Inner shelf circulation patterns and nearshore flow reversal under downwelling and stratified conditions off a curved coastline

Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113,, doi:10.1029/2007jc004487, 2008 Inner shelf circulation patterns and nearshore flow reversal under downwelling and stratified conditions off a curved coastline Rosario Sanay, 1 Alexander Yankovsky, 1 and George Voulgaris 1 Received 6 August 2007; revised 7 May 2008; accepted 21 May 2008; published 30 August 2008. [1] The role of a curved coastline and associated bathymetry in the development of downwelling circulation in a stratified inner shelf is examined through a number of numerical experiments. Different scenarios include constant versus variable wind-forcing and variations in bottom friction. The three-dimensional response of the shelf within the domain (embayment enclosed by capes) is associated with the generation of a velocity/ pycnocline disturbance at the upstream cape and its subsequent downstream advection. This disturbance is more pronounced under variable wind conditions. Its downstream advection through the bay exhibits different patterns depending on the competition between inertia and bottom friction near the cape. When inertia dominates, the disturbance separates from the cape and travels downwind with an enhanced downstream flow offshore and a countercurrent inshore. The separation occurs at a low Rossby number (Ro 0.15), which is attributed to the positive curvature of the coastline forming the cape. When friction dominates, the advection path is constrained along the coastline, resulting in an alongshore temperature gradient and a transient thermal front running almost perpendicular to the coast/isobaths. Simulations with spatially variable bottom friction, with higher friction toward the coast, result in the generation of eddy-like features. The numerical results are in agreement with both observations and surface temperature imagery from Long Bay, South Carolina, an embayment enclosed by two capes, and emphasize the role that coastline and associated shelf morphology can play in enhancing cross-shelf transport and exchange. Citation: Sanay, R., A. Yankovsky, and G. Voulgaris (2008), Inner shelf circulation patterns and nearshore flow reversal under downwelling and stratified conditions off a curved coastline, J. Geophys. Res., 113,, doi:10.1029/2007jc004487. 1. Introduction [2] Recent observations in Long Bay, South Carolina, identified the development of countercurrents on the inner shelf under downwelling wind conditions [Gutierrez et al., 2006]. [3] The in-situ measurements of near-bed velocity (Figure 1) took place at 4 different locations across the inner shelf of a curved coastline embayment (see Figure 2b) and at water depths ranging from 7.0 to 12.4 m. Three downwelling-favorable wind events were observed during the period of 1 December to 16 December 2001. During each event, the magnitude of the cross-shore component of the wind stress was at most half of the magnitude of the alongshore wind stress component. During the early stages of each downwelling event, the direction of the alongshore current at the four locations (C, D, E and F) coincides with that of the alongshore wind stress (see Figure 1a); as the wind subsides, a reversal of the flow (countercurrent) develops. The delay of reversal of the flow relative to the peak in wind-forcing is less than 2 days (Figure 1). 1 Marine Science Program, Department of Geological Sciences, University of South Carolina, Columbia, South Carolina, USA. Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JC004487$09.00 Interestingly, this observed nearshore countercurrent decays as wind relaxes. Gutierrez et al. [2006] suggested that the countercurrent was driven by a local along-shelf pressure gradient force associated with the curvilinear coastline. Similar inner shelf countercurrents driven by along-shelf pressure gradient have been observed on the New Jersey shelf [Yankovsky, 2003], in water depths approximately 10 m but under upwelling-favorable wind-forcing. These latter countercurrents were associated with the generation of coastal trapped waves that were developed after the upwelling favorable winds has subsided [Yankovsky, 2003]. The salient feature of the countercurrent observed in Long Bay is that the downwelling-favorable wind-forcing induced turbulent stresses that could easily penetrate the whole water column. [4] In addition, to the observed flow reversals, satellite images off the Carolinas coast (Figure 2) obtained under similar downwelling-favorable wind conditions, reveal substantial along-shelf variations of sea surface temperature (SST). SST was consistently higher in the upstream (northeastern) section of Long Bay (near Cape Fear) compared to the downstream (southwestern) section (near Cape Romain). Furthermore, these variations do not seem to be related to coastal outflow, suggesting that these along-shelf temperature variations might be a direct consequence of a three-dimensional circulation induced by the curvilinear 1of15

