Interaction of transient shelf currents with a buoyancy-driven coastal current

Transcription

1 Journal of Marine Research, 62, , 2004 Interaction of transient shelf currents with a buoyancy-driven coastal current by Alexander E. Yankovsky 1 ABSTRACT Observations on the inner New Jersey shelf (1996) showed that transient wind-driven currents of 3 4-day periods strongly interacted with a buoyancy-driven coastal current (or buoyant plume) originating from the Hudson estuary. In particular, the depth-averaged current fluctuations were amplified in the buoyant water. This phenomenon is studied here using a primitive equation numerical model (SPEM5). Transient (periodic) shelf currents are introduced in the form of incident barotropic shelf waves (BSW). The model domain is an idealized channel with open upstream/ downstream boundaries and the depth exponentially increasing offshore, which allows the BSW propagation through the model domain. In most cases, the wave period is five days. The buoyancydriven coastal current is forced by constant buoyant discharge through a coastal gap. Propagating BSWs reduce the growth of a buoyant anticyclonic bulge at the source region while a coastal current downstream from the source contains more buoyant water with a sharper density gradient in the frontal zone compared to the case without BSWs. The amplitude of vertically averaged transient currents increases in the buoyant layer (for instance, by 20 30% for the inflow density anomaly of 3 to 4 kgm 3 ). This amplification depends on the density anomaly of buoyant inflow. On the other hand, variations in the inflow velocity and/or the net transport do not affect the BSW amplification. The amplification of velocity amplitude is associated with the incident BSW scattering into higher wave modes. The total energy flux should remain approximately the same as BSWs propagate through the domain. The higher modes have lower group speeds and thus their amplitudes should be higher in order to maintain the same energy flux. Such interactions of transient currents with buoyant plumes are important for the mixing processes and the across-shelf exchange on the inner shelf. 1. Introduction Coastal buoyancy-driven currents rarely evolve under unforced conditions. Instead, they are often affected by the wind forcing, which both significantly modifies intrinsic structure and dynamics of the buoyant plume and mixes the buoyant layer with the ambient shelf water. The appreciation of this fact stimulated a long list of theoretical and modeling studies addressing the impact of wind forcing on coastal buoyant plumes (e.g., Chao, 1988; Garvine, 1996; Xing and Davies, 1999; Fong and Geyer, 2001; Berdeal et al., 2002). 1. Nova Southeastern University Oceanographic Center, 8000 North Ocean Drive, Dania Beach, Florida, , U.S.A. sasha@nova.edu 545

2 546 Journal of Marine Research [62, 4 In most of these studies, the wind forcing was assumed to be stationary and spatially uniform. These assumptions simplified the problem and emphasized the role of Ekman dynamics associated with the wind stress. It was found that a downwelling-favorable wind compresses the buoyancy-driven current near the coast, deepens the buoyant layer and enhances downstream (i.e., in the direction of Kelvin wave propagation) velocity (e.g., Chao, 1988). In contrary, an upwelling-favorable wind blocks the downstream penetration of buoyant flow, detaches the plume from the coast, spreads buoyant water offshore and enhances its mixing with the ambient water (e.g., Fong and Geyer, 2001; Berdeal et al., 2002). However, the wind field does vary both spatially and temporally. Individual wind events (or pulses) typically last for just a few days, while a typical spatial scale for the atmospheric system is several hundreds of kilometers. Such forcing generates a transient, pulse-like, response in the shelf currents, which propagates downstream due to generation of coastal-trapped waves (CTW) (Carton, 1984). The maximum response tends to occur farther downstream and later in time compared to the spatial and temporal structure of the forcing system. The CTWs combine two different mechanisms of wave energy trapping (e.g., Brink, 1991): in the barotropic limit, their dynamics is defined by potential vorticity conservation, and such waves are called barotropic shelf waves (BSW). When stratification becomes strong and the baroclinic Rossby radius exceeds the width of continental shelf and slope, the CTWs closely resemble baroclinic Kelvin waves at a vertical wall (that is, topographic effects become insignificant). For this reason, the structure of transient currents associated with CTWs depends on the stratification and the potential vorticity distribution, which in turn is primarily related to bottom topography. Thus, transient wind-driven currents not only can affect a buoyant plume, but also can be modified by the presence of the buoyancy-driven flow due to its contribution both to the background stratification and to the potential vorticity (the latter is due to velocity shear). This more subtle interaction of buoyancy- and wind-driven shelf currents has been ignored in previous modeling studies. However, recent observations on the New Jersey shelf indicated its likely importance (Yankovsky and Garvine, 1998; hereinafter referred to as YG). The rest of the paper is organized as follows. Section 2 briefly describes observational evidence for the interaction between the buoyant plume and the transient wind-driven currents. In Section 3, this interaction is studied by means of process-oriented numerical modeling. Section 4 discusses the results and summarizes the paper. 2. Observational motivation Observational data presented in this section were collected on the New Jersey inner shelf in the summer of The observational program was designed to study wind-driven coastal upwelling (e.g., Yankovsky, 2003). However, the results revealed that the episodic arrivals of buoyancy-driven current originating from the Hudson River discharge contrib-

