• Aqua Survey, Inc., 2005: Lower Passaic River restoration project, project number 25-068. ASI Tech. Rep., 346 pp.

  • Burchard, H., , and R. Hofmeister, 2008: A dynamics equation for the potential energy anomaly for analyzing mixing and stratification in estuaries and coastal seas. Estuarine Coastal Shelf Sci., 77 , 679687.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., , and H. Rennau, 2008: Comparative quantification of physically and numerically induced mixing in ocean models. Ocean Modell., 20 , 293311.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., 2002: Secondary circulation in a region of flow curvature: Relationship with tidal forcing and river discharge. J. Geophys. Res., 107 , 3131. doi:10.1029/2001JC001082.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., , and R. E. Wilson, 1997: Secondary circulation in a highly stratified estuary. J. Geophys. Res., 102 , 2320723216.

  • Chen, S-N., , and L. P. Sanford, 2008: Lateral circulation driven by boundary mixing and the associated transport of sediments in idealized partially mixed estuaries. Cont. Shelf Res., 29 , 101118. doi:10.1016/j.csr.2008.01.001.

    • Search Google Scholar
    • Export Citation
  • Friedrichs, C. T., , and J. M. Hamrick, 1996: Effects of channel geometry on cross-sectional variation in along-channel velocity in partially stratified estuaries. Buoyancy Effects on Coastal and Estuarine Dynamics, D. G. Aubrey and C. T. Friedrichs, Eds., Amer. Geophys. Union, 283–300.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., 1993: Three-dimensional tidal flow around headlands. J. Geophys. Res., 98 , (C1). 955966.

  • Kasai, A., , A. E. Hill, , T. Fujiwara, , and J. H. Simpson, 2000: Effect of the Earth’s rotation on the circulation in regions of freshwater influence. J. Geophys. Res., 105 , (C7). 1696116969.

    • Search Google Scholar
    • Export Citation
  • Lacy, J. R., , and S. G. Monismith, 2001: Secondary currents in a curved, stratified, estuarine channel. J. Geophys. Res., 106 , (C12). 3128331302.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., , and W. R. Geyer, 2004: Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr., 34 , 14101428.

    • Search Google Scholar
    • Export Citation
  • Li, M., , L. Zhong, , and W. C. Boicourt, 2005: Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations. J. Geophys. Res., 110 , C12004. doi:10.1029/2004JC002585.

    • Search Google Scholar
    • Export Citation
  • Nepf, H. M., , and W. R. Geyer, 1996: Intratidal variations in stratification and mixing in the Hudson estuary. J. Geophys. Res., 101 , (C5). 1207912086.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., , and C. T. Friedrichs, 2007: The importance of tidal and lateral symmetries in stratification to residual circulation in partially mixed estuaries. J. Phys. Oceanogr., 37 , 14961511.

    • Search Google Scholar
    • Export Citation
  • Seim, H. E., , and M. C. Gregg, 1997: The importance of aspiration and channel curvature in producing strong vertical mixing over a sill. J. Geophys. Res., 102 , (C2). 34513472.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., , and J. C. McWilliams, 2005: The Regional Ocean Modeling System (ROMS): A split-explicit, free-surface, topography-following coordinates ocean model. Ocean Modell., 9 , 347404.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., , J. Brown, , J. Matthews, , and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13 , 125132.

    • Search Google Scholar
    • Export Citation
  • Valle-Levinson, A., , C. Reyes, , and R. Sanay, 2003: Effects of bathymetry, friction, and rotation on estuary–ocean exchange. J. Phys. Oceanogr., 33 , 23752393.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , W. R. Geyer, , and J. A. Lerczak, 2005: Numerical modeling of an estuary: A comprehensive skill assessment. J. Geophys. Res., 110 , C05001. doi:10.1029/2004JC002691.

    • Search Google Scholar
    • Export Citation
  • Wilmott, C. J., 1981: On the validation of models. Phys. Geogr., 2 , 184194.

  • Wong, K-C., 1994: On the nature of transverse variability in a coastal plain estuary. J. Geophys. Res., 99 , 1420914222.

  • View in gallery

    Passaic River. Triangles indicate observation stations. Solid square denotes the Dundee Dam. Numerical model grid shows (a) a full horizontal curvilinear grid of 180 × 20 cells, (b) a close-up of the grid [the square area in (a)], and (c) a vertical grid for the section [the cross-channel straight line in (b)]. The cross-channel grid is subsampled by a factor of 2 for clarity in (a) and (b). The dry points are excluded in (c).

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    Comparison of modeled (dashed lines) and observed (solid lines) surface and bottom salinities at the five mooring stations. The middle column shows the station numbers.

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    Comparison of modeled (dashed lines) and observed (solid lines) depth-averaged velocities at station M2 for (a) east–west and (b) north–south components.

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    Longitudinal and lateral current during a tidal cycle. (a) Depth-averaged longitudinal velocity (ua) and water level (wl) at the thalweg. (b) Top–bottom salinity difference at the thalweg. (c) Section average of lateral velocity amplitude. (d) Advection length scale relative to channel width (4〈υ〉/σB).

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    Tidal variation of lateral circulation. Column 1 shows lateral (υ) and vertical (w) velocities. Column 2 shows the along-channel velocities (u). Column 3 shows salinity. Column 4 shows vertical eddy diffusivity (Kυ). The unit of Kυ is (×10−4 m2 s−1). Row 1 is at the maximum flood. Row 2 takes from the earlier ebb. Row 3 represents the maximum ebb. Row 4 shows the late ebb. The vertical velocity scale represents 0.4 mm s−1, and the horizontal velocity scale represents 1.5 cm s−1. Darker areas denote negative values.