Figure 1. Observations [from Gutierrez et al., 2006] of countercurrent under downwelling wind conditions in Long Bay, SC. (a) Alongshore and cross-shore wind stress; (b) mean seawater level; and (c) alongshore current velocity (at approximately 2 m above the seabed) at four stations (c e) across the inner shelf. Station water depths are 7, 9.7, 8.4, and 12.4 m for c, d, e, and f, respectively. Positive values indicate northeastward and onshore flows in the alongshore and across-shore directions, respectively. coastline and its associated bathymetry. Similar and even more dramatic along-shelf variations of SST have been observed on the South Atlantic Bight Shelf during the winter [Li et al., 2003], when across-shelf fronts were formed on the inner shelf and persisted for several days. These observational examples suggest that the bathymetry associated with a curved coastline can offset the twodimensional structure of the wind-driven downwelling circulation and enhance the across-shelf exchange, as the shelf alongshore temperature gradients imply. [5] Inner shelf has been defined as the dynamically distinctive area where surface and bottom boundary layers interact [e.g., Mitchum and Clarke, 1986; Lentz, 1994], resulting in a cross-shelf divergence of the Ekman transport. This divergence produces an across-shelf pressure gradient and corresponding alongshore currents on the shelf. Li and Weisberg [1999] and Weisberg et al. [2001] discussed the momentum balances across the inner shelf and showed that inner shelf convergence does not necessarily require merging of the boundary layers, only their interaction through divergence, so that inner shelf regime can be established even under stratified conditions. However, since our study deals with a downwelling event, here we will consider the inner shelf region inshore of the downwelling front, where the water is homogenized and the turbulent stresses transfer momentum through the entire water column [Allen and Newberger, 1996]. This definition was also applied by Austin and Lentz [2002]. [6] Wind-driven downwelling flows on a uniform shelf with straight and parallel isobaths has been the subject of numerous numerical model studies [e.g., Allen and Newberger, 1996; Austin and Lentz, 2002]. Important features of these dynamics include the formation of a downwelling front and its offshore drift in agreement with Ekman transport, the development of a downwind jet in the vicinity of the front and the occurrence of well mixed conditions inshore of the front. The highly turbulent kinetic energy in the well-mixed water column increases the Ekman depth beyond the actual water depth of the inner shelf, thus suppressing the veering of wind-induced flow. As a result, the across-shelf circulation inshore of the downwelling front is typically very weak. [7] Along-shelf variations of coastline and shelf bathymetry can modify the wind-induced downwelling circulation described above. It can be argued that the effects of coastline variation are similar to the effects caused by along-shelf changes in wind-forcing [e.g., Crépon and Richez, 1982]. If the wind stress has a limited along-shelf extension or if the coastline undergoes changes in orientation (thus altering the local alongshore component of the wind stress), a coastally trapped wavefront can be generated at the upstream edge of the forcing region that travels downstream in the sense of Kelvin wave propagation [Carton, 1984; Suginohara, 1982]. When the front arrives at a certain downstream location, it modifies the local response, sets an along-shelf pressure gradient, and overall, 2of15

Figure 2. Composite image of SST on the SAB shelf/long Bay area showing alongshore variations and/or across-shelf frontal structures. Arrows represent daily averaged wind velocity vectors for a day before (dashed line) and the day the picture was taken (solid line). Circle in b indicates location of flow measurements presented in Gutierrez et al. [2006]. induces a three-dimensional circulation, similar to that observed in New Jersey [Yankovsky, 2003]. Bottom friction can further modify these three-dimensional dynamics through lateral spreading of the coastal along-shelf current. In general, lateral spreading of the coastal along-shelf current on a sloping bottom decreases with increasing stratification. Furthermore, and more commonly, when the coastal current adjusts to the coastline promontories [e.g., Klinger, 1994a, 1994b] or topographic forms [e.g., Song et al., 2001], mesoscale eddies can be generated. Such eddy generation requires a Rossby number (Ro) greater than 1[Klinger, 1994b], where Ro = U 0 /rf, with U 0 being the characteristic flow speed, f the Coriolis parameter and r the coastline radius of curvature. However, eddy formation and 3of15

Figure 3. (left) Model domain and bathymetry in meters used in the simulations (contours in 5-m interval). The inner box in the domain delineates the area numerical results are presented in this manuscript. Transects A, B, and C and points 1 to 5 indicate locations that model results are presented in the manuscript (see text). (right) The three different wind-forcing conditions used in this study: (a) transient wind-forcing; (b) constant wind stress; and (c) oscillatory wind stress. The symbols on each line indicate times where numerical simulation output is shown in the results section. shedding from the headland can be intensified in the case of an unsteady (accelerating) flow, for instance, associated with tidal forcing [Signell and Geyer, 1991]. Thus the vorticity advection downstream from the coastline irregularities can contribute to three-dimensional circulation along with the wave dynamics. [8] The relative importance of wave dynamics, due to along-shelf forcing gradients caused by varying coastline orientation, versus eddy dynamics is something that has not been addressed explicitly to-date. The observed SST patterns and countercurrent development can be the result of either mechanism and this study aims at addressing this issue. In particular, the goal of this contribution is to understand and explain the mechanism responsible for the formation of countercurrents on the inner shelf similar to those observed by Gutierrez et al. [2006] under downwelling wind-forcing. We used a process-oriented, numerical modeling approach to assess the potential of coastal wave generation that might explain the observations. These hypotheses are compared against eddy dynamics generated by the bathymetry associated with the capes. [9] The model is forced by downwelling-favorable wind and utilizes an idealized domain with a concave-shaped bay bounded by capes, resembling the coastline morphology and bathymetry of Long Bay. In order to examine the dynamics in detail three different wind-forcings are utilized: (1) transient pulse, (2) constant wind, and (3) oscillating wind that resembles typical synoptic-scale wind variations for the study area [e.g., Austin and Lentz, 1999]. In the remainder of the paper section 2 describes the configuration of the numerical model, while section 3 presents the model results and addresses the effects of temporal wind variations and bottom friction on the downwelling circulation in the bay. The final conclusions of the study are presented in section 4. 