3 2004] Yankovsky: Coastal buoyancy-driven currents 547 Figure 1. Map of the study area. Asterisks show mooring sites; isobaths are shown in meters. uted to the observed dynamics (YG). Some of these observations relevant to the subject of this work are discussed below. The mooring array comprised three lines approximately normal to the local isobaths (Fig. 1). Moorings were deployed in water depths ranging from 10 to 25 m. A detailed description of the collected data can be found in Münchow and Chant (2000). In this paper, the following data are analyzed. An upward-looking RDI acoustic Doppler current profiler (ADCP) measured velocity at C1 with 1-m vertical resolution. Conductivity measurements were not available at C1; for this reason the salinity time series obtained at N1 and S1 with the Inter Ocean S4 current meters at 2 m depth are used here. The bottom pressure time series were measured at N3 and S3. Wind data were obtained from the NOAA National Data Buoy Center (NDBC) buoy located approximately 100 km south-southwest from the site of experiment, off the Delaware Bay mouth (38.5N, 74.7W). The wind stress was estimated following Large and Pond (1981). The sea level time series from two tide gauge stations: Sandy Hook, NY and Atlantic City, NJ, were utilized to estimate the alongshore pressure gradient (see Section 4).

4 548 Journal of Marine Research [62, 4 Figure 2. Low-pass filtered time series of alongshelf wind stress (a), alongshelf currents measured at C1 mooring (b), and salinity at 2 m depth measured at N1 and S1 moorings (c). The upstream direction is positive for the wind stress and currents. The current and wind stress data are presented in a coastal (i.e., alongshelf/across-shelf) coordinate system by 60 CCW rotation of the conventional east/north coordinates (Fig. 1). The chosen coordinate system is consistent with previous studies (e.g., Yankovsky, 2003). All time series were low-pass filtered with a Gaussian filter retaining only fluctuations with periods longer than 24 hrs. Units of time are in yeardays (yd) starting from 0 at the beginning of Upwelling-favorable (upstream) wind pulses prevailed through the period of observations, with typical peak values of the wind stress varying from 0.05 to 0.1 Pa (Fig. 2a). The alongshelf current fluctuations, in general, followed the wind forcing (Fig. 2b). However, the average direction of the alongshelf current was often downstream, in opposition to the wind stress. This tendency is particularly evident from yd 163 through yd 181. Moreover, the amplitude of the depth-averaged alongshelf velocity fluctuations from yd 170 through yd 183 was the highest throughout the record while the wind stress was not particularly strong. This was a time interval when buoyant water was present on the inner shelf

