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Peng Cheng and Arnoldo Valle-Levinson

Abstract

The influence of nonlinear lateral advection on estuarine exchange flow is examined with a scaling analysis and eight groups of idealized numerical experiments. Nonlinear lateral advection is related to the linkage between lateral circulation and the lateral shear of the along-estuary flow. The relative contribution of lateral advection to the overall dynamics of a microtidal estuary is found to be a function of width and depth, and of vertical mixing. Lateral advection is dynamically important in narrow and deep estuaries, particularly under relatively weak vertical mixing. The relative importance of lateral advection and the earth’s rotation on estuarine dynamics can be evaluated in terms of the nondimensional Rossby and Ekman numbers (Ro and Ek). Lateral advection is most effective at large Ro and small Ek and is negligible at small Ro and large Ek. As expected, the earth’s rotation is most significant at small Ro and Ek, and is negligible at large Ro and Ek. Under the influence of lateral advection and the earth’s rotation, the lateral structure of estuarine exchange flows is a function of Ro and Ek. In some instances, the exchange flow is vertically sheared and in others it is laterally sheared. Classical estuarine dynamics, which yields vertically sheared exchange flows, occurs at intermediate Ro and large Ek. The main role of lateral advection is to reduce lateral variability of estuarine exchange flow and generate a vertically sheared, two-layer exchange flow structure.

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Rosario Sanay and Arnoldo Valle-Levinson

Abstract

The wind-induced circulation over laterally varying bathymetry was investigated in homogeneous systems using the three-dimensional Regional Ocean Model System (ROMS). The investigation focused on the influence of the earth’s rotation on the lateral distribution of the flow, with particular emphasis on the transverse circulation. Along-basin wind stress with no rotation caused a circulation dominated by an axially symmetric transverse structure consisting of downwind flow over the shoals and upwind flow in the channel along the whole domain. Transverse circulation was important only at the head of the system where the water sank and reversed direction to move toward the mouth. The wind-induced flow pattern under the effects of the earth’s rotation depended on the ratio of the maximum basin’s depth h to the Ekman depth d. The solution tended to that described in a nonrotating system as h/d remained equal to or below 1. For higher values of h/d, the longitudinal flow was axially asymmetric. Maximum downwind flow was located over the right shoal (in the Northern Hemisphere, looking downwind). The transverse component of velocity described three gyres. The main gyre was clockwise (looking downwind) and occupied the entire basin cross section, as expected from the earth’s rotation and the presence of channel walls. The other two gyres were small and localized and were linked to the lateral distribution of the along-channel velocity component, which in turn was dictated by bathymetry. These results compared favorably with a limited set of observations and are expected to motivate future measurements.

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Nuvit B. Basdurak and Arnoldo Valle-Levinson

Abstract

The influence of nonlinear advection on estuarine exchange flow was investigated with observations at the transition between the James River and Chesapeake Bay, Hampton Roads, Virginia. Data were collected under different tidal forcing, wind forcing, and river discharge in 2004 and 2005. The relative contribution of nonlinear advective terms to the along-channel momentum balance had the same order of magnitude as pressure gradient and friction, verifying recent analytical and numerical model results. Both the magnitude and the spatial distribution of nonlinear advection showed fortnightly variability. Nonlinear advection was more influential on along-channel flow at spring tides than at neap tides because of increased tidal velocities, in a cross-sectionally averaged sense. The flow structures induced by each nonlinear advective process were investigated for the first time with observations. The lateral advection term υuy was found to enhance laterally sheared exchange acting along with Coriolis forcing at spring tides and opposing it at neap tides. Vertical advection wuz showed similar spatial distribution as υuy at spring tides but was vertically sheared (landward at middepth and seaward in the rest of the water column) at neaps. Longitudinal advection uux augmented landward flow in the channel.

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Cristóbal Reyes-Hernández and Arnoldo Valle-Levinson

Abstract

An analytical two-dimensional model is used to describe wind-induced modifications to density-driven flows in a semienclosed rotating basin. Wind stress variations produce enhancement, inversion, or damping of density-driven flows by altering the barotropic and baroclinic pressure gradients and by momentum transfer from wind drag. The vertical structure of wind-induced flows depends on αH, the nondimensional surface trapping layer, where α is the inverse of the Ekman layer depth d and H is the maximum water depth. For αH > 5 wind-driven flow structures are similar to the Ekman spiral; for αH < 2 wind-driven flows are unidirectional with depth. The relative importance of density to wind forcing is evaluated with the Wedderburn number W = τ −1 ρ H 2 D, which depends on water density ρ, mean depth H, a proxy of the baroclinic pressure gradient D, and wind stress τ. Because D depends on α and therefore on the eddy viscosity of water Az, wind speed and Az both modify W. Moreover, wind direction alters W by modifying the pressure gradient through the sea surface slope. The effect of Az is also evaluated with the Ekman number E = Az/fH 2, where f is the Coriolis parameter. The alterations of the density-driven flow by the wind-driven flow are explored in the E and W parameter space through examination of the lateral structure of the resulting exchange flows. Seaward winds and positive transverse winds (to the right facing up basin in the Northern Hemisphere) result in vertically sheared flow structures for most of the E versus W space. In contrast, landward winds and negative transverse winds (to the left facing up basin) result in unidirectional landward flows for most of the E versus W space. When compared to observed and numerically simulated flow structures, the results from the analytical model compare favorably in regard to the main features.

