Flood-ebb and spring-neap variations of lateral circulation in the James River estuary

Continental Shelf Research 148 (2017) 9–18

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Flood-ebb and spring-neap variations of lateral circulation in the James River estuary

MARK

⁎

Ming Lia, , Wei Liua, Robert Chantb, Arnoldo Valle-Levinsonc a b c

Horn Point Lab, University of Maryland Center for Environmental Science, 2020 Horn Point Road, P.O. BOX 775, Cambridge, MD 21613, USA Institute of Marine and Coastal Sciences, Rutgers, the State University of New Jersey, 71 Dudley Road, New Brunswick, NJ 08901, USA Civil and Coastal Engineering Department, University of Florida, PO Box 116580, Gainesville, FL 32611, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Vorticity dynamics Lateral circulation Estuarine dynamics

Mooring observations in the James River estuary show one-cell lateral circulation that persists from spring to neap tides despite large changes in vertical stratification. The lateral circulation is twice as strong on ebb than on flood during neap tide, but shows little flood-ebb asymmetry during spring tide. A numerical model is developed to simulate the lateral circulation. It captures an observed three-fold change in stratification and reproduces the observed temporal evolution of the lateral circulation. An analysis of the streamwise vorticity equation reveals that the lateral circulation is generated by the tilting of the planetary vorticity by the along-channel flow but opposed by turbulent diffusion and lateral baroclinic forcing due to sloping isopycnals. Tilting of the vertical component of relative vorticity by the along-channel flow is insignificant. Vortex stretching is also weak in the straight segment of the estuary where mooring observations were available. During neap tide, vorticity generation is larger on ebb due to stronger vertical shear in the along-channel current, thereby leading to stronger lateral circulation on ebb. During spring tide, however, turbulent mixing reduces the shear and the flood-ebb asymmetry in the vorticity generation, resulting in little flood-ebb variations in the lateral circulation strength. Such strength is comparable between spring and neap tides because of the compensative changes in the vorticity budget: increased baroclinic forcing and decreased diffusion during neap tides versus decreased baroclinic forcing and increased diffusion during spring tides.

1. Introduction In a pioneering study, Nunes and Simpson (1985) observed a floodtide axial surface front in a well-mixed estuary in North Wales, and suggested that this front was produced by a pair of counter-rotating circulation cells in the cross-channel section. They further hypothesized that these lateral circulation cells were generated by the cross-channel density gradients resulting from the non-uniform advection of the along-channel density gradient. This observation has spun off a series of numerical and analytic modeling investigations aimed at illuminating driving mechanisms for the lateral circulation in the estuaries (e.g. Li and Valle-Levinson, 1999; Li, 2001; Lerczack and Geyer, 2004; Chen and Sanford, 2009; Cheng et al., 2009; Scully et al., 2009; Huijts et al., 2009, 2011; Li et al., 2014). Using a numerical model of an idealized estuarine channel, Lerczak and Geyer (2004) reproduced the two counter-rotating lateral circulation cells and determined that they are indeed driven by differential advection and cross-channel density gradients. Their study showed that the lateral circulation is about 4 times as strong during flood than that ⁎

during ebb tides and this flood-ebb asymmetry is related to nonlinear advective processes and time-varying stratification over a tidal cycle. In a modeling study of the Hudson River estuary, Scully et al. (2009) showed that one-cell lateral circulation is generated by tidal advection due to lateral Ekman transport. They also reported flood-ebb asymmetry in the lateral circulation strength, and found that the lateral circulation is stronger under weakly stratified spring tide conditions than under strongly stratified neap tide conditions. Lateral flows can also be generated by the interactions between barotropic tidal currents and cross-channel variations in bathymetry (Li and Valle-Levinson, 1999; Li, 2001, 2002). Lateral flow convergence appeared over the edges of deep channels and was produced by the phase lag of the flow in the channel relative to the shoals (Valle-Levinson et al., 2000a). A recent modeling study by Li et al. (2014) showed that the lateral circulation switches from two circulation cells to one cell as Kelvin number, or the estuary width, increases. A major motivation for studying the lateral circulation in estuaries is that lateral advection may play a role in driving estuarine exchange flows (Lerczak and Geyer, 2004; Scully et al., 2009; Burchard et al.,

Corresponding author. E-mail address: [email protected] (M. Li).

http://dx.doi.org/10.1016/j.csr.2017.09.007 Received 19 January 2017; Received in revised form 13 September 2017; Accepted 17 September 2017 Available online 19 September 2017 0278-4343/ © 2017 Elsevier Ltd. All rights reserved.