5 2004] Yankovsky: Coastal buoyancy-driven currents 549 (Fig. 2c). The buoyancy-driven current propagated in the downstream direction, first arriving at N1 on yd 168 and then at S1 on yd 172. Since the location of the C1 mooring was approximately halfway between N1 and S1, the buoyant water with low salinity was present at C1 from approximately yd 170. The wind stress was negligible on yd At the same time, the downstream current reached its maximum and had a strong vertical shear (compare 3 m vs. 9 m depth, Fig. 2b). These features indicate the presence of a buoyancy-driven current. The vertical shear was clearly of baroclinic (nonfrictional) nature, because the water column was strongly stratified at the nearshore mooring locations shortly after the arrival of the buoyant plume (YG). Enhanced subinertial fluctuations of depth-averaged alongshelf current continued until yd 183, when the buoyant water was detached from the coast and advected offshore by sustained upwelling-favorable wind. Thus, enhanced fluctuations of subinertial wind-driven currents were observed when the buoyancy-driven current was present on the inner shelf. YG analyzed the subinertial sea level fluctuations within the southern part of the Middle Atlantic Bight (MAB) and found that they correlated with the local winds and propagated southward (downstream), gaining in amplitude. The speed of their propagation was consistent with the CTW phase speed ( 10 m s 1 ). Thus, the response of the MAB shelf flow was similar to the qualitative model of coastal currents forced by an isolated wind system (Carton, 1984). YG suggested that enhanced fluctuations of wind-driven currents in the buoyant layer were associated with the CTW scattering by the buoyant plume. This hypothesis will be investigated below. 3. Numerical modeling of buoyant plume interaction with transient currents a. Model description This study utilizes the primitive equation numerical model SPEM5.1 (Haidvogel et al., 1991; Song and Haidvogel, 1994). The model is configured similar to Yankovsky (2000) and Yankovsky et al. (2001). The model solves the nonlinear hydrostatic momentum and mass balance equations on an f-plane under rigid lid and Boussinesq approximations. The vertical turbulent viscosity and diffusivity are parameterized by the Mellor-Yamada 2.0 closure scheme (Mellor and Yamada 1974), with the minimum viscosity and diffusivity coefficients both set to 10 5 m 2 s 1. The Coriolis parameter f is set to 10 4 s 1. The rigid lid approximation assumes a nondivergent vertically integrated flow field so that the barotropic streamfunction can be introduced as x v h, y u h. Here u and v are x and y velocity components, respectively, h is depth, the subscripts denote partial differentiation, and the overbar indicates vertically averaged quantity. The model domain is a rectangular channel bounded by two vertical walls (Fig. 3). The shallower (coastal) wall has a depth h 0 7 m. The x-coordinate coincides with the coast and points downstream while the y-coordinate points offshore. The depth is uniform in the alongshelf direction and increases exponentially in the offshore direction:

6 550 Journal of Marine Research [62, 4 Figure 3. Model geometry: plan view of the model domain (upper panel) and across-shelf transect showing the vertical grid spacing. h h 0 e 2 y (1) where m 1 for the standard model geometry. The channel width W for the standard model geometry is 80 km, with the offshore wall being m deep. The across-channel open boundaries are at x 0 and 280 km. The bottom slope in the area occupied by buoyant flow (within km from the coast) varies from 3 to These values are comparable with typical slope of the MAB shelf, which is between 10 and 30 m isobaths in Figure 1. The numerical grid in the horizontal has a uniform spacing for each coordinate: x 1.75 km (161 grid cells in x) and y 1.25 km (65 grid cells in y). Slightly coarser resolution is applied in the alongshelf direction because in the coastal ocean the acrossshelf gradients are typically higher. The generalized s-coordinate in the vertical (Song and Haidvogel, 1994) is composed of 18 grid cells. It retains high resolution in surface and bottom boundary layers with a stretched (topography-following) grid in the interior. This vertical resolution is sufficient to resolve the buoyant plume, which is trapped within km from the coast, where the total depth does not exceed 35 m. On the other hand, transient shelf currents, which occupy the total shelf width, are barotropic and have no

7 2004] Yankovsky: Coastal buoyancy-driven currents 551 vertical structure, except for the bottom boundary layer. Lateral Laplacian mixing along the s-coordinate surfaces is applied for the numerical stability in both momentum and mass balance equations, with constant mixing coefficient of 15 m 2 s 1. The model time step is 600 s. The following boundary conditions are applied. A rigid lid is assumed at the surface, and no flow is allowed through the bottom and walls, with the exception of the buoyant inflow (see below). The walls are slippery while the bottom is frictional. The bottom stress is parameterized as a linear function of near-bottom velocity, with the drag coefficient of ms 1. Since both the buoyancy-driven current and CTWs propagate in the downstream (positive x) direction, a radiation boundary condition for streamfunction is specified at the downstream boundary (e.g., Yankovsky and Chapman, 1997). The incident wave is specified at the upstream boundary (see below). In addition, a smooth condition of zero x-derivative is applied to the depth-varying quantities at both open boundaries. Initially, the water in the domain is quiescent and has a uniform density of kg m 3. The model is forced by buoyant discharge through the coastal gap 59.5 x 70 km (Fig. 3) and by the BSW through the upstream boundary. The buoyant inflow has a constant density anomaly i, which is ramped from 0 over 24-hr period. The net transport at every grid cell across the mouth is held constant with a depth-averaged velocity v i. However, the inflow velocity has vertical structure which is specified to be similar to the vertical profile of v-component one step inside the domain (see Yankovsky, 2000 for details). The buoyant inflow can be characterized by nondimensional Burger and Rossby numbers, defined as S g h 0 ( fl) 2 and Ro v i ( fl) 1, respectively (where L is the inflow width). For model runs presented here, the Burger number varies within the range , and the Rossby number is ; that is, both S and Ro are small. Small S implies that Earth rotation is important for buoyant inflow adjustment (large scale discharge), while small Ro indicates that nonlinear effects are relatively unimportant. The examples of such plumes include relatively large buoyant discharges on the MAB shelf originating from Delaware and Chesapeake Bays or Hudson Estuary. The incident BSW has a specified mode number (mode 1 in all cases presented below) and period; the corresponding wave structure is determined by applying the analytical solution for exponential depth profile based on linear inviscid shallow water equations (Wilkin and Chapman, 1987): The solution for streamfunction is assumed periodic with respect to time and alongshelf coordinate: y e i t kx (2) where is the wave frequency and k is the alongshelf wavenumber. The solution for the across-shelf structure of the n-th BSW mode is: n y e y sin l n y, where l n n ; n 1,2,3... (3) W