2. Model Setup [10] The simulations of the downwelling-driven inner shelf circulation were carried out with the Regional Ocean Model System (ROMS) [Haidvogel and Beckman., 1999], a primitive equation, free surface, hydrostatic, sigma-coordinate, numerical model that has been widely used to study regional and coastal circulation processes [e.g., Marchesiello et al., 2003; Peliz et al., 2003; Sanay et al., 2007]. The model setup used in this study includes all the terms of the primitive equations except horizontal viscosity. A third order and upstream biased advection scheme is used, so no explicit horizontal viscosity is required [Haidvogel and Beckman, 1999]. Vertical turbulence mixing is parameterized using the Generic Length Scale momentum turbulence closure submodel [Umlauf and Burchard, 2003; Warner et al., 2005] and a background vertical viscosity of 5 10 6 m 2 s 1. 4of15

Figure 4. Plan view of temperature near the bed (contours in 0.5 C interval) and velocity vector in the middle of water column for the Gaussian wind-forcing case using a low drag coefficient after (a) 2 days, (b) 4 days, and (c) 6 days of simulation. [11] The numerical domain is 700 200 km in the alongshore and cross-shore directions, respectively (Figure 3). It consists of a concave-shaped embayment (300-km long) bounded by a cape both to the north and south, and two straight coastlines (200-km long each) that extend northward and southward of the capes (see Figure 3). The characteristics of the bay resemble the morphological features of Long Bay, SC, USA, from Cape Fear, NC to Cape Romain, SC from the nearshore (5-m depth) to approximately 100 km offshore (55-m isobath). Further offshore, the bathymetry is considered uniform with a constant depth. The lengths of the straight segments of the coastline on either side of the embayment were selected such that the solutions at those locations are identical to the straight coastline solution [e.g., Austin and Lentz, 2002]. This approach allows direct comparison of the straight and curved coastline solutions and avoids uncertainties that might arise due to the setup of artificial alongshore pressure gradients. The cross-shore bathymetric profiles in the middle of the bay (y = 350 km) and along the straight coastline sections are identical. [12] The numerical domain has one closed (coastline) and three open boundaries. A Cartesian orthogonal coordinate system is used, with the x-axis selected to coincide with the southern open boundary with positive offshore, while the y- axis trends along the coastline (west boundary) at x =0 (Figure 3). Free-slip condition is used at the closed boundary, and gradient conditions are used for all variables at all open boundaries. The surface boundary condition is: @ ðu; vþ A z @z ¼ t s x ; ts y 0 where t x s and t y s represent the cross-shelf and along-shelf components of the kinematic surface wind stress; A z is the vertical eddy viscosity and u and v denote the cross-shore and alongshore horizontal velocity components, respectively. The bottom boundary condition used is given by: ð1þ @ ðu; vþ A z @z ¼ C d ðu b ; v b Þ u 2 b þ 1=2 v2 b ð2þ 0 where the subscript b denotes values near the seabed and C d is a drag coefficient derived from the law of the wall equation: C d ¼ k 2 ln Dz 2 ð3þ z 0 where k is the von Karman constant, z 0 is the bottom roughness scale and Dz is half of the bottom vertical grid cell size. Three different bottom roughness parameterizations are used in the numerical experiments, where the bottom roughness scale is selected such that the C d 100 (drag 5of15

Figure 5. Time series of near-bed temperature at locations 1 and 2 (see Figure 3) with low drag coefficient for (1) base case (black lines), (2) double stratification (DS) case (light gray lines), and (3) steeper bottom slope (SB) case (dark gray lines). Solid lines represent times series at location 1 while dashed lines represent times series at location 2. coefficient evaluated at 1 m above the bed) obtains the following values: 8 < 5 10 4 C d j 100 ¼ 2 10 : 3 5 10 4 to 5 10 3 Hereafter, we refer to these values as low, normal and variable drag coefficients. In the variable case, the drag coefficient is held constant offshore (at 5 10 4 ) and increases linearly inshore the 20-m isobath. This acrossshelf variation is based on the arguments of Grant and Madsen [1979] who showed that the presence of a bottom wave boundary layer affects the logarithmic boundary layer associated with the low frequency shelf flow by enhancing the bottom roughness. Thus the effective bottom roughness and consequently the bottom friction coefficient increase as a function of wave amplitude, which usually increases with decreasing water depth due to wave shoaling. Preliminary analysis of bottom boundary layer measurements (not shown here) in Long Bay, at a water depth of 7 m [Sullivan et al., 2006], has shown that the typical drag coefficient is 3.4 10 3, which is between the extreme values used in the variable drag coefficient case, and slightly larger than the value used for