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  • View in gallery

    Map showing bathymetry and mooring sites (stars) in Chesapeake Bay. The rectangle in (a) corresponds to the zoomed-in view of the mooring area in (b).The x and y axis represent the along-channel and cross-channel directions, respectively.

  • View in gallery

    Time series of (a) the Susquehanna River discharge, (b) the wind speed vector, and (c) the along-channel (red) and cross-channel (blue) wind speed components. (d),(e) Time–depth distribution of the along-channel velocity (positive landward) at the (d) MB and (e) M3 sites. The solid and dashed vertical lines mark the downestuary events (D1, D2, . . .) and the upestuary wind events (U1, U2, …), respectively.

  • View in gallery

    (a) Time series of the along-channel wind speed during the upestuary wind event U5. Three vertical lines indicate the setup, peak, and setdown phases of U5. Cross-channel distributions of the lateral velocity (blue arrows) and salinity (red contours) during the (b) setup phase, (c) peak wind, and (d) setdown phase of U5.

  • View in gallery

    As in Fig. 3, but for the downestuary wind D2 event.

  • View in gallery

    (a)–(d) As in Fig. 4, but for the downestuary D1 event. (e) Vertical profiles of salinity measured on 27 Mar at the M4 (blue) and MB (red) sites.

  • View in gallery

    Time–depth distributions of the low-pass filtered lateral velocities at the mooring stations (a) M6, (b) MB, and (c) M3. The vertical lines mark the downestuary and upestuary wind events.

  • View in gallery

    Time series of the (a) low-pass filtered along-channel wind speed and (b) depth-mean streamwise vorticity averaged over the observational sites on the eastern half of the estuarine cross section (MB, M5, M6, and M7; red) and over the observational sites on the western half (M1, M2, M3, and M4; blue). Time series of the (c) depth-mean tilting of planetary vorticity term on the western (blue) and eastern (red) halves and the (d) depth-mean baroclinicity term on the western (blue) and eastern (red) halves. Vertical lines indicate the timings of the peak wind during the downestuary and upestuary wind events.

  • View in gallery

    (a) Averaged streamwise vorticity (red circles) and (blue circles) vs Wedderburn (W) number during the 12 wind events. (b) Vorticity generation term TPV as a function of W for the eastern (red circles) and western (blue circles) halves of the estuarine cross section. (c) Lateral baroclinic forcing LBF as a function of W for the eastern (red circles) and western (blue circles) halves.

  • View in gallery

    Time series of the near-bottom, along-channel (red) and lateral (blue) velocities at the (a) MB, (b) M5, and (c) M6 sites.

  • View in gallery

    Time series of the model-predicted, near-bottom (a) along-channel and (b) lateral velocities at the MB site. The red lines were obtained from a model that considered the effects of Earth’s rotation while the blue lines were from a model that turned off the Coriolis force.

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Baroclinic Effects on Wind-Driven Lateral Circulation in Chesapeake Bay

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  • 1 Horn Point Laboratory, University of Maryland Center for Environmental Science, Cambridge, Maryland
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Abstract

The 2-month-long mooring data were collected in a straight midsection of Chesapeake Bay to document the lateral circulation driven by along-channel winds. Under upestuary winds, the lateral circulation featured a clockwise (looking into estuary) circulation in the surface layer, with lateral Ekman forcing as the dominant generation mechanism. Under downestuary winds, however, the lateral circulation displayed a structure dependent on the Wedderburn number W: a counterclockwise circulation at small W and two counterrotating vortices at large W. The surface lateral velocity was phase locked to the along-channel wind speed. Analysis of the streamwise vorticity equation showed that the strength and structure of the lateral circulation in this stratified estuary were largely determined by the competition between the tilting of planetary vorticity by along-channel currents and lateral baroclinic forcing due to sloping isopycnals. Under strong, downestuary winds, the lateral baroclinic forcing offset or reversed the tilting of planetary vorticity on the western half of the estuarine channel, resulting in two counterrotating lateral circulation cells. A bottom lateral flow was observed in the deep channel and appeared to be generated by lateral Ekman forcing on the along-channel currents.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Xiaohui Xie, xxie@umces.edu

Abstract

The 2-month-long mooring data were collected in a straight midsection of Chesapeake Bay to document the lateral circulation driven by along-channel winds. Under upestuary winds, the lateral circulation featured a clockwise (looking into estuary) circulation in the surface layer, with lateral Ekman forcing as the dominant generation mechanism. Under downestuary winds, however, the lateral circulation displayed a structure dependent on the Wedderburn number W: a counterclockwise circulation at small W and two counterrotating vortices at large W. The surface lateral velocity was phase locked to the along-channel wind speed. Analysis of the streamwise vorticity equation showed that the strength and structure of the lateral circulation in this stratified estuary were largely determined by the competition between the tilting of planetary vorticity by along-channel currents and lateral baroclinic forcing due to sloping isopycnals. Under strong, downestuary winds, the lateral baroclinic forcing offset or reversed the tilting of planetary vorticity on the western half of the estuarine channel, resulting in two counterrotating lateral circulation cells. A bottom lateral flow was observed in the deep channel and appeared to be generated by lateral Ekman forcing on the along-channel currents.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Xiaohui Xie, xxie@umces.edu