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circulation in the James River, the southernmost tributary to Chesapeake Bay (Fig. 1). The mooring arrays at two nearby cross sections provide an unprecedented detailed documentation of the lateral circulation and salinity structure over flood-ebb and spring-neap tidal cycles. It may appear paradoxical that Pritchard (1956) developed his classic theory of estuarine dynamics in the James River and suggested the transverse dynamics in the James River to be essentially geostrophic. However, Pritchard's calculations of various terms in the alongchannel momentum balance indicated that frictional terms were comparable to the Coriolis accelerations. Later observations and analyses by Valle-Levinson et al. (2000a, 2000b) clearly showed that the ageostrophic terms such as frictional and advective accelerations were greater than Coriolis accelerations during spring tides and comparable to or smaller than the Coriolis accelerations during neap tides. Therefore, the James River estuary provides a pertinent site to study the lateral circulation. To interpret the observed temporal variability of the lateral circulation, a numerical model of the James River is developed and validated against the mooring observations. A diagnostic analysis of the streamwise vorticity equation is conducted to distill the generation and dissipation mechanisms of the lateral circulation and understand the observed flood-ebb and spring-neap variations of the lateral circulation. The paper is structured as follows. Section 2 reports observations of the lateral circulation and density structure in the James River estuary. Section 3 describes the configuration and validation of the numerical model. Section 4 presents the diagnostic analysis of the lateral circulation through the streamwise vorticity equation. This is followed by conclusions and discussions in Section 5.

2011; Geyer and MacCready, 2014). When averaged over a tidal cycle, the lateral circulation tends to force the surface water seaward but bottom water landward, thus augmenting the estuarine exchange flow. This lateral advection mechanism depends critically on the existence of a flood-ebb asymmetry in the lateral circulation strength. Over the spring-neap tidal cycle, Lerczak and Geyer (2004) found similar asymmetry in the strength of the lateral circulation. Increased lateral advection under weakly stratified spring conditions contributes, along with the baroclinic pressure gradient, to driving the exchange flow. In contrast, during stratified neap conditions, lateral flows are shut down and their contribution to driving exchange flow decreases. Consequently, the estuarine exchange flow in the Hudson River estuary changes by a factor of 2–3 over the spring-neap tidal cycle (Geyer et al., 2000), even though eddy viscosity increases by one order of magnitude from neap to spring tides (Peters and Bokhorst, 2001). Therefore, there is a need for increased understanding of the flood-ebb and spring-neap variations of the lateral circulation in estuaries. Several observational studies have been directed at the lateral circulation in recent years. In a channel in northern San Francisco Bay, Lacy et al. (2003) observed that lateral circulation produced lateral straining to restratify a well-mixed water column. Scully and Geyer (2012) observed that lateral straining by lateral circulation led to stronger stratification on the flood tide than on the ebb tide in the Hudson River estuary. Similar findings were reported for Delaware Bay by Aristizabal and Chant (2014). More recently, Hugeunard et al. (2015) observed enhanced near-surface vertical mixing during the ebb tide that is related to lateral circulation. However, there have been few detailed observations of the temporal variability of the lateral circulation in estuaries over the flood-ebb and spring-neap tidal cycles. One exception was Collignon and Stacey (2012) who documented the temporal variation and spatial structure of lateral circulation. They observed that lateral circulation reverses its sense several times during the ebb tide, featuring intratidal variability that is apparently unrelated to the flood-ebb asymmetry reported in previous modeling studies. This paper presents one-month long mooring observations of lateral

2. Field observations The James River is the southernmost tributary to Chesapeake Bay (Fig. 1a). It has a channel-shoal bathymetry, consisting of a main channel of maximum depth of 15 m, located approximately between 0 and 2 km from the north coast, and a secondary channel, 5–6 m deep, Fig. 1. (a) Map of Chesapeake Bay and its southernmost tributary - the James River (marked by the red rectangle). (b) Zoomed-in view of the observational site with mooring stations marked by red dots. (c) ROMS grid and bathymetry of the James River estuary. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 2. The vertical cross-section through the mooring line L1. The black vertical lines indicate bottom-mounted ADCP profiling measurements and the solid dots mark the locations of CT sensors.