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    Transverse distributions of major momentum terms in along-channel dynamics at the maximum ebb. The scale is 10−4. The barotropic pressure gradient is represented by Pa, Pc represents baroclinic pressure gradient, and P is the total pressure gradient. Darker areas denote negative values.

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    Tidal variations of the major terms in Eq. (3). (a) Section averages of longitudinal and lateral advection terms and (b) section averages of absolute value of major terms in Eq. (3).

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    Vertical profiles of longitudinal u, salinity, and Kυ on the shoal and thalweg over a tidal cycle with the (left) thalweg and (right) shoal. The unit of u is m s−1 and for Kυ is (×10−3 m2 s−1). Darker areas denote negative values.

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    Time series of major terms in Eq. (4) over a tidal cycle at the thalweg and shoal.

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    (a) Tidally averaged longitudinal velocity and (b)–(f) tidally averaged major terms in the along-channel momentum equation. Here Px represents the along-channel pressure gradient. The scale of momentum terms is 10−5. Darker areas denote negative values.

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Modeling Influence of Stratification on Lateral Circulation in a Stratified Estuary

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  • 1 School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, New York
  • 2 Institute of Marine and Coastal Sciences, Rutgers, The State University of New Jersey, New Brunswick, New Jersey
  • 3 Department of Marine and Ecological Sciences, Florida Gulf Coast University, Fort Myers, Florida
  • 4 School of Marine and Atmospheric Sciences, Stony Brook University, Stony Brook, New York
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Abstract

The dynamics of lateral circulation in the Passaic River estuary is examined in this modeling study. The pattern of lateral circulation varies significantly over a tidal cycle as a result of the temporal variation of stratification induced by tidal straining. During highly stratified ebb tides, the lateral circulation exhibits a vertical two-cell structure. Strong stratification suppresses vertical mixing in the deep channel, whereas the shoal above the halocline remains relatively well mixed. As a result, in the upper layer, the lateral asymmetry of vertical mixing produces denser water on the shoal and fresher water over the thalweg. This density gradient drives a circulation with surface currents directed toward the shoal, and the currents at the base of the pycnocline are directed toward the thalweg. In the lower layer, the lateral circulation tends to reduce the tilting of isopycnals and gradually diminishes at the end of the ebb tide. A lateral baroclinic pressure gradient is a dominant driving force for lateral circulation during stratified ebb tides and is generated by differential diffusion that indicates a lateral asymmetry in vertical mixing. Over the thalweg, vertical mixing is strong during the flood and weak during the ebb. Over the shoal, the tidally periodical stratification shows an opposite cycle of that at the thalweg. Lateral straining tends to enhance stratification during flood tides and vertical diffusion maintains the relatively well-mixed water column over the shoal during the stratified ebb tides.

Corresponding author address: Peng Cheng, 3600 Windmeadows Blvd., Apt. 43, Gainsville, FL 32608. Email: cheng@coastal.ufl.edu

Abstract

The dynamics of lateral circulation in the Passaic River estuary is examined in this modeling study. The pattern of lateral circulation varies significantly over a tidal cycle as a result of the temporal variation of stratification induced by tidal straining. During highly stratified ebb tides, the lateral circulation exhibits a vertical two-cell structure. Strong stratification suppresses vertical mixing in the deep channel, whereas the shoal above the halocline remains relatively well mixed. As a result, in the upper layer, the lateral asymmetry of vertical mixing produces denser water on the shoal and fresher water over the thalweg. This density gradient drives a circulation with surface currents directed toward the shoal, and the currents at the base of the pycnocline are directed toward the thalweg. In the lower layer, the lateral circulation tends to reduce the tilting of isopycnals and gradually diminishes at the end of the ebb tide. A lateral baroclinic pressure gradient is a dominant driving force for lateral circulation during stratified ebb tides and is generated by differential diffusion that indicates a lateral asymmetry in vertical mixing. Over the thalweg, vertical mixing is strong during the flood and weak during the ebb. Over the shoal, the tidally periodical stratification shows an opposite cycle of that at the thalweg. Lateral straining tends to enhance stratification during flood tides and vertical diffusion maintains the relatively well-mixed water column over the shoal during the stratified ebb tides.

Corresponding author address: Peng Cheng, 3600 Windmeadows Blvd., Apt. 43, Gainsville, FL 32608. Email: cheng@coastal.ufl.edu

1. Introduction

In estuarine channels, the strength and structure of lateral circulation are modified by stratification. Stratification can reduce lateral circulation. The lateral flow tilts isopycnals, setting up an adverse lateral baroclinic pressure gradient that tends to suppress the lateral circulation (Seim and Gregg 1997; Chant and Wilson 1997; Chant 2002; Lerczak and Geyer 2004). On the other hand, Geyer (1993) pointed out that stratification increases secondary flows in large Rossby number environments because stratification reduces vertical viscosity, supports stronger vertical shear in the stream-wise flow, and enhances the forcing to the lateral flows. Lacy and Monismith (2001) observed that the secondary circulation in the Snag Channel was stronger during the stratified ebb than during the flood tide.

