Longitudinal convergence fronts in homogeneous rotating channels

Abstract

In situ observation and remote sensing imagery indicate the presence of velocity convergences located over bathymetric channels in the mouths of tidal estuaries. In this paper we present the results of numerical simulations performed to investigate these velocity structures in a rotating channel having a single bathymetric groove. The equations of motion for a homogeneous fluid on a rotating Earth are solved using a fully spectral code in the across‐channel (i.e., the vertical or x‐z) plane. No along‐channel flow variations (in the y direction) are permitted. The bottom bathymetry is formed using a unique virtual surface approach [Goldstein et al., 1993] that generates a no‐slip bottom using feedback forcing. A Gaussian‐shaped channel is employed to simulate typical estuarine bathymetry. In the along‐channel direction a constant pressure gradient is imposed, and the flow evolves until a steady state results. The simulations are performed at high Rossby number (of order unity) based on the width of the groove and a typical surface velocity. Simulations show the development of a localized along‐channel jet colocated with an across‐channel recirculation cell. This feature results from the generation of streamwise vorticity through the tilting of planetary vorticity by the vertical shear in the along‐channel flow. The associated across‐channel surface flow above the jet exhibits convergent and divergent regions, which correlate reasonably well with features reported previously in the literature. Their number, position, and strength are seen to vary with the along‐channel Reynolds number, Ekman layer thickness, and channel aspect ratio.