located roughly at 3 km from the north coast (Fig. 1b). A field program was conducted over a relatively straight segment in the lower James River. It is sufficiently far away from the sharp bend around Newport News so that flows at the mooring site are not affected by the bend (Valle-Levinson et al., 2000a, 2000b). The experiment site consisted of two lines of moorings placed across the channel as line 1 and line 2. Moorings along line 1 were labeled L1E, L1D, L1C, L1B and L1A. Mooring L1B was at the bottom of the main channel with a depth of ~10 m (Fig. 2). A surface mooring (CG) was also deployed in the main channel. Mooring L1A was at a slightly shallower region north of the main channel. Moorings L1E, L1D and L1C were on the southern slope, distributed toward the southern shoal. Moorings along line 2 followed the same notations. The moorings along both lines were placed with an average spacing of around 0.5 km within each line and about 1.2 km between the two lines. The mooring arrays consisted of a total of 10 Acoustic Doppler Current Profilers (ADCPs), 22 Conductivity and Temperature (CT) sensors, and 4 Paroscientific pressure sensors which provided high precision pressure data (Fig. 2). The ADCPs were fixed in the center of every mooring frame mounted on the bottom. Their vertical bin resolution was 0.25 m and the ADCP data were recorded every 30 min. The CT sensors were fixed to chains hung by buoys over each mooring frame as well as on the legs of the frames. These CT sensors were evenly distributed in the vertical direction seeking to sample the entire water column. They covered most parts of the two transects with a sampling frequency of 5 min. The deployment lasted 40 days from 04/26/2010 to 06/05/2010, although some records were shorter due to bio-fouling and the ADCP at L2D failed to get any data at all. The incomplete records included current data at L1B and L2B, salinity data from L2E, L2D at 6.7 m, L2C at 6.9 m, and L1D at 6.5 m. The rest covered almost the full length of the deployment. The forcing conditions encountered during the mooring deployment period are summarized in Fig. 3. Daily river discharge Q was obtained from the stream flow data of USGS (U.S. Geological Survey) station at Richmond, Virginia. It was low (Q = 100–150 m3/s) between May 1 and 15, but doubled between May 16 and 31, with Q varying between 200 and 300 m3/s (Fig. 3a). This compares with a typical peak of 500 m3/s in March and a typical minimum of 80 m3/s in August. Water level data were obtained from the NOAA tidal station at entrance to the estuary (Sewells Point, Virginia, Fig. 3b). Tides are predominantly semidiurnal in the James River: M2, N2, and S2 are the three most energetic constituents, with M2 carrying ~80% of the total tidal energy (Browne and Fisher, 1988). Due to the interactions among the three semi-diurnal constituents, the tidal currents exhibit spring-neap variations with monthly asymmetry (only one extreme spring and extreme neap per month). Tidal range was about 0.5 m during the neap (~May 5) and 0.76 m during the spring (~May 27). Wind data were obtained from the NDBC (National Data Buoy Center) Station DOMV2, the

Fig. 3. Time series of (a) river discharge, (b) water level at the Sewells Point tidal gauge station, and (c) wind speed vector at the weather station DOMV2. The green dashed line marks the neap tide and the red dashed line marks the spring tide. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

meteorological station closest to the mooring site (Fig. 3c). The winds were weak between 05/14 and 05/27. Early in the mooring deployment, a wind event started on 05/06 and lasted until the end of 05/09. The moorings provided continuous observations of the lateral circulation and salinity field over two spring-neap tidal cycles. Fig. 4(a)(d) show two snapshots of lateral velocity, along-channel velocity and salinity during the weak neap tide of May 5: one at the peak flood and one at the peak ebb. Maximum salinity difference between the surface and bottom CT sensors was found in the deep channel, reaching 6 psu on the flood and 7 psu on the ebb. The lateral circulation consisted of a clockwise-rotating cell (looking landward) on the flood tide but a counter-clockwise rotating cell on the ebb tide. It is interesting to note that the lateral currents were appreciably stronger on ebb than on flood, despite the slightly stronger stratification. During the spring tide, the vertical stratification was much reduced, with the top-to-bottom salinity difference down to 1–2 psu (Fig. 4g-h). Unlike the previous modeling studies (Lerczak and Geyer, 2004; Scully et al., 2009), the strength of the lateral circulation during the spring tide was comparable to that during the neap tide (Fig. 4e-f). Once again, one-cell circulation occupied the entire cross-section and switched from clockwise rotation on flood to counter-clockwise rotation on ebb. However, no marked asymmetry in the circulation strength was found between the flood and ebb tidal phases during the spring tide. In summary, the observations in the James River showed a one-cell lateral circulation that is consistent with Ekman forcing, and this lateral circulation was of similar strength between the spring and neap tides despite the large differences in stratification. Furthermore, the lateral circulation showed little flood-ebb variability during the spring tide but was stronger on ebb than on flood during the neap tide. These observations are strikingly different from the previous model results and observations in other estuaries, and motivate the following modeling investigation to seek a mechanistic explanation.

3. Model configuration and validation The Regional Ocean Modeling System (ROMS, Shchepetkin and McWilliams, 2005, 2009a, 2009b; Haidvogel et al., 2008) is used to 11

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Fig. 4. Observed patterns of lateral circulation (vectors, cm/s) and along-channel current (color, m/ s, positive for landward flows) (a, b, e, f) and salinity (contours, psu) (c, d, g, h) on flood (left column) and ebb (right column) during the neap (a-d) and spring (e-h) tides along the mooring line L1.

