Effects of Winds on Stratification and Circulation in a Partially Mixed Estuary

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, C12012, doi:10.1029/2010JC006893, 2011

Effects of winds on stratification and circulation in a partially mixed estuary Yun Li1 and Ming Li1 Received 15 December 2010; revised 9 August 2011; accepted 30 September 2011; published 13 December 2011.

[1] Numerical experiments are conducted to investigate how axial winds affect stratification and circulation in the partially mixed estuary of Chesapeake Bay. In the absence of rotational effects, stratification in the estuary decreases following both down-estuary and up-estuary winds, but stratification experiences larger reduction and takes longer to recover under up-estuary winds. In the presence of rotational effects, wind-driven lateral circulations cause the lateral straining of density field and weaken the shear in the along-channel flows. Under the down-estuary winds, a counterclockwise lateral circulation steepens isopycnals in the cross-channel sections, while the Coriolis force acting on it decelerates the downwind current in the surface layer and the upwind-directed current in the bottom layer. Under the up-estuary winds, a clockwise lateral circulation flattens isopycnals in the cross-channel sections and reduces the shear between the surface and bottom currents. Hence, in the presence of rotational effects, the lateral straining offsets the effects of longitudinal straining such that the asymmetry in stratification reduction is significantly reduced between the down-estuary and up-estuary winds. Regime diagrams based on Wedderburn (W) and Kelvin (Ke) numbers are constructed to summarize the net effects of winds on estuarine stratification during both wind perturbation and postwind adjustment periods. Citation: Li, Y., and M. Li (2011), Effects of winds on stratification and circulation in a partially mixed estuary, J. Geophys. Res., 116, C12012, doi:10.1029/2010JC006893.

1. Introduction vertical shear, thus reducing stratification. Wilson et al. [2008] and O’Donnell et al. [2008] suggested that along- [2] Most of the research in estuarine dynamics has focused channel wind straining regulates stratification and turbulent on the effects of tides. Relatively little attention has been mixing, thereby influencing the flux of oxygen into hypoxic paid to the role of winds in estuarine circulation, despite regions of western Long Island Sound. early predictions of first-order effects [Bowden, 1953; [4] Using a numerical model of an idealized estuarine Rattray and Hansen, 1962] and observational evidence of channel featuring a triangular cross section, Chen and strong wind driven flows [e.g., Wang, 1979a, 1979b; Sanford [2009] found that the net effect of winds on estua- Goodrich et al., 1987; Wong and Moses-Hall, 1998; Wong rine stratification depends on the competition between and Valle-Levinson, 2002]. Recent studies have suggested wind-driven mixing and wind-induced straining: moderate that wind effects are not limited to mixing in the vertical down-estuary winds enhance estuarine stratification whereas direction. Since estuaries typically have strong horizontal strong down-estuary winds and all up-estuary winds reduce density gradients, wind-driven currents can significantly stratification. They proposed a hypothetical diagram to alter estuarine stratification through the straining of density classify the wind effects on estuarine stratification and sug- field. gested that the Wedderburn number and the ratio of the [3] North et al. [2004] and Scully et al. [2005] observed surface mixed layer to the water depth are two important stratification and exchange flows that increased during nondimensional parameters. How do the results from this moderate down-estuary winds but decreased during moder- idealized estuary apply to real estuaries with complex ate up-estuary winds. Scully et al. [2005] proposed a wind bathymetry? The Chesapeake Bay features broad shallow straining mechanism analogous to Simpson’s tidal straining: shoals and a narrow, deep center channel. What will be the down-estuary wind enhances subtidal vertical shear and net effects of wind-induced mixing and straining? Chen and strains the along-channel density gradient to increase strati- Sanford [2009] did not consider the effects of Coriolis force fication; up-estuary wind reduces or even reverses the in their modeling study. The width of Chesapeake Bay and other similar estuaries is comparable to or larger than the

1 internal Rossby radius of deformation. How does the Earth’s Horn Point Laboratory, University of Maryland Center for Environmental Science, Cambridge, Maryland, USA. rotation affect the estuarine response to wind forcing? [5] The response of wind-driven circulation in the along- Copyright 2011 by the American Geophysical Union. channel direction has previously been interpreted in terms of 0148-0227/11/2010JC006893

