Analysis of Vortex Dynamics of Lateral Circulation in a Straight Tidal Estuary*

Abstract

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.