The structure of lateral circulation also significantly varies with stratification. Under weakly stratified conditions, lateral circulation is characterized as a one-cell structure. In a straight channel with a symmetric cross section, lateral currents converge near the surface and diverge near the bottom during flood tides. This pattern is reversed during ebb tides (Lerczak and Geyer 2004). Under highly stratified conditions, however, the lateral circulation becomes more complicated. Observations in the Hudson River showed that the water column is separated into two layers by a strong pycnocline during neap tide. The surface and bottom currents are directed toward the flank, and the currents at the base of the pycnocline are directed toward the thalweg (Chant 2002; Lerczak and Geyer 2004). Chant (2002) speculated that the complicated cross-channel flows are due to a lateral sloshing associated with an internal seiche. With an idealized numerical model, Lerczak and Geyer (2004) presented a similar circulation pattern as that observed below the pycnocline. However, the observed flow toward the flank above the halocline is missed in the simulation. They attributed the missed upper-layer circulation to the improper parameterization of the vertical and temporal structures of turbulent mixing in the numerical study, which applied a constant eddy viscosity/diffusivity. The mechanism driving the vertical two-cell lateral circulation under highly stratified conditions is still being explored.

In tidally dominated estuaries, tidal straining destabilizes the water column on flood tides and increases stratification on ebb tides (Simpson et al. 1990). Well-mixed and highly stratified water columns can occur on flood and ebb tides, respectively. As a result, the structure of the lateral circulation may exhibit a prominent change over a tidal cycle because of the variation in stratification. Moreover, most estuaries have an asymmetric transverse bottom bathymetry. The deep channel and shoals may undergo different temporal evolution of stratification and yield a lateral asymmetry in turbulent mixing. The asymmetric mixing can generate oppositely directed depth-averaged residual exchange flow between the thalweg and the shoal (Scully and Friedrichs 2007). In addition, it can generate a lateral density difference, which might play an important role in driving lateral circulation in narrow estuaries.

In this study, we used a numerical model to investigate the lateral dynamics in a stratified estuary, the Passaic River estuary. Objectives include the elucidation of the tidal evolution of lateral circulation and an interpretation of the dynamics controlling a vertical two-cell lateral circulation that develops during highly stratified ebb tides. Also, the effects of lateral circulation on residual estuarine circulation are examined.

The paper is organized as follows. In section 2, we describe observations and numerical configurations. The numerical model is verified using observation datasets. In section 3, we select a transverse section and describe the temporal evolution of lateral circulation over a tidal cycle. The mechanisms for lateral circulation and the lateral momentum balance are presented. In section 4, we examine the driving forcing for cross-channel density gradient, the lateral asymmetry in vertical mixing, and the effects of lateral advection on estuarine exchange flow. Finally, we summarize our results in section 5.

2. Numerical model

a. Observations

A measurement program was carried out in the lower Passaic River from 19 November 2004 to 26 January 2005. Instruments were deployed at five stations, stretching from the mouth of the river (station M1) to past the Clay Street Bridge (station M5; Fig. 1a). Temperature and conductivity were measured in all five stations at two levels: 1 m below the surface and 1 m above the bottom. Pressure was recorded at stations M1 and M5 and an ADCP was moored 0.5 m above the bottom at station M2. Daily river discharge and water temperature data were obtained from the U.S. Geological Survey (USGS) stream gauges at Little Falls and Two Bridges, respectively. The two gauges are about 60 km from the Dundee Dam. To find the time lag of discharge between Little Falls and the Dundee Dam, we compared the time series of temperature at the Two Bridges gauge and station M5 and roughly estimated a time lag of two days. The bottom bathymetry was measured by Aqua Survey Inc. (2005).

b. Numerical model description

The model used in this study is the community model Regional Ocean Modeling System, version 2.2 (ROMS2.2). It is a free-surface, hydrostatic, primitive-equations ocean model using stretched, terrain-following vertical coordinates and orthogonal curvilinear horizontal coordinates on an Arakawa-C grid (Shchepetkin and McWilliams 2005).

The model domain in the lower Passaic River extends from station M1 to 2 km below the Dundee Dam as the river becomes very shallow near the dam, and ROMS2.2 is incapable of simulating wetting and drying. The domain is approximately 28-km long and is horizontally discretized with 180 along-channel and 20 cross-channel cells (Figs. 1a,b). The along-channel gridcell sizes range from 68 to 198 m, whereas the cross-channel gridcell sizes range from 3.5 to 21 m. The vertical dimension is discretized with 20 sigma layers, and the stretching parameters allow increased resolution near the surface and bottom boundaries (Fig. 1c). The maximum mean water depth within the domain is approximately 8.8 m, and the minimum mean depth of the domain is set to 2.0 m.

The model is forced by freshwater inflows at the river head (the Dundee Dam) and water surface elevation at the river mouth (station M1). The boundary condition on the river head is defined as a wall with freshwater point sources through which river discharge is imposed as a mass transport. The model domain was specially extended to the Dundee Dam to provide this simple but explicit boundary of river discharge. At the river mouth, Chapman condition is applied for surface elevation and Flather condition is used for barotropic velocity. Radiation boundary conditions are prescribed for the baroclinic momentum. A combination of radiation and nudging (with a relaxation time scale of 0.25 day) is applied for salinity. Water level and salinity are imposed on the open boundary using the observation data obtained at station M1. Salinity profiles are obtained by the linear interpolation of observations at the two layers. The model is initialized from rest with temperature and salinity fields obtained by an interpolation of observation data at the five stations.