the normal drag condition. [13] The value for the low drag coefficient case was selected to indirectly account for the continuous presence of brackish water on the SAB inner shelf originating from numerous riverine discharges along the coastline [Blanton and Atkinson, 1983]. While this buoyant water is usually well mixed in vertical, it produces strong across-shelf density gradient, which translates into the vertical geostrophic velocity shear. As a result, near-bottom velocity and bottom stress are substantially reduced [e.g., Garvine, 2004; Yankovsky, 2006]. For the study site, a typical acrossshelf density change is 1 kgm 3 over 10 km offshore distance [see Figure 9 in Gutierrez et al., 2006]. Assuming f =0.9 10 4 s 1 and a background water density of 1025 kg m 3, the corresponding geostrophic shear is 1.06 10 2 s 1. Such a shear in 10 m of water depth will reduce a 0.2 m s 1 downwelling surface current (upper limit observed in Gutierrez et al. [2006]) to 0.1 m s 1 at the bed, (i.e., by 50%). These simple calculations when combined with a quadratic bottom friction, suggest a bottom stress reduced by a factor 0.25 of its value for when no nearshore buoyant water is present. Since this effect is not simulated directly in the model, the low drag coefficient case (0.25 of the normal value) is used to introduce a more realistic less frictional regime. [14] The numerical domain consists of 160 231 horizontal grid points with 30 vertical levels. The horizontal grid resolution varies from 1.5 to 3 km. In the cross-shore direction, the highest resolution is found near the coast and decreases offshore. In the alongshore direction, the highest resolution is over the area of the embayment and decreases both toward the north and south boundaries, respectively. The vertical resolution varies from 0.12 m near the coast to 3.0 m in the deepest part of the domain. The external and internal time steps used are 6 and 120 s, respectively. [15] The initial density field imposed consists of a well mixed surface (4 m) and bottom layers with a linear stratified thermocline (4 10 m from sea surface) in between. The temperature ranges from 15 to 22 C, while salinity is considered constant (36 psu) throughout the domain. This initial density condition resembles typical summer vertical stratification in the South Atlantic Bight [Blanton et al., 2003; Alexabareta et al., 2006]. [16] The model is forced with a spatially uniform, southward (e.g., downwelling-favorable) wind stress. All the experiments start from rest. Three different temporal patterns are applied as wind-forcing: (1) transient, single pulse wind event; (2) constant wind stress; and (3) oscillatory wind stress. The transient wind pulse varies in time as a Gaussian function, with a maximum magnitude of 0.2 N m 2.Inthe constant wind stress case, the magnitude is ramped linearly for 6 hours up to its maximum value of 0.1 N m 2, while in the oscillatory wind case the stress fluctuates between a minimum (0.01 N m 2 ) and a maximum (0.2 N m 2 ) value as a harmonic function with a 3-day period. The three different wind stress patterns used are defined below (see Figure 3): ( 0:2 exp t 1:5 t ¼ ð Þ2 t 3 0 t > 3 0:4 t t 0:25 t ¼ 0:1 t > 0:25 t ¼ 0:105 þ 0:095 sin 2p 3 t p 2 The direction, magnitude and duration of the wind patterns are consistent with those observed in the South Atlantic Bight [Gutierrez et al., 2006]. 3. Results [17] The results from the simulations with the single pulse wind-forcing and the three different bottom drag coefficients are presented first in the following section. These are followed by the results from the constant stress runs and those of the more realistic, oscillatory wind-forcing. 6of15

[19] As wind subsides (Figure 4b, day 4), the pyconcline disturbance travels downstream, elongates and expands in the along- and cross-shelf directions respectively, while the maximum temperature anomaly maintains its x-coordinate (x 40 km, see Figure 4b). The translation speed of a nearbottom thermal front between locations 1 and 2 (Figure 3) is approximately 0.39 m s 1, which falls within the range of the wind-induced shelf current (0.3 0.5 m s 1 ). The pertinent question is whether this downstream translation of density/velocity perturbation originating from the cape is governed by wave dynamics or is an advection by a windinduced current, as both mechanisms are possible (see Introduction). For the coastal-trapped wave (CTW) dynamics, the governing parameter is a slope Burger number [e.g., Huthnance, 1978]: A ¼ N a f 1 ð4þ Figure 6. Cross-shore vertical transects of temperature (gray contours in 0.5 C interval) and alongshore velocity (black contours in 0.05 m s 1 interval) for Gaussian windforcing using low drag coefficient after 4 days of simulation. (a) transect A (upstream); (b) transect B (central bay), and (c) their difference. For locations of transects A and B, see Figure 3. 3.1. Transient Wind Pulse Stress 3.1.1. Low Drag Coefficient [18] Near-bottom temperature and midwater column velocity fields for the low drag coefficient simulations are shown in Figure 4 for 2, 4 and 6 days after the wind stress starts acting over the free surface. The highest temperature indicates the deepest displacement of the pycnocline. After 2 days (just after the wind stress has peaked, see Figure 3b), the downwelling front is approximately parallel to the coastline, with the highest temperature occurring near the coast (Figure 4a). The only exception to this is found leeward of the capes, where the maximum pycnocline displacement is detached from the coast. An anticyclonic circulation accompanies this detachment with a countercurrent present along the coastline. where N is the buoyancy frequency at the bottom and a is the bottom slope. If A < 1, the wave properties are determined primarily