C12012 1of16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012 the competition between the wind stress and barotropic Chesapeake Bay and validated against observational data [Li pressure gradient due to sea level setup [Wang, 1979b; et al., 2005, 2007; Li and Zhong, 2009; Zhong and Li, 2006; Garvine, 1985; Chuang and Boicourt, 1989; Janzen and Zhong et al., 2008]. We use this model to investigate the Wong, 2002]. While this two-layer theory seems well estab- effects of winds on the circulation and stratification in lished, a number of studies in Chesapeake Bay have shown Chesapeake Bay. that along-channel winds can drive strong lateral Ekman [9] The model domain includes eight major tributaries and flows and isopycnal movements, generating upwelling/ a part of the coastal ocean to facilitate free exchange across downwelling at shallow shoals [Malone et al., 1986; Sanford the bay mouth (Figure 1). The total number of grid points is et al., 1990; Scully, 2010]. The lateral flows can interact with 120 80. The model has 20 layers in the vertical direction. cross-channel density gradient in a way analogous to the A quadratic stress is exerted at the bed, assuming that the straining of density field in the along-channel direction. bottom boundary layer is logarithmic over a roughness Without wind forcing, a freshwater plume hugs the western height of 0.5 mm. The vertical eddy viscosity and diffusivity shore as it moves seaward and isopycnals tilt downward on are computed using the k-kl turbulence closure scheme the western side of a cross-channel section. Southward [Warner et al., 2005] with the background diffusivity and (down-estuary) winds generate downwelling on the western viscosity set at 105 m2 s1. Coefficients of horizontal eddy shore and may tilt the isopycnals toward the vertical direc- viscosity and diffusivity are set to 1 m2 s1, which produce tion, reducing stratification. On the other hand, moderate little dissipation of the resolved flow energy [Zhong and Li, northward (up-estuary) winds may flatten isopycnals in 2006]. The model is forced by sea level fluctuations, tem- cross-channel sections, enhancing stratification in the water perature and salinity at the open ocean boundary, by fresh- column. These lateral processes may offset the effects of water inflows at river heads and by winds across the water wind-driven straining in the along-channel direction. More- surface. The open-ocean boundary condition for the baro- over, recent modeling investigations of secondary flows in tropic component consists of Chapman’s condition for sur- tidally driven estuaries have shown that lateral advection can face elevation and Flather’s condition for barotropic be of first-order importance in the along-channel momentum velocity. The boundary condition for the baroclinic compo- balance [Lerczak and Geyer, 2004; Scully et al., 2009]. It is nent includes an Orlanski-type radiation condition for bar- likely that wind-driven lateral circulations will also affect the oclinic velocity. To deal with both inward and outward dynamics and structure of along-channel flows, thereby scalar fluxes across the open boundary, we use a combina- indirectly affecting the density straining in the longitudinal tion of radiation condition and nudging (with a relaxation direction. time scale of 1 day) for temperature and salinity [6] Several recent papers have investigated the dynamics [Marchesiello et al., 2001]. and effects of wind-driven lateral circulations. In the absence [10] We focus on winds in the along-channel (south– of rotational effects, Chen et al. [2009] showed that differ- north) direction since winds in the cross-channel (east–west) ential advection of the axial salinity gradient by wind-driven direction have short fetches. Weather systems passing over axial flow drives bottom-divergent/convergent lateral circu- the Chesapeake Bay have typical periods of 2 to 5 days lation during down-estuary/up-estuary winds. In an idealized [Wang, 1979a]. In this study, we impose a spatially uniform rotating basin, Reyes-Hernández and Valle-Levinson [2010] wind forcing, explored wind modifications on the lateral structure of density-driven flow. Guo and Valle-Levinson [2008] examined A sin½wðÞt 25 25 ≤ t ≤ 27:5 t ¼ ; ð1Þ how winds affect the lateral structure of density-driven cir- W 0 other times culation in Chesapeake Bay. Using a simplified oxygen model, Scully [2010] investigated wind-driven ventilation of t hypoxic waters in Chesapeake Bay and found that northward where W is the along-channel wind stress, t is the time w ¼ 2p winds were most effective at supplying oxygen to hypoxic (days), 5day is the frequency of the wind forcing, and A regions whereas eastward winds were least effective. These is the peak wind stress. We study both down-estuary interesting papers motivate the current research which is (southward) and up-estuary (northward) winds: positive tW directed at understanding how wind-driven along-channel corresponds to up-estuary winds. The maximum wind stress and cross-channel flows affect the stratification response in magnitude A ranges from 0.005 to 0.25 Pa, with the corre- the partially mixed estuary of Chesapeake Bay. sponding range of 2.35 to 12.27 m s 1 for the wind speed [7] The plan for this paper is as follows. Section 2 (Table 1). To further simplify the model setup, we fix the describes model configuration and the design of numerical total river discharge into the bay at a long-term average of experiments. In section 3 we analyze the estuary’s response 1500 m3 s 1 and distribute it to eight major tributaries to down-estuary and up-estuary wind events in a nonrotating according to observations: Susquehanna (51%), Patapsco system. In section 4 we investigate how the Coriolis force (3.67%), Patuxent (3.67%), Potomac (18%), Rappahannock and wind-driven lateral circulations affect the density strat- (4%), York (2%), James (14%), and Choptank (3.67%) ification. Regime diagrams are constructed to summarize the [cf., Guo and Valle-Levinson, 2008]. We only consider tidal wind effects on stratification in section 5. Finally, conclu- forcing at the dominant M2 frequency and fix salinity at sions are made in section 6. 30 psu and temperature at 15°C at the offshore open boundary. To spin up the hydrodynamic model, we run it without wind forcing for 3 years so that the estuarine circu- 2. Model Description lation in the bay reaches a steady state. The model is then [8] A 3-D hydrodynamic model based on the Regional forced with along-channel winds of different magnitudes and Ocean Modeling System (ROMS) has been developed for

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Figure 1. (a) Bathymetry of Chesapeake Bay and its adjacent coastal area. Major tributaries are marked. Depths are in meters. The inset indicates the geographic location of Chesapeake Bay in North America. The solid lines represent the along-channel and cross-channel transects. (b) Regional Ocean Modeling System grid for the Chesapeake Bay model. The shaded areas are used for calculating volume-averaged stratification in later analysis.

Table 1. Wind Experimentsa Ke =0 Ke = 4.26 Ke = 2.06 Ke = 6.82 Wind Stress Wind Speed (Pa) (m s1) Number W Number W Number W Number W Without Wind 0.00 0.00 1 0 18 0 35 0 52 0

Down-Estuary Wind 0.005 2.35 2 0.19 19 0.19 36 0.21 53 0.17 0.01 3.20 3 0.38 20 0.39 37 0.41 54 0.35 0.02 4.34 4 0.77 21 0.77 38 0.82 55 0.69 0.03 5.17 5 1.17 22 1.16 39 1.24 56 1.04 0.05 6.41 6 1.96 23 1.94 40 2.08 57 1.74 0.07 7.37 7 2.79 24 2.72 41 2.91 58 2.45 0.15 10.03 8 6.10 25 6.04 42 6.28 59 5.41 0.25 12.27 9 10.4 26 10.1 43 10.5 60 9.15

Up-Estuary Wind 0.005 2.35 10 0.19 27 0.19 44 0.21 61 0.17 0.01 3.20 11 0.38 28 0.39 45 0.42 62 0.35 0.02 4.34 12 0.76 29 0.78 46 0.83 63 0.70 0.03 5.17 13 1.12 30 1.16 47 1.24 64 1.06 0.05 6.41 14 1.84 31 1.94 48 2.05 65 1.78 0.07 7.37 15 2.56 32 2.71 49 2.84 66 2.50 0.15 10.03 16 5.34 33 5.67 50 5.99 67 5.33 0.25 12.27 17 8.81 34 9.32 51 9.84 68 8.94 aIdealized winds are applied from day 25 to day 27.5. Ke is Kelvin number, and W is Wedderburn number. When Ke = 0, rotation effect is not considered.