The momentum boundary condition at the surface was zero stress (no wind). A quadratic stress was exerted at the bottom based on a logarithmic velocity profile with a roughness length of 0.002 m. The vertical eddy viscosity and diffusivity are computed using the k–ω turbulence closure. Horizontal eddy viscosity and diffusivity are scaled by grid size, and the coefficient for the largest grid size is set to 0.1 m2 s−1.

c. Model validation

Simulations were performed for the observational period from 21 November 2004 to 20 January 2005 (yeardays 325–385). Because of the high sediment suspension concentration and debris, many of the bottom conductivity sensors fouled after the first 10 days and lost observational accuracy. Therefore, the simulation of the segment from day 326 to day 333 (the first day is a ramp and neglected) is selected for the comparison of model and observation.

The modeled and observed time series of salinity at the five stations are shown in Fig. 2. To quantitatively compare model results and observations, Warner et al. (2005) defined a measure of model skill based on the statistical method presented by Wilmott (1981),
i1520-0485-39-9-2324-e1
where X is the variable being compared with a time mean X and the subscripts mod and obs denote model results and observations, respectively. This parameter describes the degree to which the observed deviations about the observed mean correspond to the predicted derivations about the observed mean (Li et al. 2005). Perfect agreement between model results and observations would yield a skill of one, and complete disagreement yields a skill of zero.

The model has comparatively high accuracy for salinity with skills ranging from 0.83 to 0.99 (Table 1). The simulated surface salinities agree very well with observations with skills larger than 0.94. The bottom salinities from the model are generally lower than the observations, but they still have a relatively high skill level (larger than 0.83). At station M1, there is almost complete agreement between the modeled and observed salinity because the model is forced with observations (Skill ≈ 1.0). Figure 3 compares the times series of observed and modeled depth-averaged velocities at station M2. The model skills of the two velocity components are 0.95. The amplitude of the observed east–west component is slightly larger than the modeled velocity. Because the ADCP data excludes the bottom and surface layers, the depth-averaged velocity calculated from the ADCP data is amplified and has a larger magnitude comparing with the modeled velocity. The north–south component of the depth-averaged velocity (along the minor axis) depends on the rotation of modeled velocity and is sensitive to the angle between the model grid (along-channel direction) and east. The rotation may produce part of the difference between the observed and modeled velocities. The water surface elevation has a high skill of 0.99 at station M5.

The modeled bottom salinities have relatively large errors and low model skills. Moreover, the modeled surface salinities are generally higher than the observations, whereas the modeled bottom salinities are generally lower than the observed—particularly at stations M3 and M4 that are near the head of salt intrusion. The reduced top–bottom salinity difference may result from relatively strong vertical mixing generated by the turbulence model. A very likely source for the excess mixing is numerical mixing. Burchard and Rennau (2008) have shown how substantial the contribution of numerical mixing can be, even in models with high resolution and good advection schemes. Another candidate of the excess mixing could be the explicit horizontal mixing coefficient. ROMS does not have a turbulence scheme (e.g., Smagorinsky scheme) for horizontal mixing. It scales the horizontal mixing coefficient with grid size, and the coefficient for largest grid size is chosen by users. In this study, the horizontal mixing coefficients are determined by comparing several tests with different values of the horizontal mixing coefficients. The present model results are the best among the tests.

3. Results

The transverse section shown in Fig. 1c is chosen for this study. The section is near station M2 where the model exhibits high accuracy. It has an asymmetric bottom bathymetry with a shoal near the south bank and a deep channel near the north bank. The local horizontal coordinates of this transverse section are defined to be positive upstream (x axis) and positive to the north (y axis). The vertical coordinate is directed upward.

During the two-month simulation, the river discharge was low and nearly constant at approximately 20 m3 s−1 in the first six days. It then increased markedly with a peak discharge of approximately 120 m3 s−1 in the remaining period. The amplitude of the water level was also comparatively stable for the first six days, and it fluctuated significantly during the remaining period. To avoid the influences of increased and variable river discharge as well as neap-to-spring variations in tides, this study mainly focuses on the first six days. The simulated results on the third day are taken for analysis. Response to variations in river flow and to neap-to-spring changes in tidal forcing must await future analyses.

a. Strength of lateral circulation

Time series for water elevation and depth-averaged velocity within the center of the channel at the transverse section indicate standing wave behavior (Fig. 4a). The top–bottom salinity difference is greatest at the maximum ebb and smallest at high water slack (Fig. 4b).

Following Lerczak and Geyer (2004), the transverse section average of the lateral velocity amplitude 〈|υ|〉 is used to measure the strength of the lateral flow:
i1520-0485-39-9-2324-e2
where |υ| is the absolute value of υ and A is the area of the cross-channel section. The strength of the lateral circulation is generally correlated to the longitudinal tidal current speed and shows apparent flood–ebb asymmetry (Fig. 4c). The maximum 〈|υ|〉 is 2.4 cm s−1 and occurs at the maximum flood. The second peak of 〈|υ|〉 appears at the maximum ebb and is about 1.9 cm s−1. Lerczak and Geyer (2004) assumed that the lateral flow is accelerated by a transverse density gradient caused by differential advection and is decelerated by tilting isopycnals. The strong lateral circulation appeared at the maximum flood may be related to the high current velocity, which generates a larger cross-channel density gradient. At the maximum ebb, however, the lateral circulation is not suppressed by the strongest stratification but maintains relatively high strength. The driving mechanism for the lateral circulation on ebb tides will be discussed in the next section.