by the topographic b effect while stratification is relatively unimportant. In our case, N 0.045 s 1 (based on density difference of 1.5 kg m 3 across the 7-m thick pycnocline) while a 5 10 4, which corresponds to A 0.2. The downstream translation of the disturbances is delineated by conducting two additional model runs, with doubled stratification (case DS) and with a 50% steeper bottom slope (case SB). Both features, if waves are present, should enhance the phase speed, with a more evident effect in case SB (i.e., increased topography effect). Figure 5 compares these three model runs (base, DS and SB). In the DS case the phase speed remains virtually unchanged when compared to the standard case, while in the SB case the phase speed decreases (evident in the delayed arrival of temperature font). Hence we infer that the wind-induced current advects the perturbations downstream from the cape, with the advection speed being lower in the deeper water (case SB). [20] The density and velocity perturbations formed in the vicinity of the cape are advected downstream following the thermal front passage and alter the local response in the bay. As a result, downwelling circulation in the bay (y 300 400 km) differs significantly from the twodimensional circulation pattern observed upstream (y 500 km) at the straight coastline regime. For example, within the embayment the highest temperature is found offshore while a lower temperature and a countercurrent are developed nearshore. On day 6 the pycnocline disturbance has traveled across the bay and reached the southern cape (Figure 4c). At this time a weak downstream current resumes in the nearshore within the bay. [21] The cross-shelf vertical distribution of temperature and along-shelf velocity along transects A (straight coastline solution) and B (middle of the bay) for day 4 further illustrate the difference between the two- and three-dimensional downwelling circulation pattern (Figure 6). The downwelling front (where the pycnocline intersects the bottom) lies approximately 40 km offshore in the straight coastline case, and moves beyond 50 km offshore in the bay (transect B). The highest temperature along transect A (Figure 6a) is found near the coast, while along transect B (Figure 6b) two maxima are found: one near the coast and the other some 7of15

Figure 7. Plan view of temperature near the bed (contours in 0.5 C interval) and velocity vector in the middle of water column for the Gaussian wind-forcing case using a normal drag coefficient after (a) 2 days, (b) 4 days, and (c) 6 days of simulation. 25 30 km offshore. The second maximum is the result of the downstream advection of the temperature/pycnocline disturbance originating at the cape. The observed countercurrent occupies the whole water column from the coast to 20 km offshore. [22] The structure of the advected disturbance (that follows the thermal front) is better illustrated by taking the difference between transects B and A (Figure 6c). It is characterized by an upstream velocity near the coast (exceeding 0.3 m s 1 ) and a downstream velocity offshore (0.1 m s 1 ) with an almost vertical nodal line at x 40 km, which roughly corresponds to the offshore extension of the cape. There is a strong positive thermal anomaly near the bed at x = 40 50 km associated with the deeper position of the downwelling front in the bay. While in the straight coastline case, the downwelling front is brought offshore by the bottom Ekman transport, within the bay the offshore location of the front is related also to the downstream advection of the disturbance originated at the cape. Furthermore, there is a negative thermal anomaly nearshore, where cooler (deeper) water is advected by the countercurrent with corresponding upslope (onshore) bottom Ekman transport (also see Figure 4). [23] The across-shelf shear between the maximum upstream (v 0.35 m s 1 at x = 15 km) and downstream (v 0.1 m s 1 at x = 50 km) alongshore velocity perturbations (Figure 6c) is 1.3 10 5 s 1. This is approximately half of the vorticity associated with the anticyclonic vortex formed leeward of the cape (since @v/ @x and @u/@y are initially comparable). This vorticity generation is related with the adjustment of the windinduced coastal jet to the presence of the cape. As the coastal current encounters the cape, it is forced to turn cyclonically following the curvilinear coastline and bathymetry. The average vorticity in the circular motion is twice the angular speed w (=jvj/r). The conservation of potential vorticity requires that this gain in relative vorticity is compensated by an anticyclonic shear of a similar magnitude on the coastal flank of the jet, which is seen in Figure 4a. This anticyclonic vorticity is released in the form of an anticyclonic eddy past the cape. Thus the across-shelf shear of the alongshore velocity component (responsible for the countercurrent) and the angular speed of the curvilinear flow upstream of the cape should be of the same magnitude (both being half of the anticyclone s vorticity). Taking r 40 km and jvj 0.6 m s 1, w =1.5 10 5 s 1, which is indeed close to the above estimate for the velocity shear. It should be noted that this mechanism of headland eddy formation can only operate when the radius of curvature is positive (that is, cyclonic turning is induced). This feature distinguishes our calculations from the Klinger [1994b] model where the coastline had a negative curvature radius that resulted in the flow being turned anticyclonically following the coastline. Indeed, the Rossby number corresponding to our case is only 0.15, and yet the detachment of coastal current from the cape occurs. 8of15