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Figure 2. Along-channel distributions of (a, d, g) subtidal currents, (b, e, h) salinity, and (c, f, i) the logarithm of eddy diffusivity at the time of peak wind stress for Run 7 (down-estuary wind), Run 1 (no wind), and Run 15 (up-estuary wind). Coriolis force is switched off in these runs. The 14 psu isohalines are marked as thick lines. directions. In order to examine possible long-term impacts, wind forcing, the estuary is characterized by the two-layer the model is run for additional 70 days after each wind event. gravitational circulation with sloping isohalines in the along-channel section (Figures 2d and 2e). The tidally averaged residual flows are on the order of 0.1 m s1. 3. Longitudinal Straining and Stratification Vertical salinity differences of 4 6 psu stratify the water Asymmetry column. Strong turbulent mixing (i.e., eddy diffusivity > 104 m2 s1) is mainly confined to the tidally driven [11] Using a numerical model of an idealized estuarine bottom boundary layer (Figure 2f ). channel featuring a triangular cross section, Chen and Sanford [14] When the down-estuary wind is applied over the bay, [2009] found that the net effect of winds on estuarine stratifi- it drives a seaward directed current in the surface layer and cation depends on the competition between wind-driven causes a sea level depression at the bay’s head. The associ- mixing and wind-induced straining: moderate down-estuary ated pressure gradient subsequently drives a return flow in winds enhance estuarine stratification whereas strong down- the bottom layer. Hence the down-estuary wind drives a estuary winds and all up-estuary winds reduce stratification. two-layer baroclinic circulation in the stratified water, rein- Does this result apply to Chesapeake Bay? forcing the gravitational circulation (Figure 2a). As a result, [12] We can gauge the relative importance of wind forcing low-salinity surface water tends to spread further down- by calculating the Wedderburn number [Monismith, 1986; stream and high-salinity bottom water intrudes farther Geyer, 1997; Chen and Sanford, 2009], upstream. This would sharpen the vertical salinity gradient. t L However, the wind also produces strong mixing in the sur- W ¼ W ; ð2Þ DrgH 2 face layer (Figure 2c) and erases the stratification there. As shown in the comparison between Figures 2b and 2e, strat- where L is the length of an estuary, Dr is the horizontal ification in Run 7 is still weaker than in Run 1 since mixing density difference, g is the gravitational acceleration, and H overpowers straining effect. is the mean water depth. Assuming H = 9 m and estimating [15] When the wind blows up-estuary (Run 15), it drives a Dr over the distance L between 37.2°N and 38.9°N, we find two-layer circulation that opposes the gravitational circula- that W in Chesapeake Bay varies from 1 to 6 for wind tion (Figure 2g). At the peak wind, the sense of the circu- speeds ranging 5 10 m s1 (see Table 1). Therefore, winds lation is completely reversed: landward flow in the surface will significantly modify the estuarine circulation and strat- layer and seaward flow in the bottom layer. This shear flow ification in the bay. moves heavier water over lighter water and steepens the [13] Figure 2 shows a comparison of current and salinity isopycnals. Both the along-channel straining and wind fields among three runs: Run 1 (no wind forcing, W = 0), mixing work in concert to destabilize the water column Run 7 (down-estuary wind with the peak wind stress at (Figures 2h and 2i). As a result, there is a larger reduction in 0.07 Pa, W = 2.79), and Run 15 (up-estuary wind with the stratification in Run 15 than in Run 7. same peak stress, W = 2.56) (Table 1). We apply a 34 h low- [16] To understand how the down-estuary and up-estuary pass filter to remove tidal oscillations. In the absence of winds affect the salinity distribution in the estuary, we

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Figure 3. Time series of (a, e) subtidal salt flux due to barotropic transport (Qf S0), (b, f) shear dispersion (FE), (c, g) averaged shear in the along-channel current, and (d, h) diffusivity (Ks) for Run 7 (down- estuary wind) and Run 15 (up-estuary wind). Positive flux corresponds to the landward flux. The two dashed lines mark the wind event.

analyze the salt flux through a midbay section (location [17] The down-estuary wind initially produces a seaward indicated in Figure 1a) and decompose it as directed barotropic current that drives the water and salt out RR of estuary, as shown in Figure 3a. Subsequently, the sea level F ¼ ðÞuS ðÞh þ z ds dy S RR depression at the head drives a landward flow which advects ; ð Þ ¼ ðÞu0S0 þ uESE þ uT ST ðÞh þ z ds dy 3 salt back to the estuary. More importantly, the salt flux due to shear dispersion FE doubles during the down-estuary wind ¼Q S þ F þ F f 0 E T event, with the peak value reaching 3.44 104 kg s 1 as 4 1 where u is the velocity component orthogonal to the cross compared with the prewind value of 1.71 10 kg s section, S is salinity, h is the local depth, z is the instanta- (Figure 3b). This corresponds to an amplification of subtidal neous sea level, and s, y are vertically stretched s coordinate velocity shear (defined to be the averaged velocity shear between the surface and bottom layers) from the prewind and horizontal coordinate in the cross-channel direction 2 1 2 1 [Lerczak et al., 2006; Chen and Sanford, 2009]. The value of 1.8 10 s to the maximum of 3.5 10 s velocity and salinity are decomposed into tidally and cross- (Figure 3c). This shear flow exports less saline water seaward and imports more saline water landward, producing a net sectionally averaged (u0, S0), tidally averaged but cross- sectionally varying (u , S ), and tidally and cross-sectionally influx of salt into the estuary and increasing stratification in E E the water column. When the bay is forced by the up-estuary varying (uT, ST) component, respectively. The resultant salt flux consists of three terms: Q S includes the river- wind, however, the wind-driven barotropic flow initially f 0 transports salt into the estuary while the subsequent sea level induced salt loss and wind-induced barotropic adjustment; ’ F results from shear dispersion due to estuarine exchange pileup at the bay s head drives a seaward flow and salt out of E the estuary (Figure 3e). Since the wind-driven current cancels flow; and FT represents tidal oscillatory salt flux. Because tides in Chesapeake Bay are relatively weak, the tidal or even reverses the gravitational flow (Figure 3g), FE decreases and even becomes negative around the peak wind oscillatory salt flux F is small (F /F ≈ 0.01 at this section). T T E (1.9 104 kg s 1, Figure 3f) such that salt is removed from Since FE is the product of subtidal exchange flow and subtidal salinity variability, it is closely related to the stratifi- the estuary and vertical stratification is weakened. Therefore, cation change in the estuary: the estuarine stratification the asymmetry in stratification reduction between the down- estuary and up-estuary winds is closely related to the differ- increases when FE > 0 and decreases when FE <0. ences in the shear-dispersion salt flux FE.

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Figure 4. Time series of volume-averaged stratification for winds at different wind stress magnitudes and in the absence of rotational effects: (a, c, e, g) down-estuary wind and (b, d, f, h) up-estuary wind. The two dashed lines mark the wind event.