1. Introduction

Recent research has highlighted the importance of lateral circulation in estuarine dynamics (Geyer and MacCready 2014). Trowbridge et al. (1999) found that the local bottom stress measured from turbulence-resolving current meters does not match the stress calculated from the overall along-channel momentum balance in the Hudson River estuary and suggested that the discrepancy may be due to lateral momentum transport. In a numerical modeling study, Lerczak and Geyer (2004) demonstrated that advection by the lateral circulation is an important term in the along-channel momentum equation and the lateral circulation could be a key driver of estuarine exchange flows. Scully et al. (2009) found a similar result in a realistic simulation of the Hudson River estuary: the stronger lateral circulation during flood tides results in the advection of low-momentum fluid from shallow shoals to the deep channel, and the lateral advection becomes a source term for the estuarine circulation when averaged over a tidal cycle. Burchard et al. (2011) used a mathematical approach to analyze the contributions of individual processes to the estuarine residual circulation and found that advectively driven circulation could be as important as tidal straining circulation and gravitational circulation in weakly stratified estuaries.

Most of the previous studies focused on the lateral circulation driven by tidal flows. Differential advection (Lerczak and Geyer 2004), boundary mixing on a sloping bottom (Chen and Sanford 2009), and channel curvature (Seim and Gregg 1997) are among the processes known to generate the lateral circulation. The bottom Ekman forcing is another major mechanism driving the lateral circulation (Winant 2007; MacCready and Geyer 2010). Huijts et al. (2009) showed that the Ekman rectification is the dominant generation mechanism of lateral circulation in the narrow, northern Chesapeake Bay. Scully et al. (2009) conducted a numerical modeling study of the Hudson River estuary and found that nonlinear tidal rectification by lateral Ekman transport generates a lateral circulation that rotates clockwise (looking into the estuary) during flood tides and counterclockwise during ebb tides. Scully et al. (2009) further showed that the lateral baroclinic pressure gradient may reinforce or oppose the lateral circulation generated by the Ekman transport. Using the streamwise vorticity as a diagnostic quantity, Li et al. (2014) found that the strength of the lateral circulation in a tidally driven stratified estuary is not solely governed by the Ekman dynamics in the bottom boundary layer but depends on the three-way balance among the tilting of planetary vorticity by the vertical shear in the along-channel current, lateral baroclinic forcing, and turbulent diffusion.

Along-channel winds can also generate lateral circulation via lateral Ekman transport in the surface layer of estuaries. They can drive upwelling/downwelling flows and transport biologically important materials such as nutrients and oxygen between the deep channel and shallow shoals (Malone et al. 1986; Sanford et al. 1990; Reynolds-Fleming and Luettich 2004; Wilson et al. 2008). In a modeling study of Chesapeake Bay, Scully (2010) found that the wind-driven lateral exchange of oxygen between well-oxygenated shallow shoals and the hypoxic deep channel may be more important than direct turbulent mixing in supplying oxygen to the deep channel. Compared to the lateral circulation in tidally driven estuaries, few studies have focused on wind-driven lateral circulation (Malone et al. 1986; Sanford et al. 1990; Wilson et al. 2008; Chen et al. 2009; Scully 2010). Using a numerical model of Chesapeake Bay, Li and Li (2012) simulated the wind-driven lateral circulation under idealized wind events. They found that the clockwise circulation generated under the upestuary winds is twice as strong as the counterclockwise circulation generated under the downestuary winds and attributed this asymmetry in the circulation strength to lateral baroclinic forcing (Li and Li 2012). Furthermore, Li and Li (2011) showed that the wind-driven lateral straining of the density field may offset the effects of longitudinal straining (Scully et al. 2005).

Our current understanding of the wind-driven lateral circulation derives mostly from numerical modeling studies. Furthermore, they were primarily limited to idealized wind events such as a single wind event of certain duration or periodically rotating winds. It is not clear if these idealized model results apply to more realistic conditions in which an estuary may be affected by a succession of wind events as different weather fronts move through. More importantly, there have been no systematic observational documentations of the wind-driven lateral circulation in an estuary. In this paper, we present 2-month-long mooring observations of the wind-driven lateral circulation in Chesapeake Bay. We investigate the magnitude and structure of the lateral circulation under different wind-forcing conditions and pay particular attention to the role of the lateral baroclinic forcing.