8 552 Journal of Marine Research [62, 4 Figure 4. (a) Dispersion diagram of BSWs corresponding to the standard model geometry (only ten lowest modes are shown). Horizontal line is s 1 (5-day period); (b) across-shelf structure of streamfunction for the five lowest wave modes. For this solution, the across-shelf wave structure of a certain mode does not depend on the wave number (or frequency). The corresponding dispersion relation is 2 kf k 2 l n 2 2. (4) The dispersion diagram for the ten lowest BSW modes is shown in Figure 4a. The across-shelf streamfunction structures corresponding to the five lowest modes are shown in Figure 4b. The across-shelf structure u A ( y) ofu velocity component at the upstream boundary is determined by finite differences from the ( y) profile of the incident mode, and normalized by velocity amplitude near the coast. This velocity structure is then specified at x 0asu u A sin( t). In most cases, the incident wave period is five days ( s 1 ).

9 2004] Yankovsky: Coastal buoyancy-driven currents 553 Figure 5. Streamfunction and velocity at the surface in model run W5, day 17.5 (upper panel); density anomaly and velocity at the surface in model run BP1, day 20 (lower panel). b. Model results Before focusing on the interaction of buoyant plumes with transient shelf currents, these two elements of coastal dynamics were modeled separately. In model run W5, the propagating BSW of 1 st mode with a five-day period is introduced at the upstream boundary. The wave s alongshelf velocity amplitude at the coast is 0.2 m s 1. This upstream velocity disturbance indeed propagates through the domain as a shelf wave (Fig. 5). At the time shown, the BSW velocity at the upstream boundary is zero. It reached its maximum value 1.25 days earlier (quarter of the wave period). This peak velocity with corresponding minimum in streamfunction has traveled 200 km downstream by the moment shown in Figure 5, maintaining BSW structure both across- and alongshelf. The wave is slightly altered compared with the inviscid analytical solution, mostly due to the presence of bottom friction in the primitive equation model. The wave s phase speed is slightly reduced (that is, the wave length is shorter compared with the analytical value of 1046 km). The wave structure is also modified: first, the maximum velocity shifts from the coastal wall offshore and now occurs on the shelf. Secondly, there is an across-shelf phase difference, with the velocity fluctuations at the coast leading those farther offshore. All these features are in agreement with analytical results obtained by Power et al. (1989) for free BSW modes on a frictional shelf. The standard case buoyant plume (designated as BP1 see Table 1) on day 20 is shown in Figure 5. The plume is forced by buoyant inflow with i 3kgm 3 and v i 0.1 m s 1. This plume falls in the category of surface-advected (Yankovsky and Chapman, 1997), or surface-trapped plumes. This implies that buoyant layer is not deepened beyond its depth at the mouth by bottom Ekman layer dynamics. The characteristic feature of such

