Secondary currents in a curved, stratified, estuarine channel

Transcription

1 JOURNAL OF GOPHYSICAL RSARCH, VOL. 106, NO. C12, PAGS , DCMBR 15, 2001 Secondary currents in a curved, stratified, estuarine channel Jessica R. Lacy 1 and Stephen G. Monismith nvironmental Fluid Mechanics Laboratory, Stanford University, Stanford, California, USA Abstract. This paper presents a study of secondary circulation in a curved stratified channel in northern San Francisco Bay over a 12.5-hour tidal cycle. Secondary currents were strong at times (varying by up to 35 cm/s from top to bottom) but relatively transient, as the balance between centrifugal and lateral baroclinic forcing changed over time. The short travel time around the bend did not allow a steady state balance to develop between centrifugal and lateral baroclinic forcing. During the flood tide the confluence of two streams with different velocities produced a strong lateral gradient in streamwise velocity. As a result, lateral advection was a significanterm in the streamwise momentum balance, having the same order of magnitude as the barotropic and baroclinic pressure gradients, and the frictional terms. During the first part of the ebb, secondary currents were induced by lateral baroclinic forcing. The direction of the secondary circulation reversed later in the ebb, as the baroclinic forcing became weaker than the centrifugal acceleration. The gradient Richardso number showed that stratification was stable over most of the tidal cycle, decreasing the importance of friction and allowing secondary currents to persist. 1. Introduction The complex bathymetry and topography found in many estuaries and tidal channels can produce significant secondary currents by several different mechanisms. Differential advection of salt in channels with a cross section of varying depth produces a lateral salinity gradient which drives lateral baroclinic flow. Centrifugal acceleration in a curved channel also produces a distinct pattern of secondary circulation. Strong secondary currents, when present, play an important role in mixing out lateral and vertical gradients in momentum, salinity, and other scalars, and reducing longitudinal dispersion. A reduction in spatial gradients of momentum and salt influences the momentum balance, while mixing of nutrients, organic material, and phytoplankton has important biological consequences. Kalkwijk and Boot.'/ [1986] present the analytical solution for curvature-induced transverse flow, which compares well with laboratory results. For a logarithmic streamwise flow profile the centrifugal acceleration toward the outer bank is maximum at the surface and decreases nearly linearly with depth. The centrifugal acceleration piles up water against the outer bank, creating an opposing pressure gradient. The resulting transverse velocity profile is directed toward the outer bank in the upper part of the water column and toward the inner bank near the bottom. and found centrifugal acceleration in near balance with transverse baroclinic forcing. They observed a downstream progression of three regions: first a region dominated by centrifugal acceleration, next a region of decreased transverse circulation, and finally, a region dominated by lateral baroclinic forcing. Seim and Gregg [1997] analyzed a stratified flow around a 120 ø bend in Puget Sound and found that secondary circulation was weak when streamwise currents were less than 0.75 m/s. In this range of velocities, lateral baroclinic forcing balanced the centrifugal acceleration. However, the extent of vertical stratification at a site limits the maximum possible lateral baroclinic forcing; if the centrifugal acceleration exceeds this level, the centrifugal-baroclinic balance cannot hold. By assuming a balance in the crosschannel momentum between centrifugal acceleration and the baroclinic pressure gradient, Seim and Gregg identify the condition for centrifugal acceleration to be strong enough to overturn the density field. This condition is expressed as a Froude number Fr, given by 2 FF 2 : Us g'h ' where ux is the streamwise velocity, is the depth average of u, g' is the reduced gravity, and h is the channel depth. The value of the Froude number at the site was consistent with the observed Secondary currents can be difficult to resolve in the field because they are typically an order of magnitude smaller than streamwise threshold of 0.75 m/s for the development of centrifugally induced velocities. Geyer [1993] investigated transverse velocities due to secondary circulation. curvature in a tidal flow around a headland. Dronkers [1996] In this paper we present measurements of secondary circulation measured transverse velocities in a curved, weakly stratified in a narrow, stratified, curved channel which flows between the channel in the Volkerak estuary. The velocities were stronger than shoals of Honker Bay and Suisun Cutoff, in Suisun Bay, in would be predicted based on the curvature of the channel for an northern San Francisco Bay. At this site, a steady state balance unstratified flow. Dronkers [1996] and Chant and 145'lson [1997] between centrifugal acceleration and the baroclinic pressure grashow that transverse flow due to curvature in a stratified water dient did not develop, because of the short travel time around the column produces a lateral salinity gradient and baroclinic forcing bend. The lateral salinity gradient was produced primarily by which oppose the curvature-induced flow. Chant and Wilson differential advection and varied over the course of the tidal cycle. measured secondary circulation in a strongly stratified estuary The time-varying balance between lateral baroclinic and centrifugal forcing produced short periods of strong secondary circulation, in both the clockwise and counterclockwise directions. 1Now at U.S. Geological Survey, Menlo Park, California, USA. Copyright 2001 by the American Geophysical Union. Paper number 2000JC /01/2000JC $ Field Observations 2.1. Study Site Snag Channel is in Suisun Bay, the easternmost subembayment of San Francisco Bay, immediately down estuary from the 31283