Roads). Tidal elevation is decomposed into five major tidal constituents, M2, S2, N2, K1 and O1. Salinity at the open boundary is specified using the water-quality data obtained at Chesapeake Bay monitoring station CB7.3. The open-ocean boundary is treated with a Chapman's condition for surface elevation, a Flather's condition for barotropic velocity, and an Orlanski-type radiation condition for baroclinic velocity and scalars (Marchesiello et al., 2001). The model is initialized with no flow, a flat sea surface and a uniform salinity of 35 psu. To simplify, temperature is uniform everywhere and does not change with time. The model has been run, at a time step of 15 s, from years 2008–2010. The results of May 2010 are selected for the analysis, corresponding to the moorings deployment between 04/ 26/2010 and 06/05/2010. The model results were validated against the observations. Fig. 5 compares time-series of the depth-averaged along-channel current and bottom-to-top salinity difference at the central mooring station L2C. The model-predicted barotropic current agrees well with the measurements obtained from the ADCP. The model simulates the spring-neap variation in the current speed, ranging from ~0.4 m/s during the neap tide around May 5 to ~0.7 m/s during the spring tide around May 27. A quantitative comparison between the predicted and observed alongchannel current shows that the rms error is 0.11 m/s, the correlation coefficient is 0.94, and the model's predictive skill score is 0.96 (Warner

configure a model for the James River estuary. The model domain covers the entire James River estuary and part of the main stem of Chesapeake Bay to establish the open boundary condition (Fig. 1c). The domain extends upstream by ~100 km to damp out tides at the upstream river boundary, following the approach by Warner et al. (2005a). Bathymetry is extracted from the high-resolution Coastal Relief Model data archived at NOAA's National Geophysical Data Center. The grid spacing is about 100 m in the horizontal directions, and there are 20 layers in the vertical direction. The total number of grid points is 120×410. The horizontal eddy viscosity and diffusivity are set to 1 m2 s−1 (Zhong and Li, 2006). The vertical eddy viscosity and diffusivity are computed using the k-kl turbulence closure scheme (Warner et al., 2005b) with the background diffusivity and viscosity of 10−6 m2 s−1. A quadratic stress is implemented at the sea bed, assuming that the bottom boundary layer is logarithmic with a roughness height of 0.5 mm. The model is forced by river flow at the upstream (western) boundary and by tides at the eastern open boundary. At the upstream boundary, a momentum boundary condition is imposed on the depthaveraged velocity as determined by the river flow. The inflowing river water is prescribed to have zero salinity. Tidal forcing at the open boundary is specified using tidal harmonics analysis of the historical water level observations at a nearby tidal gauge station (Hampton 12

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the neap tide and then for the spring tide. It is followed by an analysis over the spring-neap tidal cycles. 4.1. Neap tide intratidal variations Modeled distributions of the lateral and vertical velocities, the along-channel velocity, salinity, and vertical eddy diffusivity are plotted in the cross-channel section corresponding to mooring line 1 (Fig. 7a-d). On flood, the lateral flow exhibits predominantly one-cell circulation that rotates in the clockwise direction (looking into the estuary): the bottom layer moves toward the left and the surface layer moves to the right (Fig. 7a). Flood currents are deflected toward the left inside the bottom Ekman layer. Mass conservation requires a return flow in the surface layer directed to the right. However, there are spatial variations in the circulation structure. The lateral flow appears to be 3-layered in the middle of the southern shoal (3 km from the southern coast) and the circulation sense is reversed at shallower depths. Such a 3-layer flow also appears in the ADCP current measurements at the same location (mooring L1E, Fig. 4a). Although the dominant mechanism driving the lateral circulation is the lateral Ekman forcing, other processes such as differential advection (Lerczak and Geyer, 2004) and the interaction between barotropic tidal currents and channel-shoal bathymetry (Li and Valle-Levinson, 1999; ValleLevinson et al., 2000a) could contribute to the generation of lateral currents and complicate the lateral circulation structure. The lateral circulation cell advects and rearranges the salinity field in the crosschannel section. Isopycnals are lifted upward on the gently-sloping southern shoal (to the left in Fig. 7) but become horizontally aligned over the center channel (Fig. 7c). A well-mixed bottom boundary layer can be identified above the bottom of the deep channel with eddy diffusivity reaching 10−3 to 10−2 m2/s. Increased mixing is also found on the shallow shoals near the southern and northern edges of the transect, where isopcynals are oriented vertically. The model-predicted salinity distribution is broadly similar to the CT salinity measurements at the mooring stations in the deep channel but also include the shallow shoals, which were not sampled. The predicted along-channel current on flood has a subsurface maximum at a depth of 5–6 m in the deep channel, which was observed by ADCP (compare Figs. 4a and 7a). During the ebb tide, the lateral circulation cell rotates in the opposite direction as it does on flood and extends over the whole cross section. The Coriolis force deflects the ebb current inside the bottom Ekman layer so that the lateral current is directed toward the right (looking landward). A return flow toward the left develops in the surface layer. As shown in the ADCP observations, the lateral circulation during the neap tide is stronger on ebb than on flood (compare Figs. 7a and 7b). This flood-ebb asymmetry in the lateral circulation strength is opposite to that found in the idealized modeling studies of lateral circulation driven by differential advection (Lerczak and Geyer, 2004) and will be examined later using vorticity analysis. The two-layer lateral flow steepens the isopycnals so that they intersect the southern flank at nearly right angles (Fig. 7d). The downward sloping isopycnals generate an adverse baroclinic pressure gradient that opposes the lateral bottom currents. Hence, negative feedback develops between the lateral circulation and the lateral baroclinic forcing. There are major differences in stratification and eddy viscosity (same as the eddy diffusivity) between the ebb and flood tides. Salinity shows relatively uniform stratification on the ebb tide, in contrast to a well-mixed bottom layer and a sharp pycnocline on the flood tide (see Figs. 7c and 7d). The model-predicted top-bottom salinity difference is about 8–9 psu on ebb but 7 psu on flood. The stronger ebb stratification suppresses vertical mixing and reduces the eddy viscosity by one-order of magnitude or more. These model results agree with observations, but the modelpredicted salinity distribution has a better-resolved structure because of the fine grid resolutions (as compared with 5 moorings in each crosssection). Both the ADCP observations and the ROMS model show a neap tide