2. Data collection and processing

During 2012 (16 March to 29 June), data were collected at eight mooring stations (MB and M1 to M7) anchored along a cross-channel transect (M transect) in a relatively straight midsection of Chesapeake Bay (Fig. 1). Each mooring site was equipped with a set of bottom-mounted instrumentation, including an acoustic Doppler current profiler (ADCP) and a temperature–conductivity–dissolved oxygen (TCO) sensor. Except at the M4 and M5 sites, the bottom-mounted instrumentation also included a high-frequency acoustic Doppler velocimeter (ADV). Detailed information of these ADCP and TCO data is presented in Tables 1 and 2. Except for the MB station in the deep channel, all mooring sites were equipped with a surface buoy with meteorological instrumentation. These buoys provided bulk measurements of air temperature, wind speed and direction, relative humidity, sea surface temperature, and salinity. Atmospheric measurements were made at a height of 3 m above the mean water surface, while temperature–conductivity (TC) sensors were mounted at ~1 m below the sea surface. Other TC/TCO probes were installed between the surface buoy and the bottom-mounted instrumentation. The mooring station S was located in the deep channel to the south of the M transect and was equipped with TC or TCO probes at depths of 1, 14, and 22 m (Fig. 1b). The TC data collected at the S and M5 sites were used to compute the along-channel density gradient (see section 5b). Since the observational period of the bottom-mounted instruments was shorter than that of the surface buoy, we only analyze the data recorded during the periods when ADCP measurements were available.

Fig. 1.
Fig. 1.

Map showing bathymetry and mooring sites (stars) in Chesapeake Bay. The rectangle in (a) corresponds to the zoomed-in view of the mooring area in (b).The x and y axis represent the along-channel and cross-channel directions, respectively.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

Table 1.

Mooring sites and ADCP information.

Table 1.
Table 2.

Temperature–conductivity–oxygen data information.

Table 2.

To show the three-dimensional flow field, we decompose the horizontal velocity vector into along-channel (x) and lateral (y) components (u, υ). The major axis of the depth-averaged tidal current is used to define the x direction (positive northward), while the y direction is defined to be at 90° to the x direction (positive westward; see Fig. 1b). The positive z is pointed upward. The estimated positive primary axis direction is approximately 105° with respect to the true east direction (0°). Wind speeds are averaged over all available sites along the M transect to smooth out small-scale spatial variability in the wind field (Fisher et al. 2015). A third-order Butterworth low-pass filter with a cutoff frequency of 34 h is applied to remove tidal signal in the ADCP current data.

3. Along-channel currents

Currents in the along-channel direction represent the estuary’s primary response to wind forcing and provide a basis for understanding the lateral flows. Figures 2a and 2b show the time series of the Susquehanna River discharge and the wind speed vector during the field experiment. A series of weather fronts passed through Chesapeake Bay between late March and mid-May, resulting in alternating northward and southward winds at a period of 2–4 days (Fig. 2b). Our analysis focuses on the events that were dominated by wind forcing in the along-channel direction. Wind events during which wind directions deviating more than 12° from the along-channel orientation are excluded from the analysis. We also ignore weak wind events when the maximum along-channel wind speed was less than 4 m s−1. In the following text, we use northward winds interchangeably with the upestuary winds to indicate that they work against the longitudinal salinity gradient (Chen and Sanford 2009). Similarly, southward winds are called the downestuary winds. During the spring transition period, the downestuary winds were generally stronger than the upestuary winds (Fig. 2c). There were six downestuary (D1–D6) and six upestuary (U1–U6) wind events. They are marked as the solid or dashed vertical lines in Fig. 2.

Fig. 2.
Fig. 2.

Time series of (a) the Susquehanna River discharge, (b) the wind speed vector, and (c) the along-channel (red) and cross-channel (blue) wind speed components. (d),(e) Time–depth distribution of the along-channel velocity (positive landward) at the (d) MB and (e) M3 sites. The solid and dashed vertical lines mark the downestuary events (D1, D2, . . .) and the upestuary wind events (U1, U2, …), respectively.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

As shown in previous observations (Wang 1979; Scully et al. 2005), along-channel winds drove strong currents in the along-channel direction (Fig. 2d). When winds were weak (before 24 March), the subtidal along-channel velocity displayed two-layer estuarine flows [seaward (negative u) flow in the upper layer and landward (positive u) flow in the lower layer], with a speed of 0.1–0.2 m s−1. In comparison, the along-channel currents were much stronger during the wind events, with the maximum speed reaching 0.5 m s−1. The downestuary winds amplified the two-layer flows, whereas the upestuary wind weakened the two-layer flows or even reversed them. The lower-layer flow lagged behind that of the upper-layer flow by ~12 h, while the upper-layer flow was nearly in phase with the wind speed. Such a phase difference was also found at other deep-water sites (i.e., M4, M5, and M6; not shown). At shallow mooring sites (e.g., the M3 site), however, the along-channel flows moved in the downwind direction at all depths during most wind events (Fig. 2e).

