Theoretical Aspects of Wind-Driven Currents in a Sea or Lake of Variable Depth with No Horizontal Mixing

Abstract

Steady-state wind-driven circulations in a basin of variable depth, with only vertical turbulent mixing, are considered. The geostrophic flow away from the coast is determined for an arbitrary bottom topography consisting of only closed depth contours and with depth at the coast small but larger than E1/2, where E is the Ekman number. Conditions under which cross-contour geostrophic flow can occur are investigated. A coastal boundary layer of horizontal width E1/2 is required to bring the normal transport to zero on the coast. Although the layer cannot incorporate upwelling explicitly, it does bring about mass balance by transporting mass along the coast from regions of mass surplus to regions of mass deficit. A brief comparison of conventional transport models and this three-dimensional model is made.