Steady Wind-Driven Coastal Circulation on a β-Plane

Abstract

In tropical regions, and for applications where the alongshore scale k−1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f0k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f0k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.