The significance of lateral circulation in estuarine dynamics can be measured by the ratio of the lateral advection distance relative to 0.5 times the channel width (4〈|υ|〉/σB, where σ is the semidiurnal tidal frequency and B is the channel width; Lerczak and Geyer 2004). When the ratio is larger than 1.0, lateral advection is important in estuarine dynamics. Applying the criterion to this transverse section, it shows that throughout most of the tidal cycle, the scale of cross-channel excursion is greater than the half-breadth of the transverse section (Fig. 4d). Lateral advection is expected to be an important mechanism in this narrow estuary.

b. Structure of lateral circulation

The structure of lateral circulation shows a distinctive temporal evolution over the tidal cycle. During the flood lateral circulation is, predominantly, a single clockwise gyre (facing upstream). A typical pattern at the maximum flood is shown in Fig. 5a. During the ebb, the pattern of lateral circulation varies significantly with time. Before the maximum ebb, the lateral circulation is weak and is an anticlockwise gyre (Fig. 5e). Starting from the maximum ebb, the lateral circulation exhibits a vertical two-cell structure. Above the halocline there is a persistent anticlockwise circulation; below the halocline there is an anticlockwise gyre that tends to cease at the end of ebb (Figs. 5i,m).

c. Driving mechanisms for lateral circulation

The principle mechanisms that drive lateral circulation in estuaries are differential advection, Coriolis forcing, channel curvature, and diffusive boundary layer. The first three have been shown to govern lateral dynamics in a well-mixed water column (Lerczak and Geyer 2004), whereas the fourth has been suggested as being important in a stratified system (Chen and Sanford 2008). In this study, the driving mechanisms for the single-cell lateral circulations during the flood and early ebb can be interpreted by analyzing differential advection, Coriolis force, and channel curvature, but they are not presented here. Insight into the mechanisms controlling the two-cell lateral circulation on the stratified ebb is provided by the lateral momentum balance (Fig. 6).

At the maximum ebb, in the upper layer (above 2 m), isohalines are divergent and tilt on the south shoal and north flank, showing less stratification and high pressure. In the lower layer (below 2 m), the isopycnals tilt on the south side of the channel so that the pressure decreases toward the north side of the channel (Fig. 5k). The relatively well-mixed water column over the south shoal and less stratified water column on the north flank may partially result from the relatively high vertical mixing. During the flood and the early ebb, turbulence mixing is high in the deep channel and weak on the shoals (Figs. 5d–h). At the maximum ebb, turbulence is suppressed in the deep channel while remaining relatively high on the south shoal and north flank (Fig. 5l). After the maximum ebb, strong turbulence mixing is maintained over the south shoal and the water column is destratified (Fig. 5p). The lateral asymmetry of vertical mixing tends to generate transverse density gradients.

Transverse distributions of major momentum terms in along-channel dynamics at the maximum ebb are shown in Fig. 6. Because the water surface is high in the middle of the transverse section and low on both banks, the barotropic pressure gradient is positive in the left part and negative in the right part of the transverse section (Fig. 6g). The baroclinic pressure gradient shows an opposite pattern to the barotropic pressure gradient and is consistent with the distribution of isohalines (Fig. 6h). In the upper layer, the total pressure gradient exhibits a positive barotropic pressure center near the central surface and a negative baroclinic pressure center on the left pycnocline. This distribution of pressure gradient drives a counterclockwise circulation on the left upper layer following the same mechanism that drives the along-channel gravitational circulation. In the lower layer, the distribution of total pressure gradient is similar to the left upper layer, however, both the high and low pressure centers are generated by the baroclinic pressure gradient. The lateral circulation is also counterclockwise. The Coriolis acceleration acts as another driving force, although its magnitude is smaller than the pressure gradient (Fig. 6b). The Coriolis acceleration would contribute to the maintenance of the anticlockwise circulation in the upper layer and compensate the negative pressure gradient contribution on the right upper corner. The along-channel advection term x has a similar magnitude as the Coriolis term, indicating that channel curvature is still effective for driving the lateral circulation (Fig. 6d). The advection terms υυy and z show an approximate mirror image relation and compensate each other (Figs. 6e,f).

In both upper and lower layers, the lateral circulation tends to draw denser fluid toward less stratified areas, flattens the isohalines, and reduces the baroclinic pressure gradient. This negative feedback will eventually suppress the lateral circulation. After the maximum ebb, strong vertical mixing is maintained over the south shoal (Fig. 5p), whereas the isopycnals tend to become flat in the channel (Fig. 5o). As a result, the upper layer circulation is maintained and continues to the early flood, whereas the circulation in the lower layer is suppressed and diminishes at the end of ebb because of this negative feedback (Fig. 5m).

4. Discussions

a. Driving mechanisms for lateral density gradient

Lateral baroclinic pressure gradient has been shown to be a dominant driving force for lateral circulation during stratified ebb tides. The transverse density difference is produced by a variety of processes that can be evaluated by laterally differentiating the salt transport equation
i1520-0485-39-9-2324-e3

There are five terms on the left side of this equation (horizontal diffusion has been neglected). Term 1 is the time rate of change of the cross-channel salinity gradient. Term 2 shows the differential advection, which sets up a cross-channel salinity gradient by the advection of the along-channel density gradient. Terms 3 and 4 will modify existing cross-channel gradients by the compression or expansion of cross-channel gradients and can be called a lateral advection term, which represents the contribution from the lateral circulation. Term 5 can be considered differential diffusion.