2 31284 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL ' ' 38 00' - Suisun Bay 37 Reserve Fleet / Channel.,- // 30' --l reeman San Francisco Bay Rye r SUisun Cutoff Channel x /, Snag Figure 1. Suisun Bay. The 7 m isobath is shown. Sacramento-San Joaquin Delta. Suisun Bay is typically fresh during periods of high Delta outflow in winter and spring [Walters et al., 1985]. During the dry summer and fall, salinity from the Pacific Ocean intrudes into Suisun Bay, and intermittent stratification develops [Monismith et al., 1996; Stacey et al., 1999]. Suisun Bay consists of channels with an average depth of 10 m, broad shallows (2 m average depth), and islands (Figure 1). The shallow regions, particularly Grizzly Bay and Honker Bay, are important ecologically because of their high primary productivity. Snag Channel connects Suisun Cutoff and Honker Bay. It is narrow (approximately 200 m wide) and has no shoals. In the section of channel adjacento Honker Bay there is a bend to the right with a radius of curvature of approximately 1000 m. The study was conducted within this curved region (Figure 2). The local channel depth is approximately 20 m Methods On October 30, 1998, we collected transects of velocity and salinity profiles across Snag Channel over a 12.5-hour (M2) tidal cycle (from 0650 to 1915 LT). Measurements were taken at two transects (Figure 2) to observe the evolution of the flow as it traveled around the bend. Transect 1 was 170 m long, and transect 2 was 150 m long. The two transects were 165 m apart on the west side and 135 m apart on the east side. Velocities were measured using a boat-mounted acoustic Doppler current profiler (ADCP) (600-kHz RD Instruments Workhorse Sentinel). The two transects were traversed every 15 min. It took 2.5 min to cross the channel, and the second transect was started 5 min after the first. ach recorded measurement (ensemble) averaged 16 water pings and 8 bottom pings taken over 3.5 s, while traveling 4 m. The vertical bin size was 50 cm. In processing, velocity data were averaged over two ensembles and two vertical bins to reduce noise. The number of ensembles per transect varied because of inconsistent boat speed. In order to average results over time, velocities were interpolated to evenly spaced profiles, 16 for transect 1 and 14 for transect 2, each representing 10 m of horizontal distance. The tidal range on the day of the study was approximately 1 m. The change in tidal elevation was not accounted for in temporal averaging, since it corresponded to a maximum of one depth cell (after vertical averaging). Conductivity, temperature, depth (CTD), and suspended solids measurements were taken with a Seabird profiler (SB-25) across transect 1 every 30 min and across transect 2 at six times of -] Transect 1 00m, Dutton Island Snag Island ' 12" 4 Figure 2. Study site.

3 LACY AND MONISMITH: SCONDARY CU.RRNTS IN AN STUARIN CHANNL a) Delta outflow I I I I I Jun 1 Jul 1 Aug 1 Sep 1 Oct 1 Nov 1 Date in 1998 b) Water surface elevation Days since Jan 1, 1998 Figure 3. (a) Delta outflow from June to November and (b) water surface elevation (WS) from October 15 to November 4, Delta outflow was estimated by the Department of Water Resources' WSs are from the CTD deployed near Freeman Island. 80 Dutton Island X' ransect _43o1N % 0 o, crn/s Time, hours Figure 4. Time series of tidal velocities at transect 1, averaged over'the cross section. Figure 5. Magnitude and direction of depth-averaged velocity in the centers of the two transects during maximum flood (dashed vectors) and maximum ebb (solid vectors).

4 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) Tr 1, tidally averaged velocity, cm/s 0 Tr 2, tidally averaged velocity, cm/s œ-1o ' ' c) Tr 1, flood tide average velocity, cm/s 0 d) r 2, flood tide average velocity, cm/s //( 5 ß 50 1 O0 150, Tr 1, ebb tide average velocity, cm/s Tr 2, ebb tide average velocity, cm/s O Distance across channel, m Distance across channel, rn Figure 6. (a and b) Tidally averaged, (c and d) flood, and (e and f) ebb velocities in the two transects, looking west. stronger stratification. ach pass consisted of equally spaced casts, four across transect 1 or three across transect 2. Fixed CTDs were deployed up and down estuary from the study site (Figure 1) from October 2 to November 23, to measure the longitudinal salinity gradient before and during the study. The Freeman Island CTD was,,1.5 km from the study site; the CTD in Honker Bay (at station Hdol) was 1 km from the site. In an earlier study of circulation and salt transport in Honker Bay we deployed an ADCP in Snag Channel from December 20, 1996, to March 17, 1997, and again from May 12 to August 3, Both deployments were within 50 m of transect 1; the first was down estuary and the second was up estuary from the transect. The winter and spring of 1998 were very wet. During the summer, Delta outflow was higher than usual (Figure 3a), which delayed salinity intrusion into Suisun Bay. The study was conducted at the end of neap tides, as tidal energy began to increase. In San Francisco Bay, diurnal inequality is much greater during neap tides than during spring tides. The study period spanned the long flood and shorter ebb tide on day 303 (Figure 3b). Conditions were very calm throughouthe day. 3. Results 3.1. Streamwise Velocities Figure 4 shows the tidal velocities during the study. At the start of data collection the tide was beginning to flood (positive velocity). For each transect a principal direction was defined which maximized the tidally and spatially averaged streamwise flow. Between transect 1 and transect 2 the principal direction changes from 150 ø to 134 ø because of the curvature in the channel. Magnitude and direction of the depth-averaged maximum ebb and flood flows are shown in Figure 5. The bathymetry in Figure 2 shows that during flood tides the flow at transect 1 is completing a right-hand bend as it enters the left-hand bend that