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Arnoldo Valle-Levinson, Cristobal Reyes, and Rosario Sanay

Abstract

An analytical model that includes pressure gradient, friction, and the earth's rotation in both components of the flow is used to study the transverse structure of estuarine exchange flows and the nature of transverse circulation in estuaries of arbitrary bathymetry. Analytical results are obtained for generic bathymetry and also over real depth distributions and are compared with observations. This study extends previous efforts on the topic of transverse structure of density-induced exchange flows in three main aspects: 1) the analytical model explores any arbitrary bathymetry; 2) the results reflect transverse asymmetries, relative to a midchannel centerline, associated with the effects of the earth's rotation; and 3) the transverse circulation produced by the analytical model is examined in detail. Analytical results over generic bathymetry show, in addition to the already reported dependence of exchange flow structure on the Ekman number, two new features. First, the transverse structure of along-estuary flows shows the earth's rotation effects, even in relatively narrow systems, thus producing transverse asymmetries in these flows. The asymmetries disappear under strongly frictional (high Ekman number) conditions, thus illustrating the previously documented pattern of inflow in channels and outflows over shoals for typical estuaries. Second, transverse flows resemble a “sideways gravitational circulation” when frictional effects are apparent (Ekman number greater than ∼0.1) responding to a transverse balance between pressure gradient and friction. These transverse flows reverse direction under very weak friction and reflect Coriolis deflection of along-estuary flows, that is, geostrophic dynamics. All examples of observed flows are satisfactorily explained by the dynamics included in the analytical model.

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Amy F. Waterhouse, Arnoldo Valle-Levinson, and Clinton D. Winant

Abstract

The spatial structure of tidal amplitude and phase in a simplified system of connected estuaries, an idealized version of Florida’s Intracoastal Waterway, is analyzed with a linear analytical model. This model includes friction, the earth’s rotation, and variable bathymetry. It is driven at the connection with the ocean by a co-oscillating tide. Model results compare well with observations of pressure and currents in a section of the Intracoastal Waterway on the east coast of Florida. The comparison suggests that the waterway is highly frictional, causing the amplitude of the water elevation and tidal velocity to decrease away from the inlets to a minimum in the middle of the waterway. The local phase relationship between velocity and water elevation changed nonlinearly from 90° with no friction to 45° with maximum friction. In moderately to highly frictional basins, the phase lag was consistently less than 45°.

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Peng Cheng, Arnoldo Valle-Levinson, and Huib E. de Swart

Abstract

Residual currents induced by asymmetric tidal mixing were examined for weakly stratified, narrow estuaries using analytical and numerical models. The analytical model is an extension of the work of R. K. McCarthy, with the addition of tidal variations of the vertical eddy viscosity in the longitudinal momentum equation. The longitudinal distribution of residual flows driven by asymmetric tidal mixing is determined by the tidal current amplitude and by asymmetries in tidal mixing between flood and ebb. In a long channel, the magnitude of the residual flow induced by asymmetric tidal mixing is maximum at the estuary mouth and decreases upstream following the longitudinal distribution of tidal current amplitude. Larger asymmetry in tidal mixing between flood and ebb produces stronger residual currents. For typical tidal asymmetry, mixing is stronger during flood than during ebb and results in two-layer residual currents with seaward flow near the surface and landward flow near the bottom. For reverse tidal asymmetry, mixing is weaker during flood than during ebb and the resulting residual flow is landward near the surface and seaward near the bottom. Also, the residual flow induced by tidal asymmetry has the same order of magnitude as the density-driven flow and therefore is important to estuarine dynamics. Numerical experiments with a primitive-equation numerical model [the Regional Ocean Modeling System (ROMS)] generally support the pattern of residual currents driven by tidal asymmetry suggested by the analytical model.

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Ming Li, Peng Cheng, Robert Chant, Arnoldo Valle-Levinson, and Kim Arnott

Abstract

The dynamics associated with lateral circulation in a tidally driven estuarine channel is analyzed on the basis of streamwise vorticity. Without rotational effects, differential advection and diffusive boundary mixing produce two counterrotating vortices (in the cross-channel section) whose strength and sense of circulation may change during a tidal cycle. The streamwise vorticity equation is determined by a balance between baroclinic forcing and turbulent diffusion, which explains the flood–ebb asymmetry of the lateral circulation. Analysis of the lateral salinity gradient shows that differential advection is the main driver of lateral flows, but boundary mixing can also be an important contributor in stratified estuaries. The strength of lateral circulation decreases with increasing stratification. With rotational effects, the lateral Ekman forcing in the bottom boundary layer drives a one-cell lateral circulation that switches its sense of rotation over the tidal cycle. The vorticity budget analysis reveals a three-way balance among the tilting of planetary vorticity by the vertical shear in the along-channel current, baroclinic forcing, and turbulent diffusion. The structure and magnitude of the lateral circulation change with the width of the estuary, expressed nondimensionally as the Kelvin number Ke. This lateral circulation features two counterrotating vortices in narrow estuaries, one vortex filling up the entire cross section in estuaries of intermediate widths and one vortex confined to the left side (looking into the estuary) in wide estuaries. The magnitude of the streamwise vorticity increases rapidly with Ke, reaches a maximum at , and decreases slightly in wide estuaries subject to strong rotational control.

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Knut Klingbeil, Johannes Becherer, Elisabeth Schulz, Huib E. de Swart, Henk M. Schuttelaars, Arnoldo Valle-Levinson, and Hans Burchard

Abstract

This paper presents thickness-weighted averaging (TWA) in generalized vertical coordinates as a unified framework for a variety of existing tidal-averaging concepts in seas and estuaries. Vertical profiles of resulting residual quantities depend on the specific vertical coordinate, which is held fixed during the averaging process. This dependence is demonstrated through the application to one-dimensional analytical tidal flow with sediment transport, to field observations from a tidal channel, and to model results from a two-dimensional estuary. The use of different coordinate systems provides complementary views on the residual dynamics and stresses the importance of a correct interpretation of residual quantities obtained by tidal averaging.

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