[18] To quantify the wind effects on the estuarine stratifi- not provide an explanation. Ignoring the effects of lateral cation, we select a control volume inside the main stem of flows, the stratification change in an estuary depends on the Chesapeake Bay (the shaded area in Figure 1b) and calculate balance between the straining in the along-channel direction the volume-averaged buoyancy frequency N 2 . N 2 is 2.5 and turbulent mixing (see terms 4 and 7 in equation (4)). The 103 rad2 s2 prior to the wind event. During the wind event shear ∂u/∂z at the end of the down-estuary wind is about (day 25 to 27.5), stratification decreases under both the up- 4 times of that at the end of the up-estuary wind (Figures 3c estuary and down-estuary winds (Figures 4e and 4f ). We and 3g) while the averaged eddy diffusivity Ks is about 50% conduct several other runs with wind stress ranging from smaller (Figures 3d and 3h). These differences in the shear 2 0.01 to 0.15 Pa (Table 1). In all the cases studied, the vol- and diffusivity will result in large differences in ∂N /∂t. ume-averaged stratification decreases following both the Moreover, the net reduction in N 2 at the end of the wind down-estuary and up-estuary wind events and the stratifi- event is considerably larger for the up-estuary winds than for cation reduction is larger at higher winds (Figure 4). Chen the down-estuary winds. All these differences contribute to and Sanford [2009] showed that stratification reduction the large asymmetry in the postwind stratification recovery occurs for down-estuary winds when W< 1.8. The hori- times between the two wind directions. We also note that the zontal salinity gradient dS/dx in Chesapeake Bay is about salt flux due to shear dispersion takes longer to recover 4 105 psu m1, an order of magnitude smaller than under the up-estuary wind than under the down-estuary wind that in other estuaries, such as York River [O(104)] [Scully (Figures 3b and 3f). et al., 2005] and Hudson River [O(104)] [Lerczak et al., 2006; Ralston et al., 2008]. Hence ∣W∣ > 1.8 for wind speeds over 6 m s1, placing Chesapeake Bay to the mixing- 4. Lateral Versus Longitudinal Straining dominated regime under most wind-forcing conditions. The on Stratification weak horizontal salinity gradient limits the advective buoy- [20] In Chesapeake Bay where the baroclinic Rossby ancy flux and hence its ability to create stratification during radius (about 5 km) is smaller than or comparable to the the down-estuary winds. width of the estuary (5–20 km), along-channel winds can [19] Although the stratification decreases under both wind drive lateral Ekman flows and isopycnal movements, gen- directions, it experiences larger reductions and takes longer erating upwelling/downwelling at shallow shoals [Malone to recover under the up-estuary winds than under the down- et al., 1986; Sanford et al., 1990; Scully, 2010]. In this estuary winds, as shown in Figure 4. It is particularly inter- section, we investigate how the wind-driven lateral flows esting to note that the stratification takes 1–3 weeks to affect stratification in the estuary. recover fully after the up-estuary wind event. In contrast, the [21] First we compare current and salinity fields at a stratification recovers shortly after the passage of the down- midbay cross section among three model runs: Run 18 (no estuary wind event. Chen and Sanford [2009] also noticed wind forcing); Run 24 (down-estuary wind with the peak this long adjustment time after the up-estuary winds, but did wind stress at 0.07Pa); and Run 32 (up-estuary wind with the

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Figure 5. Distributions of (a, d, g) along-channel current (contours) and cross-channel velocity vectors (arrows), (b, e, h) salinity, and (c, f, i) the logarithm of eddy diffusivity in a midbay section at the time of peak wind stress (day 26.25) for Run 24 (down-estuary wind), Run 18 (no wind), and Run 32 (up-estuary wind). The cross section is looking up-estuary, and negative flows pointing seaward are shaded in gray. The Coriolis force is included in these runs. same peak stress), all incorporating the rotational effects (see varying bottom bathymetry. The sense of the lateral circu- Table 1 and Figure 5). Without wind forcing, the brackish lation (clockwise) is reversed under the up-estuary wind plume is deflected toward the western shore owing to the forcing since the wind-driven Ekman transport is now Coriolis force. In the cross-channel section, isopycnals slope directed eastward (Figure 5g). The upwelling flows lift the downward on the western flank, with the seaward flow isopycnals on the western side up from the depressed posi- hugging the western shore and the landward flow confined to tions (Figure 5h). Compared with the down-estuary wind the deep channel (Figures 5d and 5e). The lateral flows are case (Figure 5b), the isopycnals appear to be more hori- weak (Figure 5d) and the eddy diffusivity is low (Figure 5f ). zontal, and significant stratification is retained in the water [22] When along-channel winds are applied over the bay’s column (Figure 5h) while strong turbulent mixing is con- surface, they drive strong lateral flows with speeds reaching fined to a relatively shallow surface layer (Figure 5i). The O(0.1) m s1. Under the down-estuary wind, the wind- along-channel flow is primarily a vertically sheared two- driven Ekman transport is directed westward and a coun- layer flow. The stratification lessens the effects of bottom terclockwise circulation appears over deep channel and bathymetry on the flow structure. It is noted that the clock- eastern shoal. The strong lateral salinity gradient drives an wise circulation generated during the up-estuary wind eastward flow on the western shoal. The isopycnals are appears to be stronger than the counterclockwise circulation steepened in the upper 5–10 m, featuring weak stratification generated during the down-estuary wind. and strong mixing (Figures 5a–5c). The along-channel flow [23] Wind-driven lateral flows affect the estuarine strati- reveals a laterally sheared structure, with the downwind flow fication not only by rearranging isopycnals in cross-channel in the two shallow shoals and the upwind flow over the deep sections but also by reducing the shear in the along-channel channel. This three-layer flow structure is consistent with the current and thus the effectiveness of the longitudinal wind theoretical predictions of Csanady [1973], Wong [1994], and straining of the density field. To illustrate this second effect, Winant [2004] for wind-driven barotropic flows over we plot the along-channel distributions of subtidal along-

