The Relative Importance of Wind Straining and Gravitational Forcing in Driving Exchange Flows in Tidally Energetic Estuaries

In straight tidal estuaries, residual overturning circulation results mainly from a competition between gravitational forcing, wind forcing, and friction. To systematically investigate this for tidally energetic estuaries, the dynamics of estuarine cross sections is analyzed in terms of the relation between gravitational forcing, wind stress, and the strength of estuarine circulation. A system-dependent basic Wedderburn number is defined as the ratio between wind forcing and opposing gravitational forcing at which the estuarine circulation changes sign. An analytical steady-state solution for gravitationally and wind-driven exchange flow is constructed, where tidal mixing is parameterized by parabolic eddy viscosity. For this simple but fundamental situation, is calculated, meaning that the up-estuary wind forcing needs to be 15% of the gravitational forcing to invert estuarine circulation. In three steps, relevant physical processes are added to this basic state: (i) tidal dynamics are resolved by a prescribed semidiurnal tide, leading to caused by tidal straining; (ii) lateral circulation is added by introducing cross-channel bathymetry, smoothly increasing from 0.47 (flat bed) to 1.3 (parabolic bed) due to an increasing effect of lateral circulation on estuarine circulation; and (iii) full dynamics of a real tidally energetic inlet with highly variable forcing, where results from a two-dimensional linear regression.

Baroclinic Effects on Wind-Driven Lateral Circulation in Chesapeake Bay

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

Wind Modifications to Density-Driven Flows in Semienclosed, Rotating Basins

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−1ρH2D, 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/fH2, 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.