Fig. 5. Comparison between the observed (red lines) and predicted (black lines) depthaveraged along-channel velocity (a) and vertical salinity difference (stratification) (b) at the central mooring station L2C. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

et al., 2005a). With a fine resolution of ~100 m, the model also does a satisfactory job in reproducing the spring-neap variation in stratification. It predicts a maximum bottom-to-top salinity difference of 10–11 psu during neap tide and a minimum stratification of 2–3 psu during spring tide. For the stratification prediction, the rms error is 1.68 psu, the correlation coefficient is 0.88, and the model's predictive skill score is 0.84. A wind pulse on May 6–8 caused a temporary drop in stratification. This stratification change was not captured by the model because wind forcing was turned off in the model to focus exclusively on tidal effects. Both the model and observations show small-amplitude stratification fluctuations over flood-ebb tidal cycles. The model-data agreement is only qualitative at the tidal time scales, although the fluctuations are of similar magnitude. The predicted and observed vertical profiles of currents and salinity at station L2C are compared in Fig. 6. A five-day window around the spring tide is selected to illustrate the flood-ebb tidal variations. The observed tidal fluctuations in the along-channel velocity (Fig. 6a) are captured well by the model (Fig. 6d). Moderate inter-tidal changes in the vertical shear of the along-channel current are also simulated by the model, as shown by the fluctuating depth of the maximum flood currents. The observed lateral current reveals a two-layer flow structure in the vertical direction: northward surface current and southward bottom current on flood tides, and southward surface current combined with northward bottom current on ebb tides (Fig. 6b). There is a noticeable time lag between the longitudinal and lateral currents, as it takes about half of an inertial period to fully set up the bottom Ekman flow. The model captures the observed lateral current, including the phase lag with the longitudinal flow and the phase propagation of lateral flow from the bottom to the surface (Fig. 6e). Observations also show intratidal variations with double or triple peaks in the cross-channel current speed, but these are not reproduced by the model. The observed vertical profiles of salinity show the effects of tidal advection and straining, with highest bottom salinity at the end of flood tides and lowest surface salinity at the end of ebb tides (Fig. 6c). The model basically captures these tidal variations, but the model overpredicts the bottom salinity during this five day period around the spring tide (Fig. 6f). It also slightly overpredicts the vertical stratification, as shown in Fig. 5b. Overall the model does a reasonably good job at simulating the observed currents and salinity, thereby providing a tool to analyze the lateral circulation dynamics in the James River estuary.

4. Tidal variations of lateral circulation This section presents results from the numerical simulation of the lateral circulation. The streamwise vorticity equation is analyzed diagnostically to interpret the flood-ebb and spring-neap tidal variations of the lateral circulation. The flood-ebb asymmetry is studied first for 13

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Fig. 6. Comparison between the observed (left column) and predicted (right column) long-channel velocity (a/d), cross-channel velocity (b/e) and salinity (c/f (b) at the central mooring station L2C.

flood the along-channel current is positive (upstream) so that its vertical shear generates a positive streamwise vorticity ωx (clockwise lateral circulation, looking into estuary), where the overbar stands for the average over the control volume. In contrast, ebb generates negative (downstream) along-channel current shear to generate negative ωx . Because the vertical shear in the along-channel current is about 2–3 times larger on ebb than on flood, the magnitude of TPV is larger during the ebb tide. This is the main mechanism driving the flood-ebb asymmetry in the streamwise vorticity. Turbulent diffusion acts to spin down ωx and smooth the spatial gradients in ωx . It acts as a counter-balance to the vorticity generation term. Because turbulence is stronger on flood than on ebb, VTD is larger on flood than on ebb. The imbalance between TPV and VTD results in a much larger net generating force for the streamwise vorticity on ebb. The Ekman-driven lateral circulation in an unstratified channel is controlled by the competition between the tilting and diffusion terms with no influence of baroclinicity. In a stratified estuary, however, the baroclinic forcing exerts a torque that may oppose or enhance the vortex tilting term. The counter-clockwise lateral circulation on ebb advects bottom water to the right and steepens isopycnals such that they intercept the southern flank at sharp angles (see Fig. 7d). This produces a positive lateral baroclinic torque BAR that opposes TPV on ebb (Fig. 8c). There is a phase lag of about 2 h between maximum BAR and minimum TPV. BAR is much reduced on flood but remains positive as the clockwise lateral circulation on flood tide works to lift the isopycnals to nearly horizontally lines. In narrower estuaries (Ke < 1 and Ek > 0.5) where rotation effects are weaker, BAR switches its sign over a flood-ebb cycle (Li et al., 2014). In a wide estuary (Ke > 1) such as the James River, however, the isopycnals are tilted downward on the southern flank to balance part of the vertical shear in the along-channel