Section averages of the five terms in Eq. (4), during a tidal cycle, are shown in Fig. 7. The magnitude of differential advection (term 2) and lateral advection (combined terms 3 and 4) are much larger than terms 1 and 5, and their temporal variations are mirror images (Fig. 7a). This indicates a negative feedback mechanism between differential advection and lateral advection. Differential advection sets up the lateral density gradient, whereas the lateral circulation tends to flatten isopycnals and reduce the lateral density gradient. Because differential advection and lateral circulation compensate each other in generating lateral density gradients, we combine terms 2–4 to represent the effects of the advection process (Fig. 7b). Absolute values of terms 1, 5, and the advection term have comparable orders of magnitude, suggesting both advection and vertical diffusion are important in producing the lateral salinity gradient. The relatively large magnitude of the differential diffusion term, during ebb tides, shows that the differential diffusion is more important for stratified flows.

b. Lateral asymmetry in vertical mixing

Differential diffusion is driven by a lateral asymmetry in vertical mixing that is coupled to different temporal evolutions of stratification at the thalweg and the shoals. Tidal variations of longitudinal velocity, salinity, and eddy diffusivity at stations located at the thalweg and the south shoal are compared in Fig. 8. The salinity evolution at the channel shows a typical cycle of tidal straining resulting from the advection of a longitudinal density gradient by sheared tidal currents (Simpson et al. 1990). During the flood, tidal currents destratify the water column and increase the thickness of the bottom mixed layer (Fig. 8a). During the ebb, the water column becomes highly stratified and creates a sheared velocity profile. Mixing is strong during flood tides and is suppressed during ebb tides (Fig. 8e). Over the shoal, flood tides start from a relatively well-mixed water column; the bottom mixed layer expands, and the upper water column tends to be stratified (Fig. 8b). During the ebb, the entire water column tends to remain well-mixed with a sheared velocity profile. The amplitude of the eddy diffusivity is larger during the ebb than the flood, showing a reversed cycle of stratification as at the thalweg.

Stratification in estuaries is controlled by the competing mechanisms of straining and mixing. The equation describing the temporal evolution of stratification can be obtained by vertically differentiating the transport equation of salt (Nepf and Geyer 1996). Another way of investigating stratification is the analysis of the potential energy anomaly, as defined by Simpson et al. (1990). Burchard and Hofmeister (2008) extended this approach and provided a time-dependent dynamic equation for the potential energy anomaly φ:
i1520-0485-39-9-2324-e4
with the definition of φ:
i1520-0485-39-9-2324-e5
where H is the mean water depth, η is water surface elevation D = η + H, g is the gravitational acceleration, and the overbar represents depth average—for example, , ũ = uu, and υ̃ = υ. On the basis of the definition of φ, a positive value of φt indicates increasing stratification. The first term on the right-hand side of Eq. (4) is along-channel straining, the second term is lateral straining, and the third term is vertical mixing. Because this study mainly concentrates on investigating the role of straining and vertical mixing in determining tidally periodical stratification, the other terms in Eq. (4) are omitted. The four terms in Eq. (4) at the thalweg and the shoal are compared in Fig. 9 to identify the relative contribution of the three processes. It is noticed that φt is not fully balanced by the sum of straining and vertical mixing terms because of the omitting of other terms in Eq. (4).

At the thalweg, along-channel straining and vertical mixing are the principle terms determining the stratification tendency, whereas lateral straining is relatively small. Tidal straining (both along-channel and lateral straining) diminish stratification during the flood (negative sign) and enhance it during the ebb (positive sign). Vertical mixing always reduces stratification (negative sign). The magnitude of along-channel straining has a similar order as that of vertical mixing during the flood, but it is significantly larger than the magnitudes of vertical mixing and lateral straining during the ebb. This indicates that the stratified water column during ebb tides is mainly maintained by along-channel straining.

Over the shoal, along-channel straining drives stratification tendency in the same way as it does at the thalweg, whereas lateral straining competes with along-channel straining. The lateral straining tends to enhance stratification during the flood because the lateral circulation transports denser water from the thalweg to the shoal and tends to diminish stratification during the ebb as the lateral circulation transports denser water off the shoal. Vertical mixing significantly increases at the maximum ebb and dominates along-channel and lateral straining. It is also larger than that at the thalweg. This shows that the relatively well-mixed water column over the shoal after the maximum ebb is mainly maintained by vertical mixing. The relative strong diffusion over the shoal produces the lateral asymmetry of vertical mixing during the stratified ebb tides.

c. Effects of lateral advection on residual estuarine circulation

The tidally averaged exchange flow in the transverse section shows a structure of classical estuarine circulation with outflow near the surface and landward flow near the bottom (Fig. 10a). The residual estuarine circulation also shows a distinct lateral structure that outflow is concentrated over the shoal, whereas inflow occurs primarily in the deep channel. The lateral structure of residual exchange flow has been associated with lateral variations in bathymetry (Wong 1994; Friedrichs and Hamrick 1996) and has shown to be dependent on the relative strength of friction and Coriolis acceleration as represented by Ekman number (Kasai et al. 2000; Valle-Levinson et al. 2003). However, all these theories excluded advection terms and assumed a linear momentum balance for estuarine circulation. Lerczak and Geyer (2004) pointed out that tidally averaged lateral advection results in a rectified seaward flow at the surface and a rectified landward flow near the bottom. Hence, lateral advection can act as a driving force for the estuarine circulation.