10 554 Journal of Marine Research [62, 4 Table 1. Interaction of buoyant plumes with 5-day BSW. W is the shelf width, A is the streamfunction amplification coefficient at x 112 km, y 6.25 km, U 0 is the downstream mean current. Model run i [kg m 3 ] v i [m s 1 ] W [km] U 0 [m s 1 ] A (W5) BP BP BP BP BP BP BP BP7C BP a plume is an anticyclonic bulge attached to the mouth. The bulge tends to accumulate an increasing amount of buoyant water and to grow indefinitely if not exposed to other forcing agents and/or to ambient circulation (e.g., Nof and Pichevin, 2001; Fong and Geyer, 2002; Whitney and Garvine, 2004). By day 20 in model run BP1, the anticyclonic bulge is roughly twice as wide as the downstream buoyancy-driven current. It is also filled with water of strong density anomaly ( 2kg m 3 ), close to the inflow value. In the downstream coastal current this water appears as a narrow band 5 6 km wide attached to the coast. In the next model run, BP1W5, both BSW and buoyant inflow are introduced simultaneously from the onset. The evolution of the surface density anomaly field through the one five-day wave period (day 15 through 20) is shown in Figure 6. Streamfunction contours are also shown for reference of the propagating wave s phase. The most noticeable difference between model run BP1W5 and the unforced plume in BP1 is that the growth of the bulge is significantly reduced while more buoyant water with strong density anomaly goes into the downstream buoyant current. The anticyclonic bulge shifts downstream on day 17.5 (Fig. 6b) and then upstream on day 20 (Fig. 6d) following the transient current phases with downstream/upstream alongshelf velocity. Two complementary model runs with longer wave periods were performed, BP1W10 (10-day BSW) and BP1W20 (20-day BSW). Other than incident wave period, all model parameters were the same as in BP1W5. The reduction of the anticyclonic bulge s offshore growth (not shown) becomes more pronounced when the BSW period increases, because the upstream and downstream excursions of buoyant water and the bulge in particular become larger. The BSW is also modified as it propagates through the buoyant plume. To illustrate this, two time series of streamfunction are compared in Figure 7. Both time series were obtained from the same grid point ( x 112 km, y 6.25 km). This location is downstream from the source and the anticyclonic bulge, but within the coastal buoyant current. One time series represents the case when the BSW propagates through the channel without a buoyant

11 2004] Yankovsky: Coastal buoyancy-driven currents 555 Figure 6. Model run BP1W5, instantaneous density (shade) and streamfunction (contours) fields on day (a) 16.25, (b) 17.5, (c) 18.75, (d) 20. The streamfunction contour interval is 104 m3 s 1; positive (negative) values are contoured with solid (dashed) lines. plume (W5), while the second is the case when both plume and BSW are present (BP1W5). Due to the existence of the buoyancy-driven current, the BP1W5 streamfunction value is higher (shifted upward); that is, there is an extra transport associated with the discharge. The buoyancy-driven current gradually spreads offshore, which explains an Figure 7. Time series of streamfunction at x 112 km, y 6.25 km in model runs BP1W5 (heavy line) and W5.

12 556 Journal of Marine Research [62, 4 Figure 8. Amplification coefficient for streamfunction fluctuations at x 112 km, y 6.25 km. Model runs are with standard topography and five-day period BSWs. upward trend in BP1W5 fluctuations as time increases. The important result here is that the amplitude of fluctuations is higher when the plume is present. The amplitude is estimated for time interval from day through day (marked with triangles in Fig. 7). The trend in BP1W5 series is removed by averaging the minimum values (two consecutive troughs) of on day and The ratio of (that is, maximum minus minimum through the wave cycle) for two model runs is Thus, the depth-averaged alongshelf velocity fluctuations associated with propagating BSW are enhanced by more than 20% in the buoyant layer compared to the case without a plume. This result is in qualitative agreement with the observational data from the New Jersey shelf presented in the previous section. Several other plumes were modeled with different inflow parameters (BP2 BP7, see Table 1): i varied from 1.5 to 4.5 kg m 3 while v i varied from 0.1 to 0.3 m s 1. All buoyant plumes were exposed to the impact of the same BSW as in the case described above (W5), and the amplification coefficients for were estimated at the same location and for the same time interval. The results are summarized in Figure 8. Within the considered parameter range, the amplification increases with the inflow density anomaly increase. On the other hand, inflow velocity (or net transport) variations do not show a clear tendency in transient current response. Figure 9 elucidates the interaction of transient currents with the buoyant plume, which leads to the amplification of streamfunction fluctuations in the buoyant layer. In this figure, two instantaneous (day 20) across-shelf profiles of at x 112 km are plotted. The first is