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Figure 6. Along-channel distributions of (a, d, g) subtidal currents, (b, e, h) salinity, and (c, f, i) the logarithm of eddy diffusivity at the time of maximum wind stress for Run 24 (down-estuary wind), Run 18 (no wind), and Run 32 (up-estuary wind). The Coriolis force is switched on in those runs. The 14 psu isohalines are marked as thick lines. channel current, salinity and eddy diffusivity for the rota- a reversal near the onset and termination of the wind event, tional runs (Figure 6) and compare them with those from the as in the nonrotating runs. We focus our attention on the salt nonrotational runs (Figure 2). Although the down-estuary flux due to shear dispersion FE, which is directly related to wind amplifies the two-layer circulation, the velocity shear the estuarine stratification. Similar to the nonrotating runs, is weaker in Run 24 than in Run 7 (compare Figure 6a with FE recovers more quickly under the down-estuary wind than Figure 2a). The Coriolis force acting on the westward lateral under the up-estuary wind. However, FE in the rotating runs flow decelerates the downwind current in the surface layer is different from that in the nonrotating runs in three while the Coriolis force acting the eastward lateral flow noticeable ways. First, the maximum deviations of FE from decelerates the upwind-directed current in the deep channel. its prewind equilibrium are 1.45 104 kg s1 (down-estuary Therefore, the shear in the along-channel current is weak- wind) and 3.44 104 kg s1 (up-estuary wind) in the ened in the presence of rotational effects. Analysis of the rotational runs. They are weaker than 1.73 104 kg s1 along-channel momentum balance shows that the Coriolis (down-estuary wind) and 3.62 104 kg s1 (up-estuary acceleration fv is of an order of magnitude similar to that of wind) in the nonrotating runs. Second, FE reaches its 1 ∂P þ ∂ ∂u maximum/minimum value at 6 h later than in the nonrotating the net driving force r ∂x ∂z KV ∂z (sum of pressure gradient and stress divergence) in each flow layer but has the runs. Third, the salt flux due to shear dispersion remains opposite sign. Detailed analysis of the along-channel and weak for about 10 days after the passage of the up-estuary cross-channel momentum equations as well as the stream- wind event, though it recovers to the prewind level shortly wise vorticity equation will be presented in future paper. after the down-estuary wind event. As discussed earlier, the Similarly, the along-channel flow under the up-estuary wind Coriolis force acting on the lateral flows weakens the shear (Run 32) does not feature a strong reversed two-layer cir- in the along-channel flow (compare Figures 7c and 7g with culation as seen in the nonrotating run (Run 15). It is weak Figures 3c and 3g), resulting in weak salt flux and slow over most of the along-channel section (compare Figures 6g recovery of salt in the estuary. Finally, we note that the and 2g). This weak shear is also due to the Coriolis force volume-averaged eddy diffusivity is larger in the down- acting on the clockwise lateral flows. The along-channel estuary wind case than in the up-estuary wind case during salinity distribution also exhibits large differences between the wind-perturbation period (also see Figures 5c and 5i), the rotational and nonrotational runs. Under the down-estuary but the diffusivity is slightly stronger after the up-estuary wind, the isopycnals near surface are tilted vertically and wind than after the down-estuary wind (Figures 7d and 7h). strong turbulent mixing extends down to about 10 m depth [25] To quantify the effects of winds on the stratification 2 (Figures 6b and 6c). Under the up-estuary wind, however, in the bay, we calculate the volume-averaged N for all significant stratification remains in the surface layer and rotating runs, as shown in Figure 8. Compared with the time strong turbulent mixing is limited to a shallower depth series for the nonrotating runs (Figure 4), the stratification (Figures 6h and 6i). In the absence of the rotational effects, reduction during the wind event (day 25 to 27.5) is signifi- however, the turbulent mixing in the surface layer is stronger cantly weaker. Similar to the nonrotating runs, the stratifi- under the up-estuary winds than under the down-estuary cation decreases under all the down-estuary winds. winds (see Figures 2c and 2i). However, the stratification change is very different under the [24] Next we calculate the salt flux through the midbay up-estuary winds. At moderate wind speeds, the lateral section, as shown in Figure 7. The barotropic salt flux shows advection actually causes a brief increase of N 2 (Figures 8d

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Figure 7. Time series of (a, e) subtidal salt flux due to barotropic transport (Qf S0), (b, f) shear dispersion (FE), (c, g) averaged shear in the along-channel current, and (d, h) diffusivity (Ks) for Run 24 (down-estuary wind) and Run 32 (up-estuary wind). Positive flux corresponds to the landward flux. The two dashed lines mark the wind event. and 8f). This stratification increase is caused by the flatten- winds for wind stress at 0.07 and 0.15 Pa. This contrasts ing of isopycnals at the cross-channel sections at the begin- with the large stratification asymmetry found in the nonro- ning phase of the wind event. Further upwelling at the tating runs (Figure 4). More significant difference between western shore will tilt the isopycnals toward the vertical the down-estuary and up-estuary winds lies in the postwind direction and reduce the stratification (cf. Figure 5h). At high stratification-recovery time. Under the down-estuary winds, up-estuary winds, strong upwelling associated with the N 2 recovers shortly after the passage of the wind. Under the clockwise lateral circulation and vertical titling will quickly up-estuary winds, however, the stratification recovery takes lead to a reduction in stratification. Moreover, the longitu- 1–3 weeks to complete. dinal straining and strong wind mixing contribute to further [26] To understand how the estuarine stratification stratification reduction (Figures 8f and 8h). In the presence responds to the wind forcing, we conduct a diagnostic of rotational effects, the magnitude of stratification reduction analysis of the stratification equation given by is nearly the same between the down-estuary and up-estuary

ðÞ1 ðÞ2 ðÞ3 ð Þ ðÞ ðÞ zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{ zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{ zfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflffl{ zfflfflfflfflfflffl}|fflfflfflfflfflffl{4 zfflfflfflffl}|fflfflfflffl{5 zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{6 ∂ 2 ∂ 2 ∂ 2 ∂ 2 ∂ ∂ ∂ ∂ ∂ ∂ N ¼ N þ N þ N þ b u S þ b v S þ b w S ∂ u ∂ v ∂ w ∂ g ∂ ∂ g ∂ ∂ g ∂ ∂ t |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}x y z |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}z x z y z z advection straining ; ð4Þ ðÞ ðÞ ðÞ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{7 zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{8 zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{9 ∂2 ∂S ∂2 ∂S ∂2 ∂S þgb K þgb K þgb K ∂ 2 S ∂ ∂ ∂ H ∂ ∂ ∂ H ∂ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}z z z x x z y y diffusion