4. Lateral circulation

The winds drive currents not only in the along-channel direction but also in the lateral direction. In this section, we analyze the mooring data to investigate the spatial structure and temporal variation of the wind-driven lateral circulation.

a. Spatial pattern

Three representative wind events are selected to show the lateral circulation pattern: one upestuary wind event (U5), one moderate downestuary wind event (D2), and one strong downestuary wind event (D1; marked in Fig. 2). In this section, we focus our analysis on the surface layer (down to ~15 m) directly influenced by winds. The circulation in the deep channel will be discussed in section 6.

The upestuary wind event U5 lasted for ~3 days, and the maximum speed of 7.5 m s−1 was reached at 1900 local time (LT) 7 May (Fig. 3a). During the wind setup phase, a clockwise circulation emerged in a surface layer (down to ~15 m), with an eastward flow (negative υ) in the upper layer and a westward flow (positive υ) in the lower layer (Fig. 3b). The eastward surface flow is consistent with a generation mechanism by lateral Ekman flow. The circulation was strongest at the peak wind speed (Fig. 3c), with the lateral velocity exceeding 0.1 m s−1. The lateral flow became weaker as the wind speed decreased (Fig. 3d). The lateral circulation strained the salinity field in the cross-channel section, causing isopycnals to tilt upward on the western shore and downward on the eastern shore (Figs. 3c,d). Compared with the wind setup phase, stratification during the setdown phase was much weaker. This stratification reduction may be caused by direct wind-driven mixing as well as wind-induced, along-channel straining of isopycnals (Scully et al. 2005). The cross-channel straining shown in Fig. 3c may have also contributed to the stratification decrease.

Fig. 3.
Fig. 3.

(a) Time series of the along-channel wind speed during the upestuary wind event U5. Three vertical lines indicate the setup, peak, and setdown phases of U5. Cross-channel distributions of the lateral velocity (blue arrows) and salinity (red contours) during the (b) setup phase, (c) peak wind, and (d) setdown phase of U5.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

The estuary’s response to a moderate downestuary wind event (D2) is shown in Fig. 4. D2 lasted for ~1.4 days and reached a maximum along-channel wind speed of 6 m s−1 around 1100 LT 29 March. A counterclockwise lateral circulation occupied the entire cross section and penetrated down to a depth of ~15 m (Fig. 4b). At the peak wind, the lateral velocity reached over 0.1 m s−1 (Fig. 4c). The lateral circulation weakened as the wind speed decreased (Fig. 4d). A westward flow appeared in the deep channel and will be discussed in section 6. The counterclockwise circulation lifted isohalines on the eastern half of the cross section and depressed those on the western half, as shown in Figs. 4c and 4d.

Fig. 4.
Fig. 4.

As in Fig. 3, but for the downestuary wind D2 event.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

Next we examine a strong downestuary wind event (D1). The wind speed steadily increased from 2300 LT 24 March, reached a maximum of 10 m s−1 at 1700 LT 26 March, and decreased rapidly on 27 March. Although a counterclockwise circulation was evident early during this wind event (Fig. 5b), the lateral circulation later changed to a two-cell structure (Fig. 5d). During the wind setup phase, the westward surface flows were much weaker than the subsurface eastward flows, and water was stratified all the way to the sea surface. At the peak wind speed, isopycnals in the top 5–8 m became vertically aligned except near the eastern shore (at stations M6 and M7). Two processes may have contributed to the formation of this well-mixed surface layer: 1) wind-induced mixing and 2) tilting of the isopycnals by the vertical shear in the lateral flow (Fig. 5c). At the peak wind, the westward surface currents became much stronger on the eastern half of the estuarine section and led to upwelling (i.e., uplifting of isopycnals) on the eastern shore. In contrast, the lateral currents were weak on the western half of the cross section (Fig. 5c). The counterclockwise circulation cell on the eastern half of the estuarine channel was spun down during the wind setdown phase. However, a strong clockwise circulation emerged on the western half, with the maximum lateral speed of ~0.1 m s−1 (Fig. 5d). The vertical shear in this circulation cell tilted the isopycnals toward the horizontal direction, causing restratification over the western shoal.

Fig. 5.
Fig. 5.