13 2004] Yankovsky: Coastal buoyancy-driven currents 557 Figure 9. Across-shelf streamfunction profiles on day 20 at x 112 km, model runs BP1 and BP1W5 (see text for details). from model run BP1, representing the unforced plume. The second profile (heavy line in Fig. 9) is the residual in model run BP1W5, after the corresponding solution of W5 (representing undisturbed passage of BSW) is subtracted. If no interaction between the BSWs and the plume had occurred these two profiles would be identical. However, Figure 9 shows substantial difference between the two. In the case of the quiescent ambient flow (BP1), is non-zero only within 20 km from the coast, where the buoyancy-driven current resides. Farther offshore ( y 20 km), becomes zero indicating no ambient dynamics. On the other hand, the residual from model run BP1W5 is non-zero across the whole channel, that is, beyond the location of the plume. It also varies between positive and negative values across the channel crossing 0 at y 20 and y 50 km. This feature indicates the presence of higher BSW modes, which were absent in model run W5. Indeed, Figure 4b shows that the number of zero-crossings in ( y) profile increases with the mode number and the wave structure becomes more complex. Thus, when the incident BSW mode encounters the coastal buoyant plume, it scatters into other wave modes (available at this frequency), adjusting to changing conditions of the coastal waveguide. Higher BSW modes evident in Figure 9 have shorter wavelengths compared with the incident wave (see dispersion diagram in Fig. 4a). Consequently, structures with shorter length scales should appear not only in the across-shelf, but in the alongshelf direction as well. This tendency is illustrated by Figure 10, where temporal and alongshelf evolution of residual (e.g., BP1W5 W5) at y 6.25 km is plotted. The strongest temporal variations in residual streamfunction occur at the buoyancy source (50 x 80 km). Comparison of time series obtained in model runs BP1W5 (plume/bsw interaction) and W5 (undisturbed passage of BSW) reveals that discrepancy in between the two model runs near the source of buoyancy is related mostly to the phase difference of fluctuations, not to the amplitude enhancement. Thus, the effective phase speed of BSW is reduced when the wave encounters the plume and the higher (slower) wave modes are generated. Also, the upstream edge of anticyclonic bulge shifts by approximately 15 km alongshelf through the wave period. Downstream from the source, five-day fluctuations appear as

14 558 Journal of Marine Research [62, 4 dark-gray spots, gradually expanding downstream with the every new wave cycle, following the buoyant water spreading in this direction. These fluctuations represent the enhanced amplitude of relative to the undisturbed BSW passage, the result of BSW scattering. The amplification of velocity fluctuations follows from the invariance in time of the streamfunction at the coast ( y 0). Interestingly, the amplification is not confined within the buoyancy-driven current. At the right (downstream) border of the plot (lightgray color), five-day fluctuations are still evident, albeit with smaller amplitude. This implies that the scattered wave field continues to propagate downstream beyond the buoyant layer, although the signal is modulated in the alongshelf direction due to interplay between different wave modes. Scattering of the incident wave into higher BSW modes can readily explain the amplification of velocity in terms of energy conservation: at fixed frequency the BSW energy flux is a sum of the fluxes of the individual wave modes (Huthnance, 1975). The energy flux of an individual wave mode is the product of group speed and energy density; the latter is a function of wave amplitude. At given frequency, the group speed C g / k decreases when the mode number increases (Fig. 4a). Thus, higher wave amplitude is required to compensate for the lower C g when the incident wave energy flux is transferred (scattered) into higher BSW modes. As Figure 10 indicates, the strongest disturbance of the incident wave occurs at the source region, where the anticyclonic bulge develops. Both density anomaly and vorticity associated with the plume are strongest in the anticyclonic bulge. Additional model run was conducted with the purpose of demonstrating that it was the density anomaly and not the velocity field (with corresponding shear/vorticity) that promoted the BSW scattering. In general, stronger inflow density anomaly produces a larger anticyclonic bulge at the mouth. It is then possible that stronger anticyclonic vorticity associated with the bulge can contribute to the enhanced scattering and amplification when i increases. In order to prove that the density anomaly was the primary reason for enhanced scattering, a mean (time- and depth independent) alongshelf current of 0.1 m s 1 was added in model run BP7W5. This new run (designated as BP7CW5) is compared with BP7W5 in Figure 11. While in BP7W5 the anticyclone is larger than, for instance, in model run BP1W5 (Fig. 6d), the mean current has completely eliminated the bulge at the mouth in BP7CW5 (Fig. 11). However, the amplification coefficient in BP7CW5 is 1.38, which is higher than in BP7W5 (1.32). Thus, the elimination of the anticyclone has not reduced the efficiency of scattering and the magnitude of amplification. In the final model run, BP8W5, buoyant plume was forced by the same buoyant inflow as in the standard case (BP1), but in a wider channel. The channel s width now is 120 km, which requires 97 grid points in y in order to maintain the same across-shelf resolution ( y 1.25 km) as in the previous cases. The bottom slope was reduced ( m 1 ) in order to keep the offshore wall of the same depth as before. The model geometry was modified for the following reason. Although the buoyancy-driven current is the same as in BP1, it occupies a smaller fraction of the total shelf width. Consequently,