9of16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012

Figure 8. Time series of volume-averaged stratification for winds at different wind stress magnitudes and in the presence of rotation: (a, c, e, g) down-estuary wind and (b, d, f, h) up-estuary wind. The time period between the two dashed lines marks the wind event. where terms 1–3 represent the advection terms, terms 4–6 of the lateral salinity gradient (Figure 9e). The straining of represent the straining terms, and terms 7–9 represent the ∂S/∂y by the lateral circulation leads to the titling of iso- diffusion terms. Appendix A provides details on how to pycnals toward the vertical direction and a stratification calculate these terms numerically in the ROMS model. reduction. Therefore, the lateral straining opposes the lon- [27] We compare the magnitudes of the straining terms in gitudinal straining to cause a temporal stratification increase the along-channel and cross-channel directions at the mid- in the first part of the wind event, but the lateral and longi- bay section (Figure 9). The along-channel salinity gradient tudinal straining work together to destroy stratification in the ∂S/∂x is estimated as the average value between 37.2°N and later part of the wind event. This explains why the stratifi- 38.9°N while the cross-channel salinity gradient ∂S/∂y is cation decreases after the initial spike under the up-estuary estimated as the average salinity difference between the winds (Figure 8). western and eastern shore in the midbay section. The cur- [28] The above analysis can be summarized in terms of the rents are detided through a 34 h low-pass filter and the competition between along-channel and cross-channel vertical shears (∂u/∂z, ∂v/∂z) are calculated from the surface- straining. When forced by the down-estuary wind, the to-bottom velocity difference and then averaged over the velocity shear in the along-channel direction is enhanced. cross section. Under the down-estuary wind, the along- The straining of this shear across the longitudinal salinity channel current shear is amplified (Figure 9a) and acts on ∂u ∂S > gradient leads to restratification since ∂z ∂x 0. On the other the longitudinal salinity gradient to create stratification hand, the counterclockwise secondary circulation steepens (Figure 9c). On the other hand, the counterclockwise lateral the isopycnals in the cross-channel sections, increases the circulation steepens the isopycnals to reduce the stratifica- lateral salinity gradient and reduces stratification since tion. Since ∂S/∂y is 3–5 times larger than ∂S/∂x, the lateral ∂v ∂S ∂ ∂ < 0. When forced by the up-estuary wind, the clock- straining overcomes the longitudinal straining at this midbay z y ∂u ∂s wise secondary circulation flattens the isopycnals, reduces section (Figure 9c). The relative magnitudes of gb and ∂ ∂ ∂z ∂x the lateral baroclinic gradient and increases N2 since v S > 0 gb ∂v ∂s change at different cross-channel sections, but they ∂z ∂y ∂z ∂y , even though the wind straining in the along-channel direc- are always of the opposite signs. Under the up-estuary wind, tion acts to reduce the stratification (∂u ∂S < 0). Hence the the shear in the along-channel direction is reversed ∂z ∂x wind-driven lateral flows offset the effects of the along- (Figure 9d) such that its straining over the longitudinal channel straining. The only exception to this offsetting effect salinity gradient causes a stratification reduction (Figure 9f). is found during the second half of up-estuary wind events The clockwise lateral circulation acting on the lateral salinity when the along-channel and cross-channel straining may gradient initially opposes it by flattening the isopycnals in act together to reduce the stratification in the estuary. the cross-channel sections, causing a temporal rise in the [29] We have integrated equation (4) over the same con- stratification (Figure 9f). Later on, however, upwelling and trol volume used to calculate the estuary-wide averaged lifting of isopycnals on the western shore causes a reversal

10 of 16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012

Figure 9. Time series of (a, d) vertical shear, (b, e) horizontal salinity gradient, and (c, f ) horizontal straining for the down-estuary and up-estuary winds with the maximum stress of 0.07 Pa. Each variable is decomposed into along-channel (blue) and cross-channel (red) components and then detided by a 34 h low-pass filter. The time period between the two dashed lines marks the wind event.

Figure 10. Time series of the terms in the volume-averaged stratification equation, obtained from (a) Run 24 (down-estuary wind) and (b) Run 32 (up-estuary wind): time-change rate (black), advection (gray), straining (orange), and mixing (green). A positive value represents the tendency to increase stratification. The time period between the two dashed lines marks the wind event.

11 of 16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012

Figure 11

12 of 16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012 stratification and compared the relative magnitudes of the specific to Chesapeake Bay, we change f by 50% as a advection, straining and turbulent diffusion terms, as shown preliminary way to explore estuaries of different widths in Figure 10. Before the wind event, the stratification (Table 1). reaches quasi-equilibrium owing to the balance between the [31] To characterize changes in estuarine stratification straining and turbulent diffusion. The introduction of wind during the wind-forcing period, we average the volume- forcing upsets this balance. At the beginning of the down- averaged buoyancy―― frequency over the entire duration of―― the estuary wind event, the lateral straining overcomes the lon- 2 2 wind event N and normalize it by its prewind value N0 . gitudinal straining to cause a small drop in the total straining When the normalized stratification is below unity, the net term. Subsequently, the wind-driven along-channel straining wind effect is a decrease in the stratification, and vice versa. enhances the straining term. The advection term is an order As shown in Figure 11a, the stratification always decreases of magnitude smaller than the straining term. The diffusion at large values of ∣W∣, indicating that strong wind mixing term reaches a maximum around the peak wind. The sum of overcomes straining processes to reduce stratification. In the straining, advection, and diffusion is equal to the temporal nonrotating cases (Ke = 0), the wind straining opposes/ change of the volume-averaged N 2, which is negative in the conspires with wind mixing during down-estuary/up-estuary first half of the wind event but becomes positive during the winds, as suggested by Scully et al. [2005]. Hence the second half. This explains the time series of N 2 which stratification reduction during the down-estuary winds is decreases in the first half of the down-estuary wind event but smaller than that during the up-estuary winds of the same increases in the second half (Figures 8a, 8c, 8e, and 8g). The magnitude. In the presence of rotation, this stratification- diagnostics of the stratification equation (4) reveals more reduction asymmetry is weakened. The lateral tilting offsets dramatic changes during the up-estuary winds. The total the along-channel straining to produce smaller stratification straining term is enhanced owing to the isopycnal flattening reduction under up-estuary winds. At moderate positive W in the cross-channel sections in the first half of the wind values, the lateral straining overpowers the longitudinal event but is reduced owing to the along-channel straining in straining to increase stratification. This effect is stronger at the second half. Again the advection term is much smaller higher values of Ke (strongly rotating systems or wider than the straining term. The time tendency ∂N2/∂t is positive estuaries). In comparison, the stratification reduction is rel- initially but turns negative later on. This explains the initial atively insensitive to Ke values under the down-estuary spike of N 2 and the subsequent drop in stratification under winds. the up-estuary winds (Figures 8b, 8d, and 8f). [32] As shown in Figures 4 and 8, the wind effects are not limited to the period of active wind forcing but may persist well after the termination of the wind event. For example, 5. Regime Diagram one striking difference between the down-estuary and up- [30] The effects of along-channel and lateral straining on estuary winds is the stratification recovery time after the estuarine stratification can be summarized in a regime dia- passage of the wind event. Figure 11b summarizes the gram based on dimensionless parameters. The effect of recovery time (defined as the time taken for N 2 to recover to along-channel straining can be described by the Wedderburn 95% of its prewind value) as a function of Wedderburn number W [Monismith, 1986; Geyer, 1997; Chen and number W at different values of Kelvin number Ke. There is Sanford, 2009]. The relative importance of the Earth’s a strong asymmetry in the postwind recovery time between rotation can be described by Kelvin number Ke, which is the down-estuary and up-estuary winds under all values of also known as the ratio of the basin’s width to internal Ke, although the asymmetry is somewhat weaker in the Rossby radius [Garvine, 1995; Valle-Levinson, 2008]: nonrotating case (Ke = 0). The stratification recovers quickly (less than 1 day) to the prewind values under all down- fB estuary winds in the presence of the rotational effects. In Ke ¼ pffiffiffiffiffiffiffiffiffi ; ð5Þ contrast, it takes considerably longer for the stratification to g′h S recover under the up-estuary winds. The recovery time increases with Ke and is a rapidly increasing function of W where f is the Coriolis parameter, B is the basin/estuary for W < 2 but a slowly increasing function of W for W>2. ′ width, g is the reduced gravitational acceleration determined Another way to present the postwind effects is to calculate by the density difference between the surface and bottom the average value of N 2during the postwind recovery period, layers, and hS is the mean depth of the surface layer. The as shown in Figure 11c. Since the stratification takes much rotational effect becomes important if Ke > 1. The nonro- longer to recover under the up-estuary winds than the down- tating runs correspond to Ke = 0, while the rotating runs estuary winds, the time-averaged stratification is weaker correspond to Ke = 4.26. Although the model bathymetry is