Figure 8. Time series of simulation results for the Gaussian wind-forcing case. Near-bed temperature at locations 1 (solid line) and 2 (dashed line) with (a) low drag and (b) normal drag coefficient simulations. (c) Midwater depth alongshore velocity component at location 3 (see Figure 3) for low (black line) and normal (gray line) drag coefficient simulations. 3.1.2. Normal Drag Coefficient [24] In this case, the temperature/pycnocline disturbance that originates at the cape does not separate from the coast (Figure 7) even under the maximum wind-forcing conditions. As wind subsides, it moves downstream remaining attached to the coast and exhibits itself as an alongshore temperature gradient, where isotherms run almost perpendicular to the coast (i.e., y = 370 390 km, Figure 7b). At this juncture it should be noted that a similar thermal structure (although of a smaller magnitude) is seen at the surface (not shown here), as a result of the wind-induced vertical mixing. The across-shelf structure of the disturbance (i.e., the difference between transects B and A, not shown here) is similar to that described earlier for the low drag coefficient case, but the magnitude of both density and velocity perturbations is reduced. [25] A comparison of the advection of the front for the low and normal drag cases is shown in Figure 8, where near-bed temperature time series from points 1 and 2 (for locations see Figure 3) show that the speed of the front in the normal drag coefficient case (Figure 8b) is almost 50% smaller than the speed found in the low drag coefficient case (Figure 8a), due to the enhanced bottom friction. Also, the magnitude of temperature variations associated with the front passage does not vary with downstream distance in the low drag coefficient case but gradually decreases in the normal drag coefficient case. Following the front passage, temperature in the low drag coefficient case continues to fluctuate with a timescale similar to that of the wind-forcing (3 days). The alongshore velocity reversal near the coast (point 3 in Figure 3) identified in the low drag experiment (Figure 4) is not present in the model results obtained with the normal drag coefficient (Figure 8c). Similar to the temperature, the countercurrent fluctuates over a 3-day time period. [26] The effect of bottom friction is further delineated by analyzing the temporal evolution of the vertically integrated cross-shore momentum balance terms (Figure 9) at a location just offshore and downstream of the tip of the cape (point 4 in Figure 3). In both cases (low and normal drag), the dominant terms are the Coriolis force, pressure gradient, and the advection of momentum (Figures 9a and 9b). However, their sum (hereafter referred to as the nonfrictional forcing) is comparable with the inertia and bottom friction (Figurse 9c and 9d). For both cases, the positive (offshore) acceleration develops after day 1, reaching maximum at 1.5 days (following the peak in wind-forcing). However, in the low drag case the inertia is the leading term, while in the normal drag case, the leading term is the bottom friction. The acceleration is then quickly halted and a balance is established between bottom friction and nonfrictional forcing after day 2. 3.1.3. Variable Drag Coefficient [27] This case is assumed to be representative of conditions, when surface gravity waves induce a bottom boundary sublayer inshore, thus enhancing the effective roughness for the low-frequency flow [e.g., Clarke and Brink, 1985]. The response is characterized by a bimodal structure of the transient disturbance of the pycnocline (Figure 10): it has both a detached disturbance advected downstream from the separation point at the cape, and an attached (arrested) disturbance travels along the coast at a lower speed. As a result, the countercurrent is rudimental and develops at some distance offshore. Another distinctive feature of this case is the formation of a vortical (or eddylike) structure at the leading edge of the detached disturbance, especially evident at day 4. This eddy-like feature is characterized by an anticyclonic flow filed with onshore/ offshore currents in the interior of the water column (Figure 10). The two-dimensional circulation upstream, on the other hand, is nearly parallel with the coastline and local isobaths. 3.2. Constant Wind [28] The same three bottom drag coefficients are applied in model runs forced by a constant wind stress. The wind stress magnitude (0.1 Pa) is half the peak value of the previous cases with a transient wind pulse (see Figure 3). It is anticipated that the three-dimensionality of the flow and density fields within the bay will be less pronounced since (1) the bottom friction will laterally spread with time the flow structure and (2) the downwelling front will continue to move offshore due to locally induced Ekman transport ultimately past the offshore coordinates of the capes. The results (bottom temperature and midwater column velocity fields) for the three cases after 8 days of simulation are presented in Figure 11. 3.2.1. Low Drag Coefficient [29] The countercurrent is again established nearshore due to the downstream passage of the initial anticyclonic disturbance. After this transient feature is gone, a weaker countercurrent still remains under the continuing downwel- 9of15