5 ,,,, LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUARIN CHANNL is the focus of this study. As a result, the flow direction changed a) Transect 1 16 ø between the two transects during the flood tide, whereas during the ebb tide the change in direction was only 5 ø. Separate ',q principal directions were used for flood and ebb tide data from transect 1 because the ebb and flood directions differed by 171ø rather than 180 ø. Tidally averaged velocities for transects 1 and 2 are shown in Figure 6. In all plots of the transects the southwest bank is on the left, and the northeast bank is on the right, so that the flood -10 direction is out of the page. The spatially averaged residual current was 12.1 cm/s at transect 1 and 12.3 cm/s at transect 2, in the flood direction. Data collected in 1997 show that residual currents in Snag Channel and all of Honker Bay are directed up estuary during summer when Delta outflow is low [Lacy, 2000]. The residual current increases with depth in both transects, consistent with longitudinal baroclinic forcing. In transect 2 the region of maximum residual velocity bulges upward over the Distance across channel, rn deepest part of the channel, and the regions of minimum residual velocity are concentrated at the sides. This pattern is consistent b) Transect 2 with the structure created by the interaction of baroclinic circulation with a triangular bathymetry [Wong, 1994; Friedrichs and Hamrick, 1996]. Transect 1 exhibits a similar pattern, except in the shallows on the right. Within 10 m of the northeast bank there are two narrow (less than 3 m wide) islands in between the two transects. The islands extend from 20 m north of transect 2 to ½ 5 m south of transect 1. During the ebb tide, when transect 1 was downstream of the islands, a region of back-circulation developed in the wake of the islands which decreased and sometimes reversed flow in the shallows. The islands influenced the velocities during the ebb across almost one third of the channel, a region much wider than the islands themselves. This perturbation accounts for the large positive residual current seen near the right bank in Figure 6a. 0 5O IO0 The structure of the streamwise flow differs significantly Distance across channel, m between the flood and ebb tides (Figures 6c-6f). During the flood tide the region of highest velocity is near the bottom and is inclined Figure 7. Tidally averaged transverse velocities at (a) transect 1 againsthe inside (right) bank. During ebb the highest-magnitude and (b) transect 2. velocities are at the top Secondary Currents 6 I 1 h Un, max,-,- Rs, (1) where Rs is the radius of curvature (positive indicates clockwise curvature for positive streamwise flow), assuming a logarithmic streamwise velocity profile and a parabolic eddy viscosity profile [Geyer, 1993]. For our data, (1) gives un, max : +9 cm/s during the flood tide and +6 cm/s during the ebb tide. However, the combined effects of centrifugal and baroclinic forcing produced transverse currents stronger than this predicted maximum during several periods. The conditions producing these transient intervals of strong secondary circulation are addressed in section 4. Lateral velocities averaged over the M2 tidal cycle were weak and did not exhibit the expected pattern of secondary circulation in flow around a bend (Figure 7). The structure of the residual transverse velocity is similar for the two transects, with positive velocities to the right of the center, negative flows to the left, and low magnitudes throughout. (For transverse velocities, positive is toward the inner bank.) The strongest transverse residual currents 3.3. Salinities are in the shallows close to the inner bank. Tidally averaged vertical velocities had magnitudes less than 1 cm/s throughout The time series from the fixed CTDs show that the study was the cross section for both transects. Both transects exhibit a region conducte during a period of increasing salinity (Figure 8a). Figure of upwelling over or to the right of the deepest portion of the 8b compares salinities at 7 m depth from the profiles taken at channel. transect 1 to the salinities at the fixed stations. The longitudinal Although tidally averaged transverse velocities were small, salinity gradient during the study averaged ppt/km (Figure relatively strong secondary circulation occurred at several times 8c). It was weakest early in the flood tide and was strongest about during the study. For example, during one hour of the deceleration halfway through the ebb tide. The longitudinal salinity gradient was calculated from the data from Freeman Island and transect 1, of the ebb, transverse velocities in transect 2 ranged from +18 cm/s at the bottom of the water column to -19 cm/s at the top. The because the periodic flow of fresher water from the main channel maximum transverse velocity produced by centrifugal acceleration into Honker Bay at the beginning of the flood tides produces a can be estimated as somewhat irregular salinity signal at Hdol [Lacy, 2000]. The strong variation in the longitudinal salinity gradient over the course of the tidal cycle is consistent with other observations in Suisun Bay [Stacey, 1996]. This type of variation in baroclinic forcing on the tidal timescale is not accounted for in standard analyses of estuarine circulation, such as that presented by Hansen and Rattray [1965]. The vertical gradient in tidally averaged salinity at transect 1 was approximately 0.03 ppt/m (Figure 9); the lateral gradient was negligible. Stratification was stronger during ebb than it was

6 31288 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL 10 8 a) Salinity at fixed CTDs from October 18 to November 1 I I I I I I Freeman I _ Hol I Days since January t, 1998 b) Salinities at 7 m depth during experiment 7 6 4, 2 \..,!+ + Freeman Hdol 1 + Trl Days since January 1, 1998 c) Salinity gradient from Freeman to Transect 1 during experiment I I I I i I I I I o Days since January 1, 1998 Figure 8. Time series of salinity: (a) salinity at fixed CTDs from October 18 to November 1, (b) salinities at 7 m depth during experiment, and (c) salinity gradient from Freeman to transect 1 during experiment. during flood. Maximum stratification occurred during the acceleration of the ebb, before the peak in the longitudinal salinity gradient. 4. Discussion 4.1. Interaction of Curvature and Buoyancy The structure of the streamwise and transverse velocities in Snag Channel is influenced by curvature in the channel, baroclinic forcing, the shape of the cross section of the channel, and interactions between these factors. The transverse momentum equation for an unstratified flow in a curved channel can be written [Kalkwij'k and Booij, 1986] 2 C l.d C ltn Tb, n OQUn Olin Olin lls2 -- Us (2)

7 LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUAR1N CHANNL = - 0[ a) Tidally averaged salinities I, \ O 3' / 1 0 lz O 160 b) Salinities averaged over flood '7' c) Salinities averaged over ebb ' '.7._ 4.-i----- _ '.. - 4,4 2O Figure 9. (a) Tidally averaged, (b) flood, and (c) ebb salinities in ppt at transect 1. the depth-dependent baroclinic pressure gradient from the depthaveraged mean, Ou, Ou, Ou, 2_ U s-b-j-s - U s-b-j-s q- us Rs U s + g o p(z,)az, _ O p(z,)az, (ix o /z o ) p0¾ ' -=ø' where z is the depth below the surface and p0 is the mean density. In a stratified flow around a bend, the centrifugal acceleration pushes the fresh water at the top toward the outside of the bend. This creates a lateral salinity gradient and baroclinic forcing which opposes the centrifugal acceleration [Dronkers, 1996; Chant and 145'/son, 1997; $eim and Gregg, 1997]. If the centrifugal forcing is not strong enough to overturn the stratification, it can, at steady state, be balanced by lateral baroclinic forcing rather than by frictional forces. This inviscid transverse momentum balance is expressed as Rs P0 g o 0 0/z0 ) p½')dz'. We calculated the two terms in this equation from the transect 1 data. Plate l a shows the centrifugal forcing, Plate lb shows the lateral baroclinic forcing, and Plate 1 c shows the sum of the two. We used Rs for the left-hand bend close to Honker Bay (-920 m) in calculating the centrifugal forcing. Plates lb and 1 c cover only the upper 13 m of the water column, the depth for which a lateral density gradient could be calculated. Note that missing data at 0800 and 1630 LT are represented in Plate lb by zero values at all depths. The average uncertainty in the values of centrifugal forcing shown in Plate 1 is 2.39 x 10 m/s 2 (maximum uncertainty 5.0 x 10 m/s2), and the uncertainty the lateral baroclinic forcing ranges from 2.75 x 10 at the top to 4.34 x 10 m/s 2 at the bottom of the water column (see Appendix A for details). The nonzero values in Plate l c show that the baroclinic and centrifugal forcing are not in balance. Instead, the net forcing produces secondary circulation. In the time it takes for the flow to go around this short bend, the momentum cannot reach a steady state inviscid balance between centrifugal and baroclinic forcing. The timescale Tx for achieving steady state is determined by the cross-channel baroclinic adjustment time and can be estimated from the internal wave speed as where s indicates the streamwise direction, n indicates the cross-channel direction, Az is the vertical eddy viscosity, q-, is where B is the channel width, c is the internal wave speed, and the bottom shear stress, and p is the density. This equation H is the depth of the upper layer in a two-layer system [Chant results from subtracting the depth-averaged transverse mo- and 'lson, 1997]. During most of the experimenthe vertical mentum equation from the depth-dependent equation. It stratification was 0.5 ppt and was confined to the upper 5-8 neglects transverse and vertical advection and Coriolis m. For these conditions, T was 16 min, while the advective forcing. time to flow around the bend (using a distance of 400 m) was Kalkwijk and Booij [1986] report the analytic solution to (2), 5 min during peak flood flows and 9 min during peak ebb assuming a logarithmic streamwise velocity profile and parabolic flows. eddy viscosity. The predicted transverse velocity profile is almost linear, with maximum velocity toward the outside bank at the top and toward the inside bank at the bottom. However, 4.2. Flood Tide Geyer [1993] showed that the linear transverse profile is Plate 1 shows that during the flood tide before 1000 LT the strongly dependent on the assumption of a logarithmic stream- lateral momentum is governed by centrifugal forcing. The direction wise velocity profile. In Snag Channel the velocity profiles clearly deviate from logarithmic, particularly on the flood tide (Figure 6). Lateral baroclinic forcing is included in the transverse momentum equation (2) by adding to the left-hand side the deviation of of centrifugal forcing and of the observed secondary circulation (Figure 10) during this time is opposite to that expected for a lefthand bend: The positive forcing at the top of the water column is directed toward the inner bank. The clockwise centrifugal response shown in Plate 1 was produced by the extremely nonlogarithmic B Ts B/c,- gv/_g_7_, (3)