lateral circulation that is stronger on ebb than on flood. Indeed, the ∂w ∂v ∂v streamwise vorticity, ωx = ∂y − ∂z ≈ − ∂z , a scalar representation of the lateral circulation, reaches a maximum of 0.012 1/s on ebb as opposed to 0.005 1/s on flood (Figs. 8a and 8b). To understand this flood-ebb asymmetry in the lateral circulation strength, we conduct a diagnostic analysis of the streamwise vorticity equation given by

dωx = dt

f

∂u ∂z

⏟

tiltingof planetaryvorticity

+

∂u ωz z ∂ tiltingofrelative verticalvorticity

+

∂u ωx x ∂

∂S ∂2 −gβ + (KV ωx ) 2 ∂ y ∂ z   

vortexstretching baroclinicity

vertical diffusion

(1) in which f is the Coriolis parameter, u is the along-channel velocity, ωz is the vertical vorticity, g is the gravitational acceleration, β is the saline contraction coefficient, S is salinity, and KV is the vertical eddy viscosity. The horizontal diffusion is much smaller than the vertical diffusion and neglected (Li et al., 2014). The first term (denoted as TPV hereafter) on the right hand side of Eq. (1) represents the tilting of planetary vorticity by the vertical shear in the along-channel flow, the second term is the tilting of the relative vertical vorticity by the vertical shear in the along-channel flow, the third term is vortex stretching, the fourth term (BAR) is the baroclinic forcing caused by the lateral salinity/density gradient, and the fifth term (VTD) is the vertical vorticity diffusion. Eq. (1) is averaged over a control volume representing a straight segment of estuary shown in Fig. 1c. The three dominant terms in the vorticity budget Eq. (1) are the tilting of planetary vorticity by the vertical shear in the along-channel flows TPV, the vertical diffusion VTD and the baroclinicity caused by sloping isopycnals BAR, as shown in Fig. 8c. Not surprisingly, the sign of the streamwise vorticity (or the sense of the lateral circulation) is set by the tilting of planetary vorticity by the along-channel current. On 14

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Fig. 7. Model-predicted patterns of lateral circulation (vectors, cm/s) and along-channel current (color, m/s) (a, b, e, f), and salinity (contours, psu) and the logarithm of vertical eddy diffusivity (color, m2/s) (c, d, g, h) on flood (left column) and ebb (right column) during the neap (a-d) and spring (e-h) tides along the mooring line L1.

Moreover, the magnitudes of the lateral currents are comparable between flood and ebb tides, without pronounced flood-ebb asymmetry (Figs. 7e and 7f). Field measurements also showed that the lateral currents were of comparable magnitudes between flood and ebb tides (see Figs. 4e and 4f). While stratification is stronger on ebb than flood, it does not suppress the lateral circulation in the deep channel. The along-channel current has the strongest velocity in the deep channel, with a near-surface maximum (~1 m depth) on flood and a linear decay with depth on ebb. Diagnostic analysis of the streamwise vorticity budget for the spring tide provides an explanation for the interesting similarities and differences in the lateral circulation between the spring and neap tides. The ebb values of ωx during the spring tide are only marginally larger than the flood values (Fig. 8e). As discussed, the vorticity generation term TPV depends on the vertical shear of the along-channel current. Because of increased turbulent mixing during the spring tide, the spring TPV is about 20% smaller than the neap value even though the depthaveraged current is about 20% stronger. Moreover, there are smaller flood-ebb differences in TPV during the spring tide (Fig. 8f). On the other hand, the turbulent diffusion term VTD is larger on flood than on ebb because of the flood-ebb asymmetry in mixing. During the spring

current. It is clear from Fig. 8c that both turbulent diffusion and lateral baroclinic torque are equally important in balancing the vorticity generating term during the ebb tidal phase. On the other hand, TPV is assisted by BAR in balancing VTD during the flood tidal phase. Hence, the baroclinic torque may reinforce and weaken the one-cell lateral circulation, depending on the phase of the tidal cycle. 4.2. Spring tide The lateral circulation during the spring tide is of similar magnitude as that during the neap tide, despite the much weaker stratification (Fig. 7e-h). The top-to-bottom salinity difference is ~1 psu on flood and ~4 psu on ebb. Turbulent mixing extends through most of the water column on the flood tide, with the maximum eddy viscosity reaching O (10−2) m2/s (Fig. 7g). Ebb tidal straining reestablishes stratification in the deep channel and limits the height of the bottom boundary layer to the bottom ~5 m (Fig. 7h). The lateral circulation is clockwise on the flood tide and counter-clockwise on the ebb tide, the same as during the neap tide. However, there are notable differences in the circulation pattern: the lateral circulation is confined mainly to the deep channel as turbulent mixing suppresses lateral flows on the shallow shoals. 15

