fig. 9), the vertically integrated flow turns sharply, and advection is surely an important part of the momentum balance. The discrepancy between observations and linear theory in that area is therefore no surprise.

The density-driven linear theory appears to represent the vertically integrated flow reasonably well but gives a poor representation of even the qualitative vertical structure of the flow: the observed density-driven flow reverses sign with depth at both stations whereas linear theory predicts that the flow direction should change little with depth. Given the few number of individual samples that make up the estimated density-driven flow, the lack of agreement could certainly be due to a poor estimate of the density-driven flow from the observations. We note that the two-layer structure is very similar to the structure of the density-driven subtidal flow described by Winant and Gutiérrez de Velasco (2003) in the southern part of this lagoon during neap tides. Another possible explanation for the discrepancy is that the linear model driven by a prescribed density gradient does not represent an important component of the dynamics. The transport equation is ignored as well as the attendant secondary circulation (as represented by the streamline sketched in the right-hand panel of Fig. 2) that develops as the density field adjusts to the circulation, as described by Smith (1976). That secondary circulation, through advection, will modify the velocity field in such a way as to decrease lateral gradients and reinforce vertical gradients. In principle, we could compare the amplitude of the lateral circulation at station 1 to the Smith (1976) model; however, that station is located at the center of the channel, just where the model predicts lateral velocities are zero, and the secondary circulation is vertical, toward the bottom. Although the ADCP does provide a measure of vertical velocities, the errors involved in the measurement of longer-period vertical flows are much larger than expected velocities. Our measurements are insufficient to test the Smith (1976) model. The sense of the lateral circulation is to redistribute downgradient axial velocity that is gathered toward the middle of the basin in Fig. 2. We suggest that this mechanism may explain the discrepancy between the linear theory as applied here and the observations.

7. Summary and conclusions

Winant and Gutiérrez de Velasco (2003) have shown that in the southern half of Laguna San Ignacio the subtidal circulation is driven by tidal processes, except at neap periods when the subtidal flow is vertically stratified and presumed to be forced by the buoyancy gradient. The significant correlation shown here between δp12 and τs/h0 demonstrates that, in the northern half, the circulation is forced by wind stress, and, when the winds are weak, we surmise that the circulation is driven by the buoyancy gradient. Near station 1, where the bathymetry is reasonably two dimensional, the flow in the deeper sections is upwind, driven by a sea level gradient set up to insure that there is no net axial flow across any section perpendicular to the axis, a feature of all linear models of wind-driven flows in semienclosed or enclosed basins. In the vicinity of station 2, where the topography of channels is complicated, observations show that the flow direction varies with depth and is not simply related to either local orientation of the bathymetry or the direction of the wind. The linear theory proposed by Mathieu et al. (2002) qualitatively explains the major feature of the wind-driven flow, including topographically complex areas and including qualitatively the vertical structure. The modeled and observed pressure difference agree quantitatively, and the model explains the changing flow direction with depth at station 2.

We have defined density-driven circulation as the average of the observed flow when the wind stress is very weak. This flow changes direction with depth: at station 1, where the axial variations in the bathymetry are reasonably small, the flow is directed toward fresher water near bottom and in the opposite direction closer to the surface. This observed structure is qualitatively different from predictions of linear models proposed by Fischer (1972), by Hamrick (1979), or by Wong (1994). An extension of the Mathieu et al. (2002) theory for density-driven flow that ignores modification of the density field through the transport equation also fails to reproduce the vertical structure quantitatively and qualitatively. The theory does appear to represent the vertically integrated flow reasonably well.

Acknowledgments

The work described here was the result of a collaboration between Centro de Investigatión Cientificas y de Educatión Superior de Ensenada (CICESE) and Scripps Institution of Oceanography to evaluate the potential environmental impact of the development of a sea salt production facility in Laguna San Ignacio. Funds were provided by Exportadora de Sal, S. A de C. V, Mexico. We are particularly grateful to J. Bremer, T. Miyauchi, and J. Brumm for their support and encouragement. We also acknowledge Paul Harvey, Charles Coughran, Douglas Alden, Martin Garcia Aguilar, and Hernando Torres Chavez, whose help in the filed made this work possible.

