The interaction of an eastward-flowing current and an island: Sub- and supercritical flow

Abstract

An eastward-flowing current of a homogeneous fluid with velocity U, contained in a channel of width L, impinges on an island of width of O(L), and the resulting interaction and dynamics are studied for values of the supercriticality parameter, b = βL2/U, both larger and smaller than π2. The former case is subcritical with respect to Rossby waves, and the latter is supercritical. The nature of the flow field depends strongly on b, and in particular, the nature of the flow around the island and the proportion of the flow passing to the north or south of the island are sensitive to b and to the position of the island in the channel. The problem is studied analytically in a relatively simple, nonlinear quasigeostrophic and adiabatic framework and numerically with a shallow-water model that allows a qualitative extension of the results to the equator. Although the issues involved are motivated by the interaction of the Equatorial Undercurrent and the Galapagos Islands, the analysis presented here focuses on the fundamental issue of the distinctive nature of the flow as a function of Rossby wave criticality.