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Fig. 8. Time series of (a)/(d) the center-axis barotropic velocity, (b)/(e) volume-integrated streamwise vorticity, and (c)/(f) terms in the streamwise vorticity budget during the neap/ spring tide: time rate of change (black), lateral baroclinic forcing (red), turbulent diffusion (blue), the tilting of planetary vorticity by shear in the along-channel velocity (magenta), vortex stretching (gray), and the tilting of relative vertical vorticity by the along-channel current (green): Left column – neap tide; Right column – spring tide. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

tide VTD is larger due to larger eddy viscosity, but it is offset by weaker spatial gradients in the streamwise vorticity. Reduced stratification during the spring tide makes the lateral baroclinic forcing BAR much weaker than during the neap tide. In this wide estuary, the isopycnals tilt downward on the southern shoal in order to partially balance the rotational effects on the along-channel current. Such isopycnal tilt allows BAR to remain positive throughout the flood-ebb tidal cycle. Moreover, BAR has weak flood-ebb variations. TPV and VTD display nearly identical flood-ebb asymmetries and are always opposed to each other. Therefore, the three way balance among TPV, VTD and BAR results in little flood-ebb variations of the lateral circulation strength during the spring tide. Other terms such as the tilting of relative vertical vorticity by the along-channel current and the vortex stretching in the along-channel directions are an order of magnitude smaller and do not play relevant roles in the vorticity dynamics.

4.3. Neap-spring transition Analysis of the streamwise vorticity and vorticity budget from the model results is now extended over the entire 1-month mooring period. Interactions among M2, N2, and S2 harmonics cause tidal currents in the James River estuary to exhibit spring-neap variations with monthly asymmetry. Therefore, the analysis covers two spring-neap tidal cycles: a “strong neap” on May 5; a “weak spring” on May 12; a “weak neap” on May 19; and a “strong spring” on May 25. As shown in Fig. 9a, the volume-averaged vorticity ωx on flood is remarkably constant throughout the spring-neap tidal cycles, except for a dip around the neap tide (May 5–7). In contrast, the vorticity on ebb shows marked spring-neap variations. Vorticity is larger during the period 1–14 May, encompassing the “strong neap” tide around May 5 and a “weak spring” tide around May 12. The ebb vorticity then remains unchanged from May 15 to 30, including the “strong spring” tide around 27 May. The time series of the vorticity generation related to the tilting of planetary vorticity by the vertical shear of the along-channel current

Fig. 9. Time series of (a) the volume-integrated streamwise vorticity ωx, (b) the tilting of planetary vorticity by vertical shear in the along-channel current, (c) turbulent diffusion, and (d) lateral baroclinic forcing over the spring-neap tidal cycle.

resembles the time series of vorticity itself (compare Figs. 9a and 9b). This tilting mechanism also displays little neap-to-spring variation at flood tides but is 20–30% larger on the ebb tides between May 5 and 12. Such differences are attributable to the vertical shear of the alongchannel velocity during the neap-to-spring transition. Between the “strong neap” and “weak spring” tides, the vertical salinity difference 16