8 31290 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL -2 a) Centrifugal forcing x 10 ' e b) Lateral baroclinic forcing x c) Sum of centrifugal and baroclinic forcing x Time, hours Plate 1. Time series of (a) centrifugal forcing, (b) lateral baroclinic forcing, and (c) the sum of the two at transect 1, in m/s 2. Missing data for baroclinic forcing at 0800 and 1630 LT are represented by zeros. streamwise velocity profiles shown in Figure 10c. Since velocities increased with depth in the upper m of the water column, maximum centrifugal acceleration (toward the outer bank) occurred at 12 m depth rather than at the surface. In addition, the right-hand bend upstream of transect 1 likely contributed to the observed clockwise circulation. Later, from 1000 to 1100 LT, the direction of secondary flow changed to counterclockwise (Figure 10b). Plate 1 shows that the reversal was caused by lateral baroclinic forcing. This period of strong secondary circulation did not persist; transverse circulation weakened as the flood decelerated. During the flood tide the transecting site was just downstream of the confluence of Snag Channel and the channel between Freeman and Snag Islands. We observed a surface front between the two water masses for several hours. The velocity data show that the front marked the boundary between faster-moving water traveling along Snag Channel and slower-moving water on the southwest side of the channel, which flowed in through the opening between

9 _. LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUARIN CHANNL a) V and W, Transect 1, hr b) V and W, Transect 1, hr c 7:cm/s V 20 m/s ' ' i c) U profiles, Transect 1, hr d) U profiles, Transect 1, hr Velocity, cm/s Velocity, cm/s Figure 10. (a and b) Secondary currents and (c and d) streamwise velocity profiles during the flood tide. Freeman and Snag Islands. The gradient in along-stream velocities at the confluence of these two streams produced lateral advection which influenced the streamwise momentum balance in that region. The streamwise momentum equation can be written Oux Oux Oux Oux Or/ g Op 10w ow+s7;+"fy+zz+gox p0 where g is gravitational acceleration, r/ is the water surface elevation, and q- is the total shear stress. The first term in the equation is acceleration, the second through fourth terms account for advection or inertia, the fifth and sixth terms represent the barotropic and baroclinic pressure gradients, and the seventh term accounts for bottom friction and Reynolds stresses. To examine the influence of secondary circulation and lateral advection on the momentum balance, we compare the magnitude of the lateral and vertical advection terms (calculated from the data) to the magnitudes of the other terms in the momentum equation. While data are not available to make precise estimates of these other terms, order-of-magnitude estimates serve to demonstrate that lateral advection cannot be neglected in this case. To estimate the barotropic pressure gradient, the gradient in water surface elevation was calculated from the tidal range on the day of the experiment and the local wave celerity: (4) po lop Ox - g xx Or/ - g (3-7 0r/) _ g 7 [2½ cos (_2f_t) ' where T is the M2 tidal period,.4 is the amplitude of the tidal wave, and c is the wave celerity. We determined c to be 7.2 m/s by harmonic analysis of time series measurements of r/taken in the vicinity of the study area in 1997 [Lacy, 2000]. On the day of the study,.4 was 0.75 m (see Figure 3). Using these values and averaging the magnitude of Or//Ot over the tidal cycle yields an average magnitude of the barotropic pressure gradient of 9.08 x 10 -s m/s 2, with a maximum during the tidal cycle of 1.43 x m/s 2. The tidally averaged baroclinic pressure gradient was estimated from the salinity records shown in Figure 8 as 4 x 10 -s m/s 2 at the bottom of the water column and 4 x 10-6 m/s 2 at the top. Total shear stress q- was estimated using p0 * ' where u. is the friction velocity, H is the total depth, and Ca is the drag coefficient. Using Ca = , the last term in (4) was estimated at 3 x 10 -s m/s 2. The lateral and vertical advective terms were calculated from the data. Figure 11 shows the lateral advective term for the two flood tide periods shown in Figure 10. In regions of the transect where the absolute value of the lateral advective term is less than 10 -s (shown in white in Figures 1 l a and 1 lb), we could neglect the advective term relative to the baroclinic, barotropic, and frictional terms. However, both the lateral and vertical advective terms were of order 10-4 in most of the water column, not only during the