15 2004] Yankovsky: Coastal buoyancy-driven currents 559 Figure 10. Temporal and alongshelf evolution of streamfunction at y 6.25 km in model run BP1W5; corresponding streamfunction values from model W5 are subtracted. White box at the bottom shows the alongshelf coordinate of buoyancy source. the potential vorticity disturbance associated with the buoyancy-driven current represents a finer portion of the incident BSW across-shelf structure. This would require the generation of higher BSW modes with finer across-shelf structures (Fig. 4b) in order to provide the Figure 11. Density anomaly and velocity at the surface on day 20 in model runs (upper panel) BP7CW5 and (lower panel) BP7W5.

16 560 Journal of Marine Research [62, 4 adjustment. The amplification coefficient in model run BP8W5, however, is 1.20, close to BP1W5 value, thus proving this effect insignificant. 4. Discussion and summary This study was motivated by observations of the interaction between the transient subinertial wind-driven and the coastal buoyancy-driven currents off the New Jersey coast (YG). One of the observed features was the enhanced fluctuations of wind-driven currents in the buoyant layer associated with the Hudson Coastal Current. This amplification spanned the whole water column implying that it was not simply the trapping of wind-induced momentum by the buoyant layer near the surface. Tilburg and Garvine (2003) further analyzed these observations and found that the alongshelf flow convergence/ divergence was primarily related to the interaction of wind forcing and the episodic arrivals of the buoyant plume. Thus, the amplification of wind-driven currents in the buoyant layer can affect the mass balance on the inner shelf. The enhanced current fluctuations are also important for mixing processes. In this study, the role of the transient, or propagating, component of the wind-forced response is emphasized, while the effect of Ekman dynamics in the surface layer is omitted. It has been found that periodic transient currents confine the buoyant plume closer to the coast, reducing the offshore growth of the anticyclonic bulge. This effect becomes stronger when the barotropic shelf wave (BSW) period increases. However, the study was focused on five-day current fluctuations for two reasons. First, the observed sea level data demonstrated that the transient currents generated by local wind stress on the MAB shelf had predominant periods of three four days (YG). Secondly, for longer time periods the role of Ekman transport produced by local wind stress becomes increasingly important. Still the results for longer-period current fluctuations might be applicable for the remotely generated coastally trapped waves (CTWs), which are not related to local wind forcing. The propagating BSWs are also affected by the presence of a buoyant plume. The BSW amplitude is amplified in the buoyant layer due to the incident wave scattering into other modes. This amplification primarily depends on the plume s density anomaly, while the inflow net transport and the plume s velocity field are less important. It has been found that the inflow density anomaly of 3 kgm 3 could amplify the transient currents within the buoyant layer by approximately 20%. This amplification did not require the in situ density anomaly of such a magnitude. The actual density anomaly in the grid cell where the streamfunction time series were obtained was only 2.2 kg m 3, compared to 3 kgm 3 at the source of buoyant inflow. We now revisit the observations described earlier in the paper and try to substantiate the hypothesis that the velocity amplification of transient currents in the buoyant layer was indeed associated with the CTW scattering. In order to demonstrate this, two estimates of alongshelf pressure gradient force (PGF) were obtained (Fig. 12, also see Yankovsky, 2003). The first was based on sea level difference at two locations, Sandy Hook, NY, and Atlantic City. Sandy Hook is located at the intersection of the New Jersey coast and the