(a)–(d) As in Fig. 4, but for the downestuary D1 event. (e) Vertical profiles of salinity measured on 27 Mar at the M4 (blue) and MB (red) sites.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

b. Temporal response

The above case studies showed the spatial structure of lateral circulation during individual wind events. We now investigate the temporal response of the lateral flow to wind forcing during the entire observational period. Figure 6 shows the time–depth distribution of the lateral velocity at the M6 station (on the eastern shoal), MB (in the deep channel), and M3 (on the western shoal) sites. Strong lateral flows were observed at all three sites (Figs. 6a–c). At the M6 and MB sites, the lateral flow in the surface layer (down to 3–8-m depths) was always pointed to the right of wind direction: westward flow during the downestuary winds and eastward flow during the upestuary winds (Figs. 6a,b). Moreover, the lateral flow at these two sites responded to the wind forcing without a phase lag and changed its direction as the wind direction changed. Neither was a lag detected between the upestuary wind and lateral velocity at the M3 site on the western shore (Fig. 6c). Under strong downestuary winds, however, the lateral velocity at this site was either much weaker than that at the M6 site or pointed eastward (e.g., D1, D4, and D6). At all three mooring sites, the lateral flow in the subsurface layer (~8–15 m) was generally opposite that in the surface layer. However, the lateral flow exhibited different vertical profiles at the M3 and M6 sites under the downestuary winds (cf. Figs. 6c and 6a). While the surface and subsurface flows were of similar magnitude at the M3 site, the subsurface flow was generally weaker than the surface flow at the M6 site. An enhanced, westward flow appeared below the depth of 20 m at the MB site during the downestuary winds and will be discussed in section 6.

Fig. 6.
Fig. 6.

Time–depth distributions of the low-pass filtered lateral velocities at the mooring stations (a) M6, (b) MB, and (c) M3. The vertical lines mark the downestuary and upestuary wind events.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

5. Vortex dynamics

To understand the spatial and temporal variability of the lateral circulation, such as the east–west asymmetry of the lateral circulation found during the downestuary winds, we conduct a diagnostic analysis of the streamwise (in the along-channel direction) vorticity equation, following the approach of Li and Li (2012) but using observational data to estimate the terms in the vorticity equation.

a. Diagnostic analysis of streamwise vorticity equation

Previous studies on lateral circulation mainly focused on the cross-channel momentum equation given by
e1
where (u, υ, w) are velocity components in the along-channel (x), cross-channel (y), and vertical (z) directions; f is the Coriolis parameter; ρ is the water density; P is the pressure; and Kυ is the vertical eddy viscosity. Here, we analyze the streamwise vorticity equation by taking the vertical derivative of Eq. (1). Making the Boussinesq approximation and hydrostatic approximation, we obtain the equation for the streamwise vorticity ωx = −∂υ/∂z (∂w/∂y ≪ −∂υ/∂z and is hence neglected):
e2
where g is the gravitational acceleration, β is the saline contraction coefficient, and S is the salinity. As shown in Collignon and Stacey (2012), Li and Li (2012), and Li et al. (2014), the streamwise vorticity provides a scalar representation of the lateral circulation field. If one looks into Chesapeake Bay, a clockwise/counterclockwise lateral circulation corresponds to a positive/negative integral of ωx over a cross-sectional area or a volume in the estuary. The term on the left-hand side of Eq. (2) is the time tendency (TT) of ωx. The first three terms on the right-hand side (rhs) of Eq. (2) are the advection terms. The fourth term fu/∂z is associated with the Coriolis force in the momentum equation, representing the tilting of planetary vorticity (TPV) by the vertical shear in the along-channel flow (Li et al. 2014). The fifth term is the lateral baroclinic forcing (LBF) −βS/∂y due to sloping isopycnals in cross-channel sections, and the last term ∂/∂z[Kυ(∂ωx/∂z)] is the vertical diffusion. The horizontal diffusion term is much smaller than the vertical diffusion term and is neglected (see Li and Li 2012).

The ADCP velocity measurements are used to calculate the averaged vorticity for the eastern half of the estuarine cross section (covering MB, M5, M6, and M7 stations) and the averaged vorticity for the western half of the cross section (covering M1, M2, M3, and M4 stations). A low-pass filter with a cutoff frequency of 34 h is applied to the velocity time series to remove tidal fluctuations. To focus on the lateral circulations in the surface layer (see Figs. 35), and are averaged to the depth of ~15 m (above the deep channel). Figures 7a and 7b show the time series of depth-averaged and as well as the along-channel wind speed. The wind direction largely determined the sign of the vorticity in the eastern half of the cross section. The upestuary winds generated positive , whereas the downestuary winds generated negative . In contrast, the sign of the vorticity in the western half of the cross section was not always set by the wind direction. Under the downestuary winds was either much smaller than or became positive in the setdown phase, indicating that the circulation cell was rotating clockwise over the western shoal (see Fig. 5d). Under the upestuary winds, the east–west asymmetry in the streamwise vorticity largely disappeared; and were of comparable amplitude during the wind events U2, U4, U5, and U6.