Figure 9. Vertically integrated momentum balance near the cape (point 4 in Figure 3): (a) all terms for the low drag case; (b) all terms for the normal drag case; (c) inertia, bottom friction, and nonfrictional forcing (NFF) for the low drag case; (d) inertia, bottom friction, and nonfrictional forcing for the normal drag case. (Key: prg = pressure gradient; cor = coriolis force; had = horizontal advection; str = stress; acc = local acceleration; NFF = nonfrictional forcing. ling-favorable wind stress. It occupies only a northern part of the bay (leeward of the cape) and the upstream velocity extends some distance offshore 10 20 km from the coast, while at the coast the flow is in the downstream direction. This rudimental countercurrent appears to be a permanent feature (at least through day 8). Adjacent to the countercurrent is the warmest near-bottom water. This local deepening of the pycnocline is associated with the anticyclonic vorticity of the countercurrent (Figure 11a). 3.2.2. Normal Drag Coefficient [30] As in the case with wind pulse forcing, the pycnocline/temperature disturbance originates at the cape and moves downstream along the coastline forming an alongshore temperature gradient with isotherms running almost perpendicular to the coastline (Figure 11b). This acrossshelf thermal front extends through the whole water column due to well mixed conditions on the inner shelf. However, after the passage of this disturbance, the difference between transects B and A (i.e., between three- and two-dimensional conditions) continuously diminishes with time. On day 4, the maximum velocity anomaly is only 0.1 m s 1 (not shown) while on day 8 this difference becomes insignificant. Thus in this case the shelf circulation in the bay is least affected by the three-dimensional topography compared with the other cases presented in this study. 3.2.3. Variable Drag Coefficient [31] The transient response that follows the wind onset is similar to the wind pulse case, but of a smaller magnitude. No vortex feature is seen in the near-surface velocity field where the wind-induced drift dominates. After 8 days of simulation, the dynamics within the bay still exhibit threedimensional features: the water is warmer and the pycnocline is deeper in the upstream segment of the bay. The downstream part, on the other hand, is characterized by relatively cooler water and faster alongshore current (Figure 11c). 3.3. Oscillatory Wind [32] The last set of model runs utilizes a somewhat more realistic forcing compared with the previous sets. The wind-forcing is still persistently downwelling-favorable, but it oscillates around the average value of 0.1 Pa that was used in the constant wind-forcing runs (see Figure 3). It peaks at 0.2 Pa and comes down to 0.01 Pa over a 3-day period as commonly observed along the South Atlantic Bight [Austin and Lentz, 1999]. The same three bottom 10 of 15

Figure 10. Plan view of temperature near the bed (contours in 0.5 C interval) and velocity vector in the middle of water column for the Gaussian wind-forcing case using a spatially variable drag coefficient after (a) 2 days, (b) 4 days, and(c) 6 days of simulation. friction conditions used before are also utilized in this set of simulations. 3.3.1. Low Drag Coefficient [33] Near-bottom temperature and midwater column velocity fields for the low drag coefficient case are shown in Figure 12 at three different times, which correspond to two different wind stages: after a maximum wind stress (2.25 and 5.25 days) and after a wind relaxation (3.75 days) (see Figure 3). A separation of the coastal jet from the cape with a corresponding detachment of the pycnocline disturbance from the coast follows the peaks of wind stress, when the inertia of coastal jet off the cape is maximal. The detached disturbance is advected downstream (as in the Gaussian wind experiment discussed above) and forms a countercurrent nearshore (on its coastal flank), which can be viewed as a part of the anticyclonic structure. When the wind relaxes, the inertia of coastal flow off the cape decreases and the coastal jet reattaches to the coastline, thus suppressing the countercurrent leeward of the cape. Similar to the results for the transient wind-forcing (see section 3.1), the location of the downwelling front (where the pycnocline intersects the bottom) lies further offshore within the embayment due to the passage of the pycnocline disturbance (e.g., 3.75 days) when compared to its location at the upstream (straight coastline) locations. This difference, however, gradually diminishes with time, due to the continuous offshore Ekman transport near the bed. [34] Time series at three inner shelf locations (2 km, 4 km and 10 km offshore) along transect B show that the reversal of the flow here occurs during the periods of wind relaxation (Figure 13b). That is, a decrease of local wind-forcing exposes a remotely generated transient countercurrent which is advected through the region. Although a countercurrent has a quasiperiodic nature (following harmonic wind stress fluctuations), its magnitude decreases from the 1st to the 2nd wind event (especially inshore). At the same time, phase difference develops in the across-shelf direction: fluctuations inshore lead those further offshore. These features indicate increasing effects of bottom friction with time, as the flow on the inner shelf is gradually homogenized (also compare shelf currents in the bay on Figure 12a versus 12c). [35] Temperature time series at point 5 (x = 42 km, y = 350 km, see Figure 3) for the pulse and oscillatory windforcing cases show that the temperature evolution is similar in both cases for approximately the first 4.5 days (Figure 14), which results from advection of the initial pycnocline disturbance. Subsequently, the temperature subsides rather slowly in the case of a Gaussian wind, and fluctuates with a 3 day period in the case of oscillatory wind-forcing. Although the period of temperature fluctuations matches that of the wind-forcing, the response does not change in time as a harmonic function. It forms steep intermittent temperature peaks of approximately one day in duration 11 of 15