10 31292 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) Lat adv, m/s 2, Tr 1, hr x 10-4 b) Lat adv, m/s 2, Tr 1, hr X 10 ' œ c) U in cm/s, Tr 1, hr d) U in cm/s, Tr 1, hr 0 0 '/4/1///// I 'X I x.. ) o ' ' ' f) U in cm/s, Tr 2, 1 00_ 1100 hr O O0 Distanco, m Distanco, m Figure 11. (a and b) Lateral advection and (c-f) contours of streamwise velocity during the flood tide. times shown in Figure 11 but throughout much of the tidal cycle. The average uncertainty the lateral advective term is 7 x 10 -s m/s 2 (standard deviation is 5 x 10), as shown in Appendix A. These results show that in this flow, lateral and vertical advection contribute significantly to the streamwise momentum balance. The lateral and vertical advective terms are of the same order of magnitude as, or are larger than, the pressure gradient and frictional terms in much of the water column. The importance of the advective terms indicates that the momentum balance commonly assumed for tidal channel flows (between the streamwise pressure gradient and the frictional terms) does not hold for estuaries with complex topographies. To close the momentum balance in Snag Channel, the lateral and vertical advective terms must be included. High magnitudes of the lateral advective term occur in regions where strong lateral gradients in streamwise velocities coincide with strong transverse velocities. arly in the flood, there was a strong gradient in u at the front between the slower water entering through the opening between Freeman and Snag and the faster water in Snag Channel. Transverse velocities near the surface were positive. The positive gradient in u and the positive v together

11 ,, LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) V and W, Transect 2, hr b) V and W, Transect 1, hr / :m/s c) U in cm/s, Transect 2, hr ' ' d) U in cm/s, Transect 1, hr ½ e) U profiles, Transect 2, hr f) U profiles, Transect 1, hr ½ ½ Velocity, cm/s Velocity, cm/s Figure 12. (a and b) Secondary currents, (c and d) contours of along-stream velocity, and (e and f) along-stream velocity profiles, LT. produced a positive lateral advective term on the southwest side of the channel (Figure 11a). The influence on the flow can be seen by comparing Figures 11c and 11e: The slower moving water was advected from the southwest side out into the channel as the water while a negative gradient in ux and positive u, produced the negative region on the right. In both cases, the negative lateral advection transported higher-momentum water from the center of the channel toward the sides and intensified along-stream velocities flowed from transect 1 to transect 2. The reduction in along-stream (Figures 11 d and 11 f). velocities in the upper part of the water column created the nonlogarithmic profiles observed during this period. From 1000 to 1100 LT the transverse circulation was counter bb Tide clockwise. A positive gradient in ux and negative u, combined to produce the negative lateral advection on the left of Figure l lb, During the ebb the secondary circulation was stronger and more consistent between the two transects than it was during

12 ,,,, LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) Transect 2, 1320 hr b) Transect 1, 1340 hr 5 t-- I' 5.4% -10-2O -2O i i i i! 2O c) Transect 2, 1420 hr 0 5 d) Transect 1, 1410 hr o -2O 2O i i i! i i i 2O e) Transect 2, 1530 hr f) Transect 1, 1445 hr l O 2O i i i i i BO BO 1 O O0 150 Figure 13. Salinity transects during ebb tide. Figures 13a, 13c, and 13e show results for transect 2, and Figures 13b, 13d, and 13f show results for transect 1. the flood tide. Our discussion focuses on three 1-hour periods of strong secondary circulation. The first was from 1400 to 1500 LT, when strong clockwise circulation was observed at both transects (Figure 12). This direction of secondary circulation is inconsistent with Plate l c, which shows a net counterclockwise lateral forcing at transect 1. The strong lateral gradient in salinity observed at transect 2 during this period (Figure 13c) suggests that the reverse flow was baroclinically driven. Figure 13 shows the evolution of the lateral structure of salinity during the early ebb. (Note that during the ebb, transect 2 is upstream of transect 1.) Fresh water appears first in the upper left of the channel in transect 2 at 1320 LT, creating a lateral salinity gradient. The lateral salinity gradient is stronger, and extends deeper, in transect 2 than in transect 1. At 1420 LT the strong stratification in transect 2 increased the internal wave speed ci and reduced T to 8 min (equation(3)). Because of the increased ci the internal wave crossed the 100-m-wide central section of the

13 ,,, LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUAR1N CHANNL a) Transect 2, 1320 hr b) Transect 1, 1340 hr 0 0 c) Transect 1, 1410 hr -- -e ' o v o curvature baroclinic I e Forcing, m/s 2 4 x i i, Forcing, m/s 2 4 x i i i Forcing, m/s 2 4 x 10 '4 d) Transect 2, 1420 hr e) Transect 1, 1445 hr f) Transect 1, 1520 hr ½ -10 i i i i! i i l z Forcing, m/s 2 x 10 '4 Forcing, m/s 2 x 10-4 Forcing, m/s 2 Figure 14. Lateral baroclinic forcing and centrifugal acceleration during the ebb. Uncertainty calculations for error bars are shown in Appendix A. For clarity, Figure 14f does not show error bars for lateral baroclinic forcing; uncertainty is the same as in Figures 14a-14e. 4 x 10-4 channel during the 6-min advection time between the two transects (Figures 13c and 13d). In transect 1 at 1445 LT a region of fresher water appears in the upper fight of Figure 13f. The progression of salinities (Figures 13c-13f) suggests that when fresh water reaches the inner bank, turbulence in the region of the islands mixes the fresh water downward. As a result of the mixing, the right side is fresher than the center down to a depth of 15 m, reversing the direction of baroclinic forcing. The forcing from centrifugal acceleration and the lateral baro- clinic pressure gradient in transects 1 and 2 during LT are shown in Figure 14. Figures 14a and 14d show that in transect pure frictional / pure inertial response response,-"",, /,.,"''" forcing "'...,' ',,' ' inertial + frictional response Distance downstream Figure 15. Conceptual diagram of inertial and frictional response to baroclinic forcing. The short-dashed line shows the oscillatory response that develops in the absence of friction [Heaps and Ramsbottom, 1966].