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APPENDIX

The Linear Model

Excluding rotation, the linearized, hydrostatic, steady-state, horizontal momentum equation for a well-mixed fluid is
i1520-0485-34-5-1103-ea1
with boundary conditions
i1520-0485-34-5-1103-ea2
where u is the horizontal velocity vector, τs is the wind stress vector, and η is the position of the surface relative to z = 0; ∇ρ is the horizontal density gradient, considered to be prescribed, and the depth is h(x, y). The vertical eddy viscosity K is taken to be constant. Lateral friction is assumed to be much smaller than vertical friction, and so lateral boundary conditions, beyond impermeability of the walls, are not required. The solution is
i1520-0485-34-5-1103-ea3
and the vertically integrated transport is
i1520-0485-34-5-1103-ea4
The vertically integrated momentum equation is
i1520-0485-34-5-1103-ea5
or, using Eq. (A4), τb becomes
i1520-0485-34-5-1103-ea6
Equation (A5) can then be used to express the elevation gradient:
i1520-0485-34-5-1103-ea7
The elevation gradient can be eliminated by taking the curl of Eq. (A7). In terms of a transport streamfunction ψ defined as k × ∇ψ = U, the resulting vorticity equation is
i1520-0485-34-5-1103-ea8
Define
i1520-0485-34-5-1103-ea9
where h0 is the maximum basin depth and B is a representative width. Then ψτ, the nondimensional streamfunction for the wind-driven problem, is the solution of
i1520-0485-34-5-1103-ea10
where t is a unit vector in the direction of τs, h* = h/h0, and ∇* is the dimensionless horizontal gradient operator. With
i1520-0485-34-5-1103-ea11
the nondimensional wind-driven velocity is
i1520-0485-34-5-1103-ea12
In a similar way, ψρ, the nondimensional streamfunction for the density-driven flow, solves
i1520-0485-34-5-1103-ea13
where r is a unit vector in the direction of ∇ρ. Then
i1520-0485-34-5-1103-ea14
and the nondimensional buoyancy-driven velocity is
i1520-0485-34-5-1103-ea15

Fig. 1.
Fig. 1.

Location map. Moorings were deployed at locations noted by open circles, and the locations of anemometers are shown by solid circles. Wind measurements are available at La Laguna for 1 Dec 1997–15 Feb 1998 and at San Angel for Jun–Dec 1998. The grayscale for depth saturates at 10 m to emphasize the depth distribution in the northern part of the lagoon. The inset map shows the location of Laguna San Ignacio on the Baja California peninsula

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 2.
Fig. 2.

(left) Wind- and (right) density-driven flow in a section near the center of a rectangular basin. The view is toward positive x, with positive wind stress and ρx. The contours and shading represent the axial velocity. Shaded areas correspond to negative axial flow: either upwind or downgradient. The contour interval is 0.1. The sense of the lateral circulation (Smith 1976) in the density-driven flow is represented by the heavy streamline

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 3.
Fig. 3.

Axial currents at station 1 during July of 1998. The light lines represent the current at 5 depths; there is so little difference between currents measured at different depths that these lines can barely be distinguished. A positive current is toward the closed end. The heavy line represents minus the wind stress at San Angel. The sign of the wind stress is chosen to emphasize the correlation between negative wind stress and currents: the flow is upwind in this central part of the channel

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 4.
Fig. 4.

Pressure differences (light line) between stations 1 and 2 (δp12) and stations 2 and 3 (δp23) in comparison with τs (heavy, top frame) and Ft, the index of tidal amplitude (heavy, bottom frame). The period for which current profile observations are available at stations 1 and 2 is indicated between the two frames

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 5.
Fig. 5.

(top) Vertical structure of mean currents and of the principal EOF. (bottom) Time dependence of the principal EOF (solid) and of the axial pressure gradient (dashed)

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 6.
Fig. 6.

(top) Vertical structure of mean currents and of the two largest EOFs. (bottom) Time dependence of the largest and second largest EOFs along with δp12

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 7.
Fig. 7.

Vertical structure of the observed (left) wind-driven and (right) density-driven currents at (top) station 1 and (bottom) station 2. The profiles correspond to positive wind stress and density gradient

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 8.
Fig. 8.

(left) Wind-driven and (right) density-driven streamline patterns from the solutions to Eqs. (A10) and (A13) in a basin with a parabolic bottom, with width equal to one-half of the length. The wind-driven solution is the same as given in Mathieu et al. (2002). The wind-driven flow is upwind in the center of the basin, and the density driven flow is downgradient in the center of the basin

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 9.
Fig. 9.

(left) Wind-driven and (right) density-driven streamline patterns for Laguna San Ignacio. The shading in the lagoon is related to depth; the darkest tone corresponds to a depth of 0.5 m, and the lightest tone corresponds to 10 m. Stations 1 and 2 are represented by the solid circles

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Fig. 10.
Fig. 10.

A comparison of observed and modeled vertical structure of the (left) wind-driven and (right) density-driven currents at (top) station 1 (bottom) and station 2. The solid symbols refer to the northward flow, and the westward flow is shown by the open symbols

Citation: Journal of Physical Oceanography 34, 5; 10.1175/1520-0485(2004)034<1103:WADCIA>2.0.CO;2

Table 1.

Current statistics. The subtidal current is obtained by low-pass filtering the observations with a cutoff period of 34 h, and the tidal band is the product of high-pass filtering with the same filter. All angles are measured in degrees relative to north. Speeds and major- and minor-axis units are meters per second. Depths are in meters. Statistics for the vertically averaged current are in the last row for each station

Table 1.
Table 2.

Correlations between response (pressure gradients and major-axis subtidal currents) and forcing (τ s /h0 and Ft). The correlation with wind stress is computed for three distinct periods, corresponding to changes in location of the anemometer and to availability of current observations. The reference depth h0 is taken as 5 m, the average of the maximum depth in the channel between stations 1 and 2; u1 designates the major-axis vertically averaged subtidal current at station 1, and υ 2 is the major-axis vertically averaged subtidal current at station 2. The regression coefficient (ratio of response to forcing) is included in parentheses if the correlation is significantly different from zero at the 95% confidence level. Correlations with Ft are computed over a year-long period

Table 2.
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