Fig. 7.
Fig. 7.

Time series of the (a) low-pass filtered along-channel wind speed and (b) depth-mean streamwise vorticity averaged over the observational sites on the eastern half of the estuarine cross section (MB, M5, M6, and M7; red) and over the observational sites on the western half (M1, M2, M3, and M4; blue). Time series of the (c) depth-mean tilting of planetary vorticity term on the western (blue) and eastern (red) halves and the (d) depth-mean baroclinicity term on the western (blue) and eastern (red) halves. Vertical lines indicate the timings of the peak wind during the downestuary and upestuary wind events.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

To understand what drove the east–west circulation asymmetry under the downestuary winds, we calculate the major terms (TPV and LBF) in the streamwise vorticity equation using the ADCP and TC measurements. Both velocity and salinity time series are low-pass filtered to remove high-frequency noise and tidal signal. Salinity data are linearly interpolated onto the same space–time grids as velocity. TPV is calculated by differencing the along-channel velocity in the vertical direction. To calculate LBF, salinity obtained at the M1–M7 sites is differenced in the lateral direction at the same depth using a backward difference ΔS(Mi) = S(Mi) − S(Mi-1), where Mi (i = 2, . . . , 7) represents the mooring site. To explore the east–west differences in the vorticity balance, we average TPV and LBF over the eastern and western halves of the cross section, respectively, and use subscripts E and W to indicate the regional averages. The lateral advection LA (−υωx/∂y) term is also calculated, but it is much smaller than TPV and LBF. The diffusion term could not be estimated because turbulence measurements were only available near the bottom boundary, but previous modeling studies suggested that the diffusion is an important term in the streamwise vorticity equation and generally works against the vorticity generation terms to spin down the lateral circulation (Li and Li 2012).

The time series of TPV and LBF are shown in Figs. 7c and 7d. TPV was positive when winds blew upestuary and negative when winds blew downestuary. Therefore, TPV drove a clockwise circulation under the upestuary winds and a counterclockwise circulation under the downestuary winds. However, there were noticeable differences between TPVE and TPVW during the downestuary winds. TPVE has larger magnitude than TPVW, especially during the strong downestuary wind events (e.g., D1 and D6; Fig. 7c). The downestuary winds enhanced stratification over the deep channel (Scully et al. 2005), allowed strong shear to develop, and led to larger TPVE. On the shallow western shoal, the along-channel straining was offset by wind mixing and lateral straining of the salinity field by the lateral circulation (see Fig. 5b), resulting in weaker stratification, weaker shear, and smaller TPVW. TPV did not determine the vortex strength alone. The lateral baroclinic term LBF was of a similar magnitude as TPV (cf. Figs. 7c and 7d). The counterclockwise circulation tilted isopycnals upward on the eastern shore and generated positive LBF, which acted against negative TPV. Similarly, the clockwise circulation tilted isopycnals upward on the western shore, generating negative LBF, which acted against positive TPV. There were noticeable differences between LBFE and LBFW. The baroclinic forcing on the western shoal was much larger, especially during the setdown phase of the downestuary winds. The combination of larger LBFW and smaller TPVW led to smaller or vorticity sign reversal on the western shore. This explains why the lateral circulation over the western shoal was often weaker or rotated clockwise under the downestuary winds.

b. Summary diagram

To put these site-specific observations into a broader context of estuarine dynamics, we summarize the vorticity analysis results in terms of nondimensional parameters. The most important parameter to characterize the effect of wind forcing is the Wedderburn number defined as
e3
where τw is the along-channel wind stress (positive for upestuary winds), L is the length of an estuary, Δρ is the horizontal density difference, and H is the mean water depth (Monismith 1986; Geyer 1997; Chen and Sanford 2009). The Wedderburn number compares the wind forcing with the longitudinal baroclinic pressure gradient and measures the strength of the wind-driven circulation relative to the gravitational circulation. The term W is relevant to the wind-driven lateral circulation because the wind stress and lateral Ekman forcing drive the lateral circulation, while the longitudinal baroclinic pressure gradient is a key driver to set the stratification in an estuary and affects the lateral baroclinic forcing. Chen and Sanford (2009) used W and a mixing parameter (the ratio of an entrainment depth to water depth) to summarize the effects of along-channel winds on stratification in an idealized narrow estuarine channel. They found that stratification decreases as the upestuary wind increases (W > 0) but shows an increase then decrease transition as the downestuary wind increases (W < 0). Such parabolic stratification dependence on W during the downestuary wind events reflects the competition between wind straining and direct wind mixing. In a wide estuary like Chesapeake Bay, the numerical modeling studies of Li and Li (2012) showed that both W and the Kelvin number are important in determining the strength of wind-driven lateral circulation. Here, we estimate L and Δρ using the distance and low-pass filtered density difference between the M5 and S mooring sites and calculate H as the mean water depth of the M transect. The maximum along-channel wind speed during each wind event is used to compute τw.