17 2004] Yankovsky: Coastal buoyancy-driven currents 561 Figure 12. Band-pass filtered time series of alongshelf depth-averaged current at C1 (upper panel) and low-pass filtered alongshelf pressure gradient force (lower panel). The upstream direction is positive. southern coast of Long Island, approximately 120 km upstream from Atlantic City. YG showed that three four-day wind-driven transients propagating along the southern part of MAB originated from this corner of the coastline. The Atlantic City location represents a local sea level for the area of experiment. Thus, the sea slope between these two locations can be considered as an alongshelf pressure gradient in the incident CTW. The local alongshelf PGF was estimated based on bottom pressure time series at N3 and S3 moorings. Both PGF time series reveal similar absolute values and sign, except for the time interval from yd 168 through yd 182. During this period, the buoyant water was present near the coast and the depth-averaged velocity fluctuations with three four-day periods were enhanced (shown for reference in Fig. 12, upper panel). In order to emphasize the modulation of three four-day fluctuations, the alongshelf velocity in Figure 12 was band-pass filtered with the high frequency cutoff period of 24 hrs and the bandwidth of 96 hrs. Due to the scattering process, higher wave modes are excited and shorter alongshelf scales are introduced in the flow field (e.g., Fig. 10). As a consequence, the alongshelf pressure gradient in the scattering region also increases. Indeed, this feature is seen in Figure 12: along with the enhanced velocities, the local alongshelf PGF was 2 3 times

18 562 Journal of Marine Research [62, 4 stronger than the upstream PGF. It is important to note that buoyant water was inshore of the moorings N3 and S3 prior to the upwelling event on yd 181 (Yankovsky, 2003), and thus it could not directly affect the alongshelf PGF at these moorings location. Typical range (i.e., consecutive maximum minus minimum) of alongshelf velocity fluctuations in Figure 12 is 0.1 m s 1, occasionally up to 0.15 m s 1 ; while during the yd period, it exceeds 0.2 m s 1. Thus, the amplitude of three four-day velocity fluctuations increased by more than 50% in the presence of buoyant water. The peak value of density anomaly in the buoyant layer measured at N1 was 4 kgm 3 (YG, their Fig. 12). The amplification coefficient used in numerical experiments is not a rigorous estimation for the efficiency of BSW scattering. Obviously, the choice of the particular grid cell can alter its value. But this coefficient demonstrates in a straightforward manner the dynamical implication of BSW scattering. Typically, the strength of scattering would have been determined by the fraction of total energy flux that is transferred from the incident to other BSW modes (Wilkin and Chapman, 1987). However, this procedure cannot be applied in the presence of a sheared mean current (such as the buoyancy-driven coastal current), since the wave modes then don t form an infinite orthogonal set. Besides, the energy flux is not perfectly conserved in model experiments due to friction. The results of this study are applicable to many regions of the coastal ocean because of the ubiquity of both wind- and buoyancy forcing. However, this interaction might be particularly important in high latitudes, where the coastal ocean is covered by ice during a long period of the year. In this case the buoyant plumes are not exposed directly to the wind-induced mixing. On the other hand, in high latitudes the diurnal tides belong to the subinertial frequency band and often propagate in the form of coastally-trapped waves. Their interaction with large-scale plumes (e.g., Mackenzie River or Siberian Rivers) can enhance mixing processes and ultimately affect the dispersal of fresh water on the Arctic shelf. Acknowledgments. Financial support was provided by National Science Foundation grants OCE and OCE The author is thankful to Rich Garvine, Steve Lentz and an anonymous reviewer for their insightful comments and suggestions. REFERENCES Berdeal, I. G., B. M. Hickey and M. Kawase Influence of wind stress and ambient flow on a high discharge river plume. J. Geophys. Res., 107(C9), 3130, doi: /2001JC Brink, K. H Coastal-trapped waves and wind-driven currents over the continental shelf. Ann. Rev. Fluid Mech., 23, Carton, J. A Coastal circulation caused by an isolated storm. J. Phys. Oceanogr., 14, Chao, S.-Y Wind-driven motion of estuarine plumes. J. Phys. Oceanogr., 18, Fong, D. A. and W. R. Geyer Response of a river plume during an upwelling favorable wind event. J. Geophys. Res., 106, The alongshore transport of freshwater in a surface-trapped river plume. J. Phys. Oceanogr., 32, Garvine, R. W Buoyant discharge on the inner continental shelf: A frontal model. J. Mar. Res., 54, 1 33.

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