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spring-neap variations of the lateral circulation using mooring observations in the James River estuary. In this relatively wide estuary, the lateral circulation consists of one circulation cell that is primarilly driven by the lateral Ekman forcing. The lateral circulation strength changes little between spring and neap tides despite large differences in the vertical stratification. Moreover, the lateral circulation is twice stronger on ebb than on flood during the neap tide, but shows little flood-ebb asymmetry during the spring tide. These observations differ from previous modeling studies that showed flood-ebb asymmetries and spring-neap differences in the lateral circulation strength. A numerical model is developed to simulate the James River estuary and interpret the observed temporal variability of the lateral circulation. The diagnostic analysis of the streamwise vorticity equation reveals that the lateral circulation is primarily driven by the tilting of the planetary vorticity related to the vertical shear of the along-channel flow. The analysis also shows that the lateral circulation is hindered by turbulent diffusion and is opposed or augmented by lateral baroclinic forcing on ebb/flood from sloping isopycnals. Both the vortex stretching and the titling of the relative vertical vorticity by the alongchannel flow are small in the streamwise vorticity budget. During the neap tides, the vorticity generation is larger on ebb due to stronger shear in the along-channel current, thereby leading to stronger lateral circulation on ebb. During the spring tides, however, turbulent mixing reduces the vertical shear and the flood-ebb asymmetry in the vorticity generation, resulting in negligible flood-ebb variations in lateral circulation strength. The compensative changes in the vorticity budget between spring and neap tides are larger baroclinic forcing and weaker diffusion during the neap versus weaker baroclinic forcing and stronger diffusion during the spring. Consequently, the lateral circulation is of comparable strength between spring and neap tides. The model-predicted time series of the streamwise vorticity are in good agreement with the mooring observations over the entire mooring period. Observations and model results presented in this study show that the lateral circulation has dynamics that may not subscribe to a particular mode of temporal variability. There is a great deal of interest in the lateral circulation because lateral advection may be a driving force of estuarine exchange flows. This lateral mechanism is contingent upon flood-ebb asymmetries in the lateral circulation, namely stronger lateral circulation on flood tides than on ebb tides. However, the observed lateral circulation in the James River estuary showed no flood-ebb asymmetry during spring tides, and a reversed asymmetry during the neap tides, with stronger lateral circulation on ebb than on flood. Furthermore, the lateral circulation during neap tides was of comparable strength to that during spring tides, despite that neap stratification was 3–4 times stronger than spring stratification. Measurements in the James River estuary show that the alongchannel residual flow underwent modest changes over the spring-neap tidal cycles. This contrasts predictions by classic estuarine theory: a five-fold increase in the residual current from spring to neap tides for an estimated five-fold reduction in the vertical eddy viscosity. A preliminary analysis of the subtidal momentum balance using the model results shows that lateral advection is nearly as large as the longitudinal pressure gradient and the vertical stress divergence. Further analyses using both model results and mooring measurements could shed light on the role of lateral advection in driving residual estuarine circulation. It is also possible that the apparent persistence of estuarine exchange flows over the spring-neap tidal cycles in the James River estuary may be explained by other mechanisms/processes. For example, tidal waves propagating into an estuary produce residual currents which may oppose the gravitational circulation (Ianniello, 1977; Li and O’Donnell, 1997; Li et al., 1998). Further research is needed to understand all the processes driving the estuarine circulation.

is > 5 psu (see Fig. 5b), allowing strong vertical shear to develop in the along-channel current during the ebb tides. The diffusion term VTD has spring-neap variability different from TPV (Fig. 9c). Although the eddy viscosity is mainly set by tidal currents and is larger during the spring tide than during the neap tide, VTD depends on both the eddy viscosity and the spatial gradients of ωx . Diffusion of vorticity is moderately larger during the spring tide than during the neap tide. However, the strongest diffusion of vorticity is found on the flood tides between May 8 and 14, around the “weak spring” tide, representing a best combination of high eddy viscosity and relatively strong vorticity gradient. In addition, the ebb values of VTD during this period are appreciably smaller than the ebb values at other times. As shown in Fig. 9d, the time series of lateral baroclinic forcing BAR resembles the stratification time series (compare with Fig. 5b). The lateral salinity gradient derives from the vertical stratification and hence tracks the stratification time series. The stratification reaches a peak 3 days after the neap tide (May 8 instead of May 5) while the peak of lateral baroclinic forcing BAR lags behind the stratification peak by about 4 days (May 12). The period between May 8 and 14 provides the best combination of strong vertical stratification and strong lateral circulation such that the isopycnals increase their tilt away from their stable horizontal positions by the lateral circulation. To summarize the streamwise vorticity budget analysis, the spring-neap variation of the lateral circulation is mainly determined by TPV, but is opposed by VTD, and modified by BAR, particularly during the “strong neap” tide. Because this segment of the James River estuary is not perfectly straight, three-dimensional effects could be important. The previous 2D analysis of the streamwise vorticity equation (e.g. Li et al., 2014) is extended here into three dimensions. Under the hydrostatic and Boussinesq approximations, the two additional terms in the vorticity equation are the vortex stretching by the along-channel velocity shear and the tilting of the relative vertical vorticity by the along-channel velocity [i.e. the second and third terms in Eq. (1)]. As shown in Fig. 10, these two terms are one order of magnitude smaller than TPV, VTD and BAR. The above model diagnostics are broadly consistent with observed spring-neap variations of the streamwise vorticity. In Fig. 11, the timedepth distribution of the vorticity or ∂v/∂z obtained from the ADCP velocity measurements at the central location of L1B. The vorticity at this deep channel location is strongest between May 4 and 14. This is consistent with the time series of the volume-averaged streamwise vorticity shown in Fig. 9a.

5. Conclusions and discussions This paper presents detailed documentation of the flood-ebb and

Fig. 10. Time series of the volume-integrated time rate of change of vorticity (green), vortex stretching (black) and the tilting of the relative vorticity (yellow) over the springneap tidal cycle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Acknowledgements We are grateful to NSF (OCE-0825826, OCE-0825833, OCE17

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Fig. 11. Time-depth distribution of the streamwise vorticity (in units of s−1) estimated from the ADCP measurements at the mooring station L1B.

0825876) for the financial support. We thank Chunyan Li and two anonymous reviewers for their helpful comments. This is UMCES contribution number 5412.

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