Figure 11. (a) Stratification change during the wind perturbation, (b) stratification recovery time, and (c) mean stratification during the recovery stage as functions of Wedderburn (W) and Kelvin (Ke) numbers. Positive Wedderburn number corresponds to up-estuary wind. The stratification is averaged over the wind event in Figure 11a and over the recovery period in Figure 11c and then normalized against its prewind level, so that values below 1 indicate stratification reduction. The recovery time is defined as the time required for the volume-averaged stratification to resume 95% of its prewind level after the passage of the wind.

13 of 16 C12012 LI AND LI: WIND EFFECTS ON STRATIFICATION C12012 after the up-estuary winds than after the down-estuary wind forcing requires the documentation of the three- winds. dimensional flow and density fields.

6. Conclusions Appendix A [33] We have conducted process-oriented numerical experiments to investigate how the Chesapeake Bay estuary [37] The equation for the salt conservation is given by responds to down-estuary and up-estuary winds. In the absence of rotational effects, stratification in the estuary ∂S ∂S ∂S ∂S ∂ ∂S ∂ ∂S decreases following both down-estuary and up-estuary ¼ u þ v þ w þ KS þ KH ∂t ∂x ∂y ∂z ∂z ∂z ∂x ∂y winds, but the stratification experiences larger reduction and ∂ ∂S takes longer to recover under up-estuary winds. In the þ KH ; ðA1Þ presence of rotational effects, the down-estuary/up-estuary ∂x ∂y winds drive counterclockwise/clockwise lateral circulations which rearrange isopycnals in cross-channel sections and where S is the salinity, u, v, and w are the velocity compo- reduce shear in the along-channel currents. Therefore, the nents in the x, y, and z directions, and KS and KH are the lateral straining weakens the effects of the longitudinal vertical and horizontal eddy diffusivity. Assuming that the straining and reduces the asymmetry in stratification reduc- stratification in the estuary is dominated by the salinity dif- tion between the down-estuary and up-estuary winds. 2 ¼ b ∂S ference, that is, N g ∂z, we obtain from equation (A1) [34] Regime diagrams are constructed to summarize the wind effects on estuarine stratification and postwind ∂ 2 ∂ 2 ∂ 2 ∂ 2 recovery time in the nondimensional parameter space of N ¼ N þ N þ N ∂ u ∂ v ∂ w ∂ Wedderburn (W) and Kelvin (Ke) numbers. For the down- t |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}x y z estuary winds (W < 0), the estuarine stratification decreases advection with increasing magnitude of ∣W∣ but is nearly independent ∂u ∂S ∂v ∂S ∂w ∂S þ gb þ gb þ gb of Ke. For the up-estuary winds (W > 0), the stratification ∂z ∂x ∂z ∂y ∂z ∂z decreases with increasing W but increases with Ke. The |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} postwind stratification recovery time shows a strong asym- straining ∂2 ∂S ∂2 ∂S ∂2 ∂S metry between the down-estuary (W < 0) and up-estuary gb K þ K þ K : ∂ 2 S ∂ ∂ ∂ H ∂ ∂ ∂ H ∂ (W > 0) winds. The stratification recovers quickly (less than |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}z z z x x z y y 1 day) to the prewind values under all down-estuary winds, – diffusion but it takes 1 3 weeks to recover under the up-estuary ðA2Þ winds. The regime diagrams are based on the model results for Chesapeake Bay. Although the bay is a good example of a partially mixed estuary, it is somewhat special since it receives freshwater inputs from western tributaries, in addi- [38] To evaluate the terms in equation (A2) numerically tion to that from the Susquehanna River at its northern end. on the Arakawa C-grid used in ROMS, we rewrite the Nevertheless, the regime diagrams could provide a starting advection terms in the flux form such that the flux out of point to assess the relative importance of lateral versus lon- each grid cell is identical to the flux into the adjacent cell and gitudinal straining in different types of wind-forced estuar- the sum of the grid point values conserves the advected ies, such as Long Island Sound, York River, and Albemarle quantity in the finite difference approximation. Similarly, we and Pamlico Sound. can rewrite the straining terms for the easy and accuracy of [35] We have examined the sensitivity of model results to numerical calculations. Then equation (A2) becomes turbulence closure schemes and conducted parallel numeri- termð1Þ termð2Þ cal experiments using the KPP model. The model results are zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{ ∂N 2 ∂uN 2 ∂u ∂vN 2 ∂v quantitatively similar to those based on the k-kl turbulence ¼ þ N 2 þ þ N 2 model. Our previous model simulations [Li et al., 2005, ∂t ∂x ∂x ∂y ∂y

