Dynamics of a Two-Dimensional Topographic Rectification Process

Abstract

Forcing mechanisms for the residual currents induced by nonlinear interactions between tidal current and two-dimensional structure of bottom topography are fairly complicated and have not been examined carefully. An example of this topographic rectification process on a simple circular bank is studied using a three-dimensional tidal model. The bank is situated in a channel oriented from west to east. The model is forced on the western boundary by a Kelvin wave. The model produces a clockwise residual circulation on the central portion of the bank, and two anticlockwise residual flows on the southeastern and northwestern edges of the bank. The clockwise circulation has an elongated shape resulting in strong cross-isobath residual currents, which in turn induce strong residual upwelling and downwelling (named ?topographic upwelling and downwelling"). Upwelling is generated by the residual current flowing from deep to shallow waters, and downwelling by the residual current flowing from shallow to deep waters. Because of the close correlation between vertical and horizontal residual currents, dynamics of the three-dimensional residual circulation can be studied by examining the forcing mechanisms for the horizontal residual current. The importance of cross-isobath residual current in producing the residual upwelling and downwelling shows the need to examine the residual circulation structure in detail. This examination is carried out by studying the distribution, advection and dissipation of two-dimensional (depth averaged) tidal and residual vorticity. There are three forcings for the tidal vorticity: 1) the Coriolis forcing produced by vortex squeezing and stretching as a fluid column crosses an isobath, 2) the frictional forcing produced by a torque between the tidal current and the gradient of frictional coefficient, and 3) the forcing by surface elevation produced also by vortex squeezing and stretching as the sea surface oscillates with a tidal frequency. The contribution of these forcings, and the effects of the topographic upwelling and downwelling on the residual circulation are described. Dynamics of the forcing mechanisms and the Stokes drift circulation are discussed in detail.