14 ,,, LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUAR1N CHANNL a) 730 hr b) 830 hr -10 _ -10-2O 0 log(rig/0.25) -2o 0 5 log(rig/0.25) c) 1035 hr d) 1410 hr -2O 0 5 log(rig/0.25) -2o 0 log(rig/0.25) e) 1540 hr f) 1725 hr ' ' ' log(rig/0.25) log(rig/0.25) Figure 16. (a-f) Gradient Richardso number versus depth at six times during the study, from data taken in transect 1. The plot shows In (Rig/0.25), so the stability threshold Rig = 0.25 is at zero. 2 the lateral baroclinic forcing strengthened between 1320 and 1420 LT. In transect 1 the lateral baroclinic forcing is weaker, because baroclinically induced flow caused the lateral salinity gradient to relax during the 6-min travel time from transect 2 to transect 1. The net lateral forcing at transect 2 as shown in Figure 14d accounts for the observed clockwise secondary circulation from 1400 to 1500 LT (Figure 12), while that shown in Plate 1 and Figure 14c does not. The clockwise transverse circulation in transect 1 is comparable to that in transect 2, indicating that the baroclinically induced flow persisted longer than the baroclinic forcing. In a frictionally dominated system the location of maximum baroclinic response coincides with the location of maximum baroclinic forcing, while in a system dominated by inertia the maximum baroclinic response occurs downstream of the maximum baroclinic forcing (Figure 15). In Snag Channel, salinity stratification reduced the influence of bottom friction on the upper water column.

15 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) V and W. Transect hr b) V and W. Transect hr o o,,.,.,.. _ o,, v:20cm/s / '] w: I ' 5 cm/s { o o - - o _ o,,. 1, ' - - o ;,n s, r nse t, oo- oo,r,n m s, ;;):2 ; oo- OO,r 0,,, -1 ' ' e) U profiles. Transect 2, hr 0 0 f) U profiles, Transect 1, hr :J - o :J - o Velocity. cm/s Velocity, cm/s Figure 17. (a and b) Secondary currents, (c and d) contours of along-stream velocity, and (e and f) along-stream velocity profiles, LT. The importance of friction to the flow depends on water column while a value less than 0.25 indicates that mixing is active stability, which is typically measured by the gradient Richardson [Rohr e! al, 1988]. Figure 16d shows Ri as a function of number Rig. Rig is the ratio of buoyant energy to shear-induced depth at transect 1 at 1410 LT. Ri was well above the stability turbulent mixing, calculated as threshold of 0.25 throughout the water column, except at four points close to the bottom. Thus stratification was strong enough to limit the influence of frictional forces, consistent with Rig: pooz g Op(du) -2 the persistence of the baroclinic response after the lateral baroclinic gradient was mixed out. The acceleration of the ebb A gradient Richardson number greater than 0.25 indicates that was the most stratified part of the tidal cycle; however, the stratification is strong enough to dampen turbulent mixing, stratification was stable through most of the tidal cycle. The

16 ,, LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL a) V and W, Transect 2, hr b) V and W, Transect 1, hr ' ' 0 ½. -10 V: 20 cm/s.._ t 5 cm/s c) U in cm/s, Transect 2, hr d) U in cm/s, Transect 1, hr pm ø /½Zol; -10-2O e) U profiles, Transect 2, hr ' ' ' f) U profiles, Transect 1, hr ½ ½ Velocity, cm/s Velocity, cm/s Figure 18. (a and b) Secondary currents, (c and d) contours of along-stream velocity, and (e and f) along-stream velocity profiles, LT. only unstable period was during the strongest part of the flood at 0830 LT. The variation over the tidal cycle in the balance between stratification and turbulent mixing is consistent with previous characterizations of northern San Francisco Bay as intermittently stratified [Monismith et al., 1996; Stacey et al., 1999]. However, the gradient Richardson number indicates that in this study, turbulence was limited by stratification during more of the tidal cycle, and through more of the water column, than in the tidal cycle studied by Stacey et al. Two factors contributing to the importance of stratification are the weakness of the tides at the time of the study and the confluence of different sources of water (with, at times, different salinities) in Snag Channel. Because of the stable stratification, secondary currents are stronger and persist longer than in an unstratified system. The decoupling of the water column from bottom-induced friction also allows for the nonlogarithmic along-stream velocity profiles observed throughout the study, particularly during the flood.

17 _ LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL loo a) Streamwise velocity I I I I I 50 o,m o o -loo b) Shear in transverse velocity Days since January 1, c) Streamwise velocity I I I I I 50 o -loo d) Shear in transverse velocity I I I Days since January 1, 1997 Figure 19. Streamwise velocities and top-to-bottom shear in transverse velocities during two periods in Figures 19a and 19b are from February 1997, when conditions were fresh; Figures 19c and 19d are from June 1997, when conditions were stratified. From 1600 to 1700 LT the strongest transverse flows of the study were observed at transect 2 (Figure 17), with a top-to-bottom shear greater than s - in one profile. The direction of the secondary circulation was consistent with the centrifugal acceleration at the site and opposite to that shown in Figure 12. The secondary circulation was stronger than that predicted by (1), suggesting that it was enhanced by counterclockwise lateral baroclinic forcing. In the deepest part of the channel the direction of shear in the transverse velocity profiles was reversed below 12 m depth, perhaps a residual effect of the clockwise baroclinic flow seen an hour earlier. However, downstream at transect 1 the secondary circulation was weaker and less well structured. This can be explained by the change in sign in baroclinic forcing just prior to 1600 LT, shown in Plates lb and l c. A lateral salinity gradient of almost 0.5 ppt/ 100 m extended to a depth of 10 m at transect 1 at 1520 LT and