The term W varied from −3 to 1.1 for the 12 wind events studied. The streamwise vorticity and are averaged over each wind event (hereinafter referred as and ). Under the upestuary winds (W > 0), both and are positive (clockwise circulation) and increase almost linearly with W (Fig. 8a). This relationship could be explained by the result that the vorticity generation term TPV increases with W while the baroclinic forcing LBF is weak (Figs. 8b,c). At moderate wind speeds (|W| < 1.5), a simple scaling analysis suggests , where is the friction velocity.

Fig. 8.
Fig. 8.

(a) Averaged streamwise vorticity (red circles) and (blue circles) vs Wedderburn (W) number during the 12 wind events. (b) Vorticity generation term TPV as a function of W for the eastern (red circles) and western (blue circles) halves of the estuarine cross section. (c) Lateral baroclinic forcing LBF as a function of W for the eastern (red circles) and western (blue circles) halves.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

Under the downestuary winds (W < 0), is negative (counterclockwise circulation) and appears to be a parabolic function of W, reaching a minimum at W ≈ −2 (Fig. 8a). TPVE on the eastern half shows a similar parabolic dependence on W (Fig. 8b). At moderate wind speeds TPVE increases with W because stronger downestuary winds tend to drive stronger two-layer flows in the along-channel direction. However, at high wind speeds (e.g., events D3 and D6), strong wind mixing reduces the vertical shear in the along-channel current and hence TPV (Fig. 8b). LBF is also small at W < −2, presumably because strong mixing and lateral straining reduce the lateral salinity gradient. Another possible factor contributing to the weak lateral circulation might be strong vorticity diffusion at high wind speeds, but we do not have the necessary turbulence measurements to estimate this term. There are noticeable differences between and during the downestuary winds (W < 0); straddles around the zero line, indicating weak lateral circulation. Although the LBF averages for the eastern and western halves are about the same at W < 0, the magnitude of TPVW is significantly smaller than that of TPVE. In the vorticity budget for , LBFW offsets and sometimes reverses TPVW at W < 0 (Figs. 8b,c). Under the downestuary winds, therefore, the lateral baroclinic force due to the sloping isopycnals could shut down the lateral circulation or generate a clockwise circulation over the shallow western shoal, as shown in Fig. 5d.

Chesapeake Bay is a relatively wide estuary where the effects of Earth’s rotation are important. Will the results summarized in Fig. 8 be applicable to narrower estuaries? As shown in Li and Li (2012), the dimensionless parameter characterizing the rotational effects is the Kelvin number
e4
where B is the estuary width, g′ is the reduced gravitational acceleration determined by the density difference between the upper and lower layers, and hS is the mean depth of the upper layer. The Kelvin number is the ratio of the estuary width to the internal Rossby radius of deformation (e.g., Valle-Levinson 2008). For the middle Chesapeake Bay, Ke ≈ 2.5 during the observational period. Li and Li (2012) conducted numerical experiments by varying f to explore estuaries of different widths. They found that the lateral circulation is weaker at smaller values of Ke or in narrow estuaries but showing similar dependence on W at a given Ke. For example, the circulation strength decreases by about 50% if Ke decreases by a factor of 3 or the estuary’s width is reduced to one-third. Based on these numerical investigations, we infer that the lateral circulation in narrower estuaries may show a similar dependence on W as shown in Fig. 8a but at a reduced magnitude.

6. Lateral circulation in the deep channel

Our data analysis has so far focused on the lateral circulation in the surface Ekman layer directly influenced by winds. However, as shown in Figs. 3d, 4d, and 5d, significant lateral velocity was often observed in the deep channel. During the upestuary wind event U5, the lateral flow in the deep channel pointed eastward. During the downestuary wind events D2 and D1, the lateral flow pointed westward. In the time–depth plot of the lateral velocity at the mooring station MB, strong westward currents were observed in the bottom depths shortly after the peak wind speed during the downestuary wind events (Fig. 6b). In comparison, the bottom lateral flows were much weaker during the upestuary winds.