The five tidally averaged major terms are moved to the right-hand side of the longitudinal momentum equation and are found in Figs. 10b–f. The advection terms have comparable magnitude as the pressure gradient (Px) and friction, whereas the Coriolis term is negligible. The pressure gradient is obviously unbalanced by vertical stress, indicating that the advection terms are important in the momentum balance. The tidally averaged lateral advection (υuy + wuz) exhibits a distinct transverse structure in the upper water column that the lateral advection compensates seaward flow over the shoal (positive value) but strengthens inflow over the thalweg (negative value). It appears that the tidally averaged lateral advection acts as a source for reducing the lateral structure of estuarine exchange flow. According to the tidal evolution of lateral circulation, the clockwise circulation during the flood transports low-speed surface inflow from the shoal to the thalweg and returns high-speed inflow to the shoal. This process reduces the lateral structure of the estuarine exchange flow. During the ebb, the persistent anticlockwise circulation in the upper layer transports high-speed surface outflow from the thalweg to the shoal and returns low-speed current from the shoal to the thalweg. This process reinforces the lateral structure of estuarine circulation. Therefore, the contribution of lateral advection to the estuarine exchange flow is determined by the competition between the two processes. Because the strength of lateral circulation is stronger during the flood than the ebb, the competition between the two processes may result in weaker outflows over the shoal and stronger inflow in the deep channel, thus reducing the lateral structure of the estuarine exchange flow.

5. Summary and conclusions

Stratification in partially mixed and stratified estuaries can vary significantly, over a tidal cycle, as a result of tidal straining. This modeling study found that the pattern of the lateral circulation will, therefore, change significantly in a tidal period. Particularly during stratified ebbs, the lateral circulation remains relatively strong and shows a vertical two-cell structure that cannot be predicted by curvature effects, the earth’s rotation, and differential advection. The lateral baroclinic pressure gradient has been shown to be the principle driving forcing for the vertical two-cell lateral circulation.

The transverse density gradient at stratified ebb tides is mainly produced by a lateral asymmetry in vertical mixing between the thalweg and the shoal. At the thalweg, the strong stratification caused by tidal straining significantly suppresses turbulent mixing below the halocline. Over the shoal, however, the water column above the halocline remains well mixed. As a result, in the upper layer, the water is denser on the shoal and is fresher over the deep channel. This lateral density gradient drives a lateral circulation with surface currents directed toward the shoal and the currents at the base of the pycnocline directed toward the deep channel.

The lateral asymmetry of vertical mixing results from the different tidal evolutions of stratification over the thalweg and the shoal. At the thalweg, the stratification shows a typical cycle of tidally periodical stratification that along-channel straining produces stratification over ebb tides, whereas vertical mixing always tends to reduce stratification. Over the shoal, lateral straining acts in an opposite way of along-channel straining to determine stratification tendency. Vertical mixing becomes important and maintains the relatively well-mixed water column over the shoal during ebb tides. Tidally averaged lateral advection tends to reduce the lateral structure of the estuarine exchange flow. It compensates outflows on the shoals and strengthens inflow over the thalweg.

Acknowledgments

This study is a resulting product from Project R/CTP04 funded under Award NA16RG1645 from the National Sea Grant College Program of the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration and the U.S. National Park Service under Award CA452099007. RJC and DCF acknowledge support from the New Jersey Department of Transportation and thank Chip Haldeman and Elias Hunter for their field and data analysis efforts. We thank two anonymous reviewers for their insightful comments, which helped to improve this manuscript.

REFERENCES

  • Aqua Survey, Inc., 2005: Lower Passaic River restoration project, project number 25-068. ASI Tech. Rep., 346 pp.

  • Burchard, H., , and R. Hofmeister, 2008: A dynamics equation for the potential energy anomaly for analyzing mixing and stratification in estuaries and coastal seas. Estuarine Coastal Shelf Sci., 77 , 679687.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., , and H. Rennau, 2008: Comparative quantification of physically and numerically induced mixing in ocean models. Ocean Modell., 20 , 293311.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., 2002: Secondary circulation in a region of flow curvature: Relationship with tidal forcing and river discharge. J. Geophys. Res., 107 , 3131. doi:10.1029/2001JC001082.

    • Search Google Scholar
    • Export Citation
  • Chant, R. J., , and R. E. Wilson, 1997: Secondary circulation in a highly stratified estuary. J. Geophys. Res., 102 , 2320723216.

  • Chen, S-N., , and L. P. Sanford, 2008: Lateral circulation driven by boundary mixing and the associated transport of sediments in idealized partially mixed estuaries. Cont. Shelf Res., 29 , 101118. doi:10.1016/j.csr.2008.01.001.

    • Search Google Scholar
    • Export Citation
  • Friedrichs, C. T., , and J. M. Hamrick, 1996: Effects of channel geometry on cross-sectional variation in along-channel velocity in partially stratified estuaries. Buoyancy Effects on Coastal and Estuarine Dynamics, D. G. Aubrey and C. T. Friedrichs, Eds., Amer. Geophys. Union, 283–300.

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., 1993: Three-dimensional tidal flow around headlands. J. Geophys. Res., 98 , (C1). 955966.

  • Kasai, A., , A. E. Hill, , T. Fujiwara, , and J. H. Simpson, 2000: Effect of the Earth’s rotation on the circulation in regions of freshwater influence. J. Geophys. Res., 105 , (C7). 1696116969.

    • Search Google Scholar
    • Export Citation
  • Lacy, J. R., , and S. G. Monismith, 2001: Secondary currents in a curved, stratified, estuarine channel. J. Geophys. Res., 106 , (C12). 3128331302.