18 31300 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL was strong enough to reverse curvature-induced transverse circulation (Plate 1). At transect 2 the lateral gradient was weaker and did not extend as deep (Figure 13). The secondary currents in transect 1 between 1600 and 1700 LT were dominated by the strong downwelling at 100 m from the outer bank (Figure 17b). During this time a large wake developed behind the island at the side of the channel. The negative transverse velocities of the wake combined with the very strong lateral gradient in streamwise velocity at the edge of the wake to produce positive lateral advection, which slowed down the flow more than 50 m into the channel from the island (Figure 17d). The negative lateral velocities of the wake converged with the positive transverse velocities of the main flow, creating strong downwelling. From 1700 to 1800 LT, at the end of the ebb, a clear pattern of counterclockwise, curvature-induced transverse circulation was present in both transects (Figure 18). The strength of the transverse circulation at transect 2 is less than that during LT, consistent with the decrease in streamwise velocities. The size and strength of the wake in transect 1 is much less than that during LT, allowing the curvature-induced secondary circulation to persist. The direction of shear is no longer reversed at the bottom. As discussed by Dronkers [ 1996], transverse circulation due to centrifugal acceleration in a vertically stratified water column will produce a lateral salinity gradient and baroclinic forcing opposing the centrifugal acceleration. If these two forces are similar in magnitude, transverse circulation will be weak. Chant and 'lson [ 1997] observed a spatial progression in a flow around a headland in the estuary of the Hudson. Moving downstream, first there was a region dominated by centrifugally driven transverse flows, next a transverse baroclinic response which damped secondary currents, and finally, downstream of the curvature, reverse flows due to baroclinic forcing. In Snag Channel there is a temporal evolution, in which secondary flows during the ebb are dominated first by lateral baroclinic forcing and later by centrifugal forcing. Here, as in Dronkers' observations in the Volkerak, the lateral salinity gradient was created by differential streamwise advection, rather than by curvature-induced transverse flows. The differential advection is shown in Figure 12: arly in the ebb, the strongest downstream velocities were in the upper left part of the channel, coincident with the lowest salinities. Later in the ebb the greatest velocities were in the center of the channel (Figure 17). At this site, centrifugal acceleration is not balanced by lateral baroclinic forcing, because the travel time through the curve is too short for such a balance to develop and because differential advection, rather than centrifugal forcing, produces the strongest lateral salinity gradients. Because centrifugal forcing and baroclinic forcing are not in balance, the Froude number presented by Seim and Gregg [1997] does not determine when secondary flows will develop. Instead, secondary currents respond to the sum of centrifugal and lateral baroclinic forcing, which varies over the tidal cycle. The velocity data we collected in Snag Channel in 1997 show that the observed progression of clockwise, baroclinically forced secondary circulation early in the ebb followed by counterclockwise, centrifugally forced secondary circulation later in the ebb occurs repeatedly (Figure 19). The shear in transverse velocity shown in Figures 19b and 19d was calculated by subtracting the velocity at the bottom from the velocity at the top; hence counterclockwise flow is represented by negative shear, and clockwise flow is represented by positive shear. Figures 19a and 19b show velocity data from 6 days in February 1997, representative of freshwater conditions. High freshwater inflows produced greater ebb than flood velocities. During this period, counterclockwise (centrifugal) transverse velocities developed during each ebb tide. Figures 19c and 19d show data from June 28 to July 3, 1997, when conditions were stratified. Transverse circulation developed during strong ebbs. The pulse of clockwise secondary circulation at the beginning of the strong ebbs on days , before the counterclockwise secondary circulation develops, is consistent with the progression from baroclinically induced to centrifugally induced transverse circulation seen in the transecting data. 5. Conclusions Curvature and a channel junction produce both lateral structure in streamwise currents and strong secondary circulation in this narrow channel. The lateral variability in streamwise velocities was stronger on flood than on ebb and produced lateral variability in tidally averaged residual currents. The tidally averaged salinities did not vary laterally; however, at certain times during the tidal cycle the lateral salinity gradient, produced primarily by differential advection, was strong enough to dominate secondary circulation. Similarly, the tidally averaged transverse currents were not particularly strong, but distinct patterns of strong secondary circulation, which caused significant mixing, were observed during several 1-hour periods. The lateral and vertical advective terms calculated from the data were comparable to estimates of the barotropic and baroclinic pressure gradients and the frictional terms in the streamwise momentum equation, during periods of strong transverse currents. The travel time around the bend is too short for a steady state balance to develop between centrifugal acceleration and lateral baroclinic forcing. arly in the ebb, a lateral salinity gradient developed because of differential advection and produced clockwise baroclinic circulation opposing the centrifugal acceleration. As the ebb progressed, the salinity gradient was mixed out, and counterclockwise centrifugal acceleration dominated the transverse circulation. Secondary currents persisted farther downstream than the original forcing, because of stable stratification during the study. Data collected in 1997 at this site confirmed that, when Delta outflow is low, transverse circulation exhibits a progression from clockwise to counterclockwise during ebb tides. Snag Channel connects the shallows of Honker Bay to Suisun Cutoff and, potentially, to the shallows of Grizzly Bay. The episodes of strong secondary circulation in Snag Channel mix the phytoplankton, nutrients, and suspended solids originating in the shallows into the less productive channel waters. The complexity of the lateral structure in this channel presents a challenge to modelers. We estimate that a model would require a grid spacing of 20 m to resolve the observed lateral structure and accurately simulate this flow. The lateral structure must be resolved not only to reproduce the secondary currents and lateral variability in transport but also to generate the lateral advective term of the streamwise momentum equation, which cannot be neglected for this flow. The curvature and junctions responsible for the lateral variability in Snag Channel are typical of channels in northern San Francisco Bay and the Sacramento-San Joaquin Delta, suggesting that significant lateral variability is widespread as well. Appendix A. Uncertainty Analysis A1. Uncertainty in Horizontal and Vertical Velocities In measuring velocities with a boat-mounted ADCP, uncertainty is introduced by boat motion as well as instrument error. The single-ping standard deviation for a 600-kHz ADCP using a 50-cm bin size with a depth range of 20 m is 8 crn/s for horizontal velocities [RD Instruments, 1995]. ach ensemble averaged 16 water pings, reducing the per-ensemble