What drives the lateral circulation in the deep channel? In Fig. 9, we plot the time series of the near-bottom, along-channel, and lateral velocities at the MB, M5, and M6 sites. Over the entire period of ADCP measurements, the lateral velocities were phase locked to the along-channel velocities. The lateral flow was always at the left angle to the along-channel flow, suggesting that the near-bottom lateral flow may be generated by the lateral Ekman forcing in the bottom boundary layer. Profiling CTD measurements made during D1 showed a well-mixed bottom boundary layer extending to ~10–12 m above the seafloor in the deep channel (see Fig. 5e for an example).

Fig. 9.
Fig. 9.

Time series of the near-bottom, along-channel (red) and lateral (blue) velocities at the (a) MB, (b) M5, and (c) M6 sites.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

The along-channel flow in the deep channel displayed a strong asymmetry between the upestuary and downestuary winds because of the interaction between the two-layer, wind-driven circulation and gravitational circulation. The landward flow in the deep channel was amplified by the estuarine return flow under the downestuary winds. Under the upestuary winds, the along-channel bottom flow was weaker because the gravitational and wind-driven currents were opposed to each other in the deep channel. As a result, the lateral flow in the deep channel was generally larger during the downestuary winds than during the upestuary winds (Fig. 9).

To investigate whether the large, near-bottom lateral flow in the deep channel was indeed generated by the lateral Ekman forcing, we conduct numerical experiments using a 3D hydrodynamic model of Chesapeake Bay based on ROMS (Li and Li 2011, 2012). The model resolution and configuration are identical to those used in Cheng et al. (2013). We conduct two model runs: one with the Coriolis force (run A) and one without the Coriolis force (run B). Run A reproduces the strong lateral flows in the deep channel, particularly during the downestuary winds (Fig. 10). It also shows that the near-bottom lateral flows are phase locked to the along-channel currents in the deep channel. In run B, the westward flow largely disappears during the downestuary winds. This model comparison confirms that the lateral flows in the deep channel are likely driven by the lateral Ekman forcing. Numerical experiments that incorporate the effects of the Coriolis force also reproduce the observed patterns of the lateral circulation during the up- and downestuary wind events and will be reported in a future study.

Fig. 10.
Fig. 10.

Time series of the model-predicted, near-bottom (a) along-channel and (b) lateral velocities at the MB site. The red lines were obtained from a model that considered the effects of Earth’s rotation while the blue lines were from a model that turned off the Coriolis force.

Citation: Journal of Physical Oceanography 47, 2; 10.1175/JPO-D-15-0233.1

7. Conclusions

Using 2-month-long mooring data, we have investigated the spatial structure and temporal variation of wind-driven lateral circulation in a midsection of Chesapeake Bay. Under the upestuary winds, a clockwise circulation was observed in the surface layer. Under the downestuary winds, however, the lateral circulation in the surface layer displayed a structure dependent on the wind speed: a counterclockwise circulation under moderate winds (small W) versus two counterrotating vortices under strong winds (large W). The observed surface lateral current showed a linear response to the time-varying, along-channel wind. The diagnostic analysis of the streamwise vorticity equation shows that both the tilting of planetary vorticity by the along-channel current and the lateral baroclinic forcing affected the lateral circulation. The lateral baroclinic forcing opposed the lateral Ekman forcing to generate a two-cell vortex structure under strong downestuary winds. Because of the limitation of mooring data, the effects of turbulent diffusion on the lateral circulation could not be studied in this paper. In addition to lateral circulation in the surface layer, the enhanced lateral Ekman forcing on the along-channel currents also drove a bottom lateral flow in the deep channel.

This observational study focuses on a straight midsection of Chesapeake Bay. How did the whole estuary respond to the wind forcing? This question will be addressed in a future numerical modeling study for the entire Chesapeake Bay. Another related question is how the up- and downestuary winds affect the estuarine stratification. Based on limited data collected in the York River, Scully et al. (2005) suggested along-channel winds can cause straining in a way similar to the tidal straining: downestuary winds increase stratification, while upestuary winds decrease stratification. Observations in the Long Island Sound appeared to confirm the dependence of stratification to the wind direction, with important implications for estuarine hypoxia (Wilson et al. 2008; Wilson et al. 2014). On the other hand, the modeling studies by Li and Li (2011) suggested that the cross-channel straining may offset the along-channel straining such that the stratification response is not very sensitive to wind direction. The previous modeling studies (e.g., Chen et al. 2009; Li and Li 2011) also showed a long recovery time after an individual wind event, but this has not been observed. The effect of winds on estuarine stratification will be addressed in a future study.

Acknowledgments

We thank Larry Sanford, Malcolm Scully, Carl Friedrich, Alex Fisher, and other members of our wind project team for helpful and stimulating discussions. We thank Carole Derry and Steve Suttles for the assistance in data processing. We are grateful to NSF (OCE-1061609) for the financial support.

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