    • Search Google Scholar
    • Export Citation
  • Lerczak, J. A., , and W. R. Geyer, 2004: Modeling the lateral circulation in straight, stratified estuaries. J. Phys. Oceanogr., 34 , 14101428.

    • Search Google Scholar
    • Export Citation
  • Li, M., , L. Zhong, , and W. C. Boicourt, 2005: Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations. J. Geophys. Res., 110 , C12004. doi:10.1029/2004JC002585.

    • Search Google Scholar
    • Export Citation
  • Nepf, H. M., , and W. R. Geyer, 1996: Intratidal variations in stratification and mixing in the Hudson estuary. J. Geophys. Res., 101 , (C5). 1207912086.

    • Search Google Scholar
    • Export Citation
  • Scully, M. E., , and C. T. Friedrichs, 2007: The importance of tidal and lateral symmetries in stratification to residual circulation in partially mixed estuaries. J. Phys. Oceanogr., 37 , 14961511.

    • Search Google Scholar
    • Export Citation
  • Seim, H. E., , and M. C. Gregg, 1997: The importance of aspiration and channel curvature in producing strong vertical mixing over a sill. J. Geophys. Res., 102 , (C2). 34513472.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., , and J. C. McWilliams, 2005: The Regional Ocean Modeling System (ROMS): A split-explicit, free-surface, topography-following coordinates ocean model. Ocean Modell., 9 , 347404.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., , J. Brown, , J. Matthews, , and G. Allen, 1990: Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries, 13 , 125132.

    • Search Google Scholar
    • Export Citation
  • Valle-Levinson, A., , C. Reyes, , and R. Sanay, 2003: Effects of bathymetry, friction, and rotation on estuary–ocean exchange. J. Phys. Oceanogr., 33 , 23752393.

    • Search Google Scholar
    • Export Citation
  • Warner, J. C., , W. R. Geyer, , and J. A. Lerczak, 2005: Numerical modeling of an estuary: A comprehensive skill assessment. J. Geophys. Res., 110 , C05001. doi:10.1029/2004JC002691.

    • Search Google Scholar
    • Export Citation
  • Wilmott, C. J., 1981: On the validation of models. Phys. Geogr., 2 , 184194.

  • Wong, K-C., 1994: On the nature of transverse variability in a coastal plain estuary. J. Geophys. Res., 99 , 1420914222.

Fig. 1.
Fig. 1.

Passaic River. Triangles indicate observation stations. Solid square denotes the Dundee Dam. Numerical model grid shows (a) a full horizontal curvilinear grid of 180 × 20 cells, (b) a close-up of the grid [the square area in (a)], and (c) a vertical grid for the section [the cross-channel straight line in (b)]. The cross-channel grid is subsampled by a factor of 2 for clarity in (a) and (b). The dry points are excluded in (c).

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 2.
Fig. 2.

Comparison of modeled (dashed lines) and observed (solid lines) surface and bottom salinities at the five mooring stations. The middle column shows the station numbers.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 3.
Fig. 3.

Comparison of modeled (dashed lines) and observed (solid lines) depth-averaged velocities at station M2 for (a) east–west and (b) north–south components.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 4.
Fig. 4.

Longitudinal and lateral current during a tidal cycle. (a) Depth-averaged longitudinal velocity (ua) and water level (wl) at the thalweg. (b) Top–bottom salinity difference at the thalweg. (c) Section average of lateral velocity amplitude. (d) Advection length scale relative to channel width (4〈υ〉/σB).

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 5.
Fig. 5.

Tidal variation of lateral circulation. Column 1 shows lateral (υ) and vertical (w) velocities. Column 2 shows the along-channel velocities (u). Column 3 shows salinity. Column 4 shows vertical eddy diffusivity (Kυ). The unit of Kυ is (×10−4 m2 s−1). Row 1 is at the maximum flood. Row 2 takes from the earlier ebb. Row 3 represents the maximum ebb. Row 4 shows the late ebb. The vertical velocity scale represents 0.4 mm s−1, and the horizontal velocity scale represents 1.5 cm s−1. Darker areas denote negative values.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 6.
Fig. 6.

Transverse distributions of major momentum terms in along-channel dynamics at the maximum ebb. The scale is 10−4. The barotropic pressure gradient is represented by Pa, Pc represents baroclinic pressure gradient, and P is the total pressure gradient. Darker areas denote negative values.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 7.
Fig. 7.

Tidal variations of the major terms in Eq. (3). (a) Section averages of longitudinal and lateral advection terms and (b) section averages of absolute value of major terms in Eq. (3).

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 8.
Fig. 8.

Vertical profiles of longitudinal u, salinity, and Kυ on the shoal and thalweg over a tidal cycle with the (left) thalweg and (right) shoal. The unit of u is m s−1 and for Kυ is (×10−3 m2 s−1). Darker areas denote negative values.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 9.
Fig. 9.

Time series of major terms in Eq. (4) over a tidal cycle at the thalweg and shoal.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Fig. 10.
Fig. 10.

(a) Tidally averaged longitudinal velocity and (b)–(f) tidally averaged major terms in the along-channel momentum equation. Here Px represents the along-channel pressure gradient. The scale of momentum terms is 10−5. Darker areas denote negative values.

Citation: Journal of Physical Oceanography 39, 9; 10.1175/2009JPO4157.1

Table 1.

Model skill of the model and observation comparison for the first eight days.

Table 1.
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