19 LACY AND MONISMITH: SCONDARY CURRNTS 1N AN STUAR1N CHANNL instrument error to 2 cm/s. In processing, the data were where n is the index of the depth cell for which Pt, is calculated, averaged spatially over two depth cells and two lateral cells, so with n = 1 at the top. The subscripts y= 1 andy= 3 denote that each reported velocity value is the average of four ensem- evaluation at the first and third stations for CTD drops in transect 1, bles. The total per-ensemble uncertainty, including the effect of and Ay is the distance between the two stations. boat motion, was estimated as the standard deviation of the four From (A3) the uncertainty in Pt, can be estimated as measurements contributing to each spatially averaged value. For us the mean standardeviation for 360 average values from four times is 4.9 cm/s, while for Un it is 5.0 cm/s, substantially greater -p0-y _ g /2 p k + l) k than the instrument error. The uncertainty the spatially averaged values is represented by the standard error (s.d./xf ), which is 2.5 cm/s for both Un and us. This is the uncertainty associated with most of the horizontal velocities reported, and is used in the = + + error propagation calculations below. The average standar devi- p0 y ation in the w measurements is 1.4 cm/s, giving an average standard error of 0.7 cm/s. Since the standard error seemed lower Here, % is estimated 0.07 kg/m 3 (approximately 0.1 ppt), N = 13 (the number of depth cells m stmions 1 and 3), d y is 100 m. than the uncertainty w, we estimated the uncertainty at 1 cm/s. The velocities displayed in Figures 10, 12, 17, and 18 are This estimate of ov is a Dnction only of depth, ranging from 2.75 x 10 -s at the top to 4.34 x 10 -s s 2 at the bosom of the water averages of four transects, which reduces their uncertainty to column (see Figure 14) cm/s. A2. Uncertainty in Calculations of Lateral Forcings Centrifugal acceleration is calculated as and the uncertainty in Ac is A c -- us us Rs (A1) A3. Uncertainty in Calculation of Lateral Advection Lateral advection in the along-channel momentum equation (unoux/oy) was calculated from the data using central differencing as Us,j- 1 except at the sides, where forward or backwardifferencing was used. The uncertainty Au.,. = Us, j+ - Us, j_ is x/ o.. Thus The uncertainty c can be expressed as a function of c u : 2_ 1 U s - U 2 where N is the number of depth cells (17 in our case). Substituting (A2) into (A1) gives J (A2) In this case, o.. = o.,, = m/s, so (A4) The values of lateral advection shown in Figure 11 are averages from four transects; thus OF is a factor of 2 lower than it is in (A4). Average uncertainty for the 58 points in Figure 11 with F > 2 x 10-4 II1/S 2 is 9.0 x 10 m/s 2 (standard deviation is 5.4 x 10-s). The average uncertainty for all 140 points in the water column is 7.2 x 10 -s m/s 2 (standard deviation is 4.9 x 10-s). Derek Fong of the FML for assisting with the fieldwork. Our manuscript benefited from the comments of two anonymous reviewers. This work was The uncertainty ou. is estimated above as m/s, and or, is funded by CALFD as well as NSF grant OC to SGM. estimated as 100 m. The average c% for the resultshown in Plate 1 is 2.39 x 10 -s m/s 2, and the maximum is 5.02 x 10 -s. Figure References 14 shows crac for six transects during the ebb tide. The uncertainty oac is smaller during the ebb tide than during the flood, when the Chant, R. J., and R.. Wilson, Secondary circulation in a highly stratified highest values of lu, I occurred. estuary, J. Geophys. Res., 102, 23,207-23,215, Dronkers, J., The influence of buoyancy on transverse circulation and on The lateral baroclinic pressure gradient estuarine dynamics, in Buoyancy ffects on Coastal and stuarine Dynamics, edited by D. G. Aubrey and C. T. Friedrichs, pp , was calculated from the data as rb(zn)---- oo YY i=1 P(Zi)y=3- i=1 P(Zi)y=I i=1 /=1 (A3) Acknowledgments. Thanks to Jon Burau of the USGS California District for his contribution to the study design and for providing resources for the fieldwork and to Jay Cuetara and Jon Yokomizo of the USGS and AGU, Washington, D.C., Friedrichs, C. T., and J. M. Hamrick, ffects of channel geometry on crosssectional variations in along-channel velocity in partially stratified estuaries, in Buoyancy ffects on Coastal and stuarine Dynamics, edited by D. G. Aubrey and C. T. Friedrichs, pp , AGU, Washington, D. C., Geyer, W. R., Three-dimensional tidal flow around headlands, J. Geophys. Res., 98, , Hansen, D. V., and M. Rattray, Jr., Gravitational circulation in straits and estuaries, J. Mar. Res., 23, , Heaps, N. S., and A.. Ramsbottom, Wind effects on the water in a narrow two-layered lake, Philos. Trans. R. Soc. London, Ser. A, 259, , 1966.

20 31302 LACY AND MONISMITH: SCONDARY CURRNTS IN AN STUARIN CHANNL Kalkwijk, J.P. T., and R. Booij, Adaptation of secondary flow in a nearly- lence in a partially stratified estuary, J. Phys. Oceanogr., 29, , horizontal flow, J. Hydraul. Res., 24, 19-37, Lacy, J. R., Circulation and transport in a semi-enclosed estuarine subem- Walters, R. A., R. T. Cheng, and T. J. Conomos, Time scales of circulation bayment, Ph.D. dissertation, 226 pp., Stanford Univ., Stanford, Calif., and mixing processes of San Francisco Bay waters, in Temporal Dy- May namics of an stuary: San Francisco Bay, edited by J.. Cloem and Monismith, S. G., J. R. Burau, and M. T. Stacey, Stratification dynamics F. H. Nichols, pp , Dr. W. Junk, Norwell, Mass., and gravitational circulation in northern San Francisco Bay, in San Fran- Wong, K. C., On the nature of transverse variability in a coastal plain cisco Bay, The cosystem, edited by T. Hollibaugh, pp. 1233, AAAS, estuary, J. Geophys. Res., 99, 14,209-14,222, Washington, D.C., RD Instruments, Direct reading and self-contained broadband acoustic Doppler current profiler technical manual, San Diego, Calif., 1995 J. Lacy, U.S. Geological Survey, Coastal and Marine Geology, 345 Rohr, J. J.,. C. Itsweire, K. N. Helland, and C. W. Van Atta, Growth and Middlefield Road, MS-999, Menlo Park, CA 94025, USA. (jlacy usgs. decay of turbulence in a stably stratified shear flow, J. Fluid Mech., 195, gov) , S. Monismith, nvironmental Fluid Mechanics Laboratory, Department Seim, H.., and M. C. Gregg, The importance of aspiration and channel of Civil and nvironmental ngineering, Stanford University, Stanford, curvature in producing strong vertical mixing over a sill, J. Geophys. CA 94305, USA. (monismit cive.stanford.edu) Res., 102, , Stacey, M. T., Turbulent mixing and residual circulation in a partially stratified estuary, Ph.D. dissertation, 209 pp., Stanford Univ., Stanford, Calif., July (Received August 23, 2000; revised July 9, 2001; Stacey, M. T., S. G. Monismith, and J. R. Burau, Observations of turbu- accepted July 13, 2001.)