2007] also found such insensitivity to different turbulence termð3Þ parameterization schemes. zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ ∂wN 2 ∂w ∂ ∂uS ∂u [36] For the future work, we plan to conduct model þ þ N 2 þ gb S termð1Þ simulations using idealized but more generic estuarine- ∂z ∂z ∂z ∂x ∂x channel geometry (such as those used by Chen and Sanford ∂ ∂vS ∂v þ gb S termð2Þ [2009], Chen et al. [2009], and Lerczak and Geyer [2004]) ∂z ∂y ∂y and examine if the regime diagrams are sensitive to details in the estuarine bathymetry. Further work is also needed to ∂ ∂wS ∂w þ gb S termð3Þ relate these idealized mechanistic studies to field observa- ∂z ∂z ∂z tions of the estuarine response to wind events. In wide ∂2 ∂S ∂2 ∂S ∂2 ∂S estuaries such as Chesapeake Bay, our modeling investiga- gb K þ K þ K : ∂ 2 S ∂ ∂ ∂ H ∂ ∂ ∂ H ∂ tions demonstrate that the rotational effects are important z z z x x z y y and a full understanding of the estuarine response to the ðA3Þ

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[39] In the ROMS model, which uses a terrain-following Guo, X. Y., and A. Valle-Levinson (2008), Wind effects on the lateral vertical coordinate, the form of the stratification equation structure of density-driven circulation in Chesapeake Bay, Cont. Shelf Res., 28(17), 2450–2471, doi:10.1016/j.csr.2008.06.008. used for the diagnostic analysis is given by Janzen, C. D., and K. C. Wong (2002), Wind-forced dynamics at the estuary-shelf interface of a large coastal plain estuary, J. Geophys. Res., termð1Þ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ 107(C10), 3138, doi:10.1029/2001JC000959. ∂N 2 1 ∂uH N 2 ∂uH Lerczak, J. A., and W. R. Geyer (2004), Modeling the lateral circulation in ¼ Z þ N 2 Z straight, stratified estuaries, J. Phys. Oceanogr., 34(6), 1410–1428, ∂t HZ ∂x ∂x doi:10.1175/1520-0485(2004)034<1410:MTLCIS>2.0.CO;2. Lerczak, J. A., W. R. Geyer, and R. J. Chant (2006), Mechanisms driv- ð Þ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{term 2 ing the time-dependent salt flux in a partially stratified estuary, J. Phys. Oceanogr., 36(12), 2296–2311, doi:10.1175/JPO2959.1. 1 ∂vH N 2 ∂vH þ Z þ N 2 Z Li, M., and L. J. Zhong (2009), Flood-ebb and spring-neap variations of HZ ∂y ∂y mixing, stratification and circulation in Chesapeake Bay, Cont. Shelf Res., 29(1), 4–14, doi:10.1016/j.csr.2007.06.012. ð Þ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{term 3 Li, M., L. Sanford, and S. Y. Chao (2005), Effects of time dependence in unstratified tidal boundary layers: Results from large eddy simulations, 1 ∂ H N 2 ∂ H – – þ Z þ N 2 Z Estuarine Coastal Shelf Sci., 62(1 2), 193 204, doi:10.1016/j.ecss. HZ ∂s ∂s 2004.08.017. Li, M., L. Zhong, W. C. Boicourt, S. L. Zhang, and D. L. Zhang (2007), gb ∂ 1 ∂uHZ S ∂uHZ Hurricane-induced destratification and restratification in a partially mixed þ S termð1Þ estuary, J. Mar. Res., 65(2), 169–192. HZ ∂s HZ ∂x ∂x Malone, T. C., W. M. Kemp, H. W. Ducklow, W. R. Boynton, J. H. Tuttle, gb ∂ 1 ∂vH S ∂vH and R. B. Jonas (1986), Lateral variation in the production and fate of þ Z S Z termð2Þ phytoplankton in a partially stratified estuary, Mar. Ecol. Prog. Ser., HZ ∂s HZ ∂y ∂y 32(2–3), 149–160, doi:10.3354/meps032149. Marchesiello, P., J. McWilliams, and A. Shchepetkin (2001), Open bound- b ∂ ∂ ∂ þ g 1 HZ S HZ ð Þ ary conditions for long-term integration of regional oceanic models, S term 3 Ocean Modell., 3(1–2), 1–20, doi:10.1016/S1463-5003(00)00013-5. HZ ∂s HZ ∂s ∂s Monismith, S. (1986), An experimental study of the upwelling response of b ∂ ∂ ∂ stratified reservoirs to surface shear stress, J. Fluid Mech., 171, 407–439, g Ds þ DX þ DY ; ð Þ ∂s ∂s ∂s A4 doi:10.1017/S0022112086001507. HZ North, E. W., S. Y. Chao, L. P. Sanford, and R. R. Hood (2004), The influence of wind and river pulses on an estuarine turbidity maximum: Numer- where s is the vertical distance from surface as a fraction of ical studies and field observations in Chesapeake Bay, Estuaries, 27(1), ≤ s ≤ W 132–146, doi:10.1007/BF02803567. total water depth HZ ( 1 0), is the vertical velocity O’Donnell, J., H. G. Dam, W. F. Bohlen, W. Fitzgerald, P. S. Gay, A. E. in the s coordinate, and DX, DY, and Ds represent the hori- Houk, D. C. Cohen, and M. M. Howard-Strobel (2008), Intermittent zontal and vertical diffusion terms. ventilation in the hypoxic zone of western Long Island Sound during the summer of 2004, J. Geophys. Res., 113, C09025, doi:10.1029/ [40] Acknowledgments. We thank Bill Boicourt, Malcolm Scully, 2007JC004716. and Peng Jia for helpful discussions and two reviewers for thoughtful com- Ralston, D. K., W. R. Geyer, and J. A. Lerczak (2008), Subtidal salinity ments. We are grateful to NSF (OCE-082543 and OCE-0961880) and and velocity in the Hudson River estuary: Observations and modeling, NOAA (CHRP-NA07N054780191) for the financial support. This is J. Phys. Oceanogr., 38(4), 753–770, doi:10.1175/2007JPO3808.1. UMCES contribution 4566 and CHRP contribution 150. Rattray, M., and D. V. Hansen (1962), A similarity solution for circulation in an estuary, J. Mar. Res., 20(2), 121–133. Reyes-Hernández, C., and A. Valle-Levinson (2010), Wind modifications to density-driven flows in semienclosed, rotating basins, J. Phys. References Oceanogr., 40, 1473–1487, doi:10.1175/2010JPO4230.1. Sanford, L. P., K. G. Sellner, and D. L. Breitburg (1990), Covariability of Bowden, K. F. (1953), Note on wind drift in a channel in the presence of dissolved-oxygen with physical processes in the summertime Chesapeake tidal currents, Proc. R. Soc. London, Ser. A, 219(1139), 426–446, Bay, J. Mar. Res., 48(3), 567–590. doi:10.1098/rspa.1953.0158. Scully, M. E. 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