Figure 11. Plan view of temperature near the bottom (contours in 0.5 C interval) and velocity vector in the middle of water column after 8 days of integration for the constant wind pattern using (a) low drag, (b) normal drag, and (c) variable drag. followed by a gradual growth of the temperature until the arrival of a new front associated with the next wind pulse. 3.3.2. Normal Drag Coefficient [36] As in the previous cases application of a normal bottom drag coefficient, the initial disturbance of the pycnocline at the cape travels downstream maintaining contact with the coastline, which results in the across-shelf thermal front moving downstream (Figure 15a). This attachment inhibits the formation of the countercurrent in the nearshore (Figure 13c). Subsequent wind pulses produce similar across-shelf transient fronts but of lesser magnitude. Due to well-mixed conditions inshore of the downwelling front, the across-shelf thermal fronts on the inner shelf extend from the bottom to the surface and should be visible in the remotely sensed SST images (similar to what is shown in Li et al. [2003]). 3.3.3. Variable Drag Coefficient [37] An eddy-like vortical feature is generated in the case of a variable bottom drag, but only during the first wind event (pulse) (Figure 15b).This vortical feature gradually elongates and forms a long narrow filament turning offshore in the direction roughly parallel with the coastline in that part of the embayment (not shown here). 4. Conclusions [38] A variety of mesoscale features are produced when the downwelling regime develops in the presence of a curvilinear coastline. These features are better pronounced when the wind-forcing varies with time. The response within the embayment depends on whether the flow and pycnoline disturbance at the cape detaches from the coast or remains close to the coastline. The latter case depends on the competition between the inertia and the bottom friction in the vicinity of the cape. In the case of a lower friction and a stronger inertia, a perturbation separates from the cape and it is advected downstream by the wind-induced current, with the enhanced downstream flow offshore and the countercurrent inshore. The detachment occurs at a low Rossby number (Ro 0.15), which is attributed to the positive curvature of the coastline forming the cape. In the case of stronger friction and lower inertia, the disturbance is arrested by the coastline, resulting in a significant alongshore temperature gradient and a transient thermal front running almost perpendicular to the coast/isobaths. Variations in bottom friction result in the formation of eddy-like features, especially during the first wind event. All mesoscale features described above enhance the across-shelf transport and exchange, which is usually very weak in two-dimensional downwelling regime on the inner shelf. [39] The in situ observations in Long Bay, SC [Gutierrez et al., 2006] and SST imageries [Li et al., 2003] reveal inner shelf circulation patterns similar to those obtained in the numerical simulations presented in this manuscript. However, the pattern of flow reversal observed is similar to that found in our model results for the inertial-dominance solution, which suggests that the recirculation observed at 12 of 15

Figure 12. Plan view of temperature near the bottom (contours in 0.5 C interval) and velocity vector in the middle of water column for the oscillatory wind pattern using low drag after (a) 2.25 days, (b) 3.75 days, and (c) 5.25 days. the inner shelf off Long Bay, SC can be the result of the detached and subsequent downstream advection of the disturbance generated at the upstream cape during a downwelling event. It is also noticeable that the magnitude of the countercurrent decreases in each subsequent downwelling event (see Figure 1), again consistent with our model Figure 13. Time series of (a) wind stress, (b) near-bottom alongshore current at 2, 4, and 10 km offshore along the line located at y = 350 km for the case of oscillatory wind, small drag (i.e., development of countercurrent inshore), and (c) the same as (b) but for the normal drag. Figure 14. Time series of near-bottom temperature at location 5 (x = 42 km, y = 350 km) for both oscillatory (solid line) and Gaussian (dashed line) wind using low bottom drag. 13 of 15

Figure 15. Plan view of temperature near the bottom (contours in 0.5 C interval) and velocity vector in the middle of water column after 3.75 days of integration for the oscillatory wind pattern using (a) normal drag and (b) variable drag. results (Figure 13b). We should mention that the countercurrent observed in the in situ data might be enhanced by the cross-shore component of the wind stress which can further accelerate the offshore directed flow at the tip of the cape. This can shift the dynamics toward the detachment path described earlier. [40] Furthermore, our numerical results are in agreement with satellite imagery of SST taken at the same geographic location (see Figure 2). The SST imagery reveals a cross-shore thermal front observed during downwelling-favorable wind conditions. This thermal feature is also found in bottom friction-dominance numerical solutions (e.g., normal bottom drag cases), reinforcing the notion that the processes described through our idealized numerical work occur in embayments along the Carolina coasts. [41] Acknowledgments. We are thankful to Rich Garvine and the two anonymous reviewers for their valuable comments and suggestions. Funding for this work was provided by U.S. Geological Survey as part of the South Carolina Coastal Erosion Study and South Carolina Sea Grant Consortium (grant V169). Support for A. Yankovsky was provided by the National Science Foundation (award OCE-0650194). Partial support for G. Voulgaris was also provided by the National Science Foundation (awards OCE-0451989 and OCE-0535893). References Alexabareta, A., J. R. Nelson, J. O. Blanton, H. E. Seim, F. E. Werner, J. M. Bane, and R. 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