A Rossby Wake due to an Island in an Eastward Current

Abstract

A mathematical barotropic model based upon the conservation of absolute vorticity is used to determine the effect of the spherical shape of the rotating earth [approximated by the beta (?) effect] on a steady uniform eastward current streaming past a cylindrical island in an unbounded ocean of uniform depth. Upstream far-field conditions are introduced that confine the disturbance pattern produced by the island to the region downstream from the island. For an initially uniform eastward flow of velocity u0 streaming past a cylindrical island of radius a, the downstream disturbance consists of a trail of meanders and eddies. The amplitude of these features depends upon the magnitude of the Island number [Is=(?a2/u0)½ and the radial wavenumber equals (?/u0)½, which is, the Rossby wavenumber for stationary planetary waves. In order to confirm the theoretical results of the beta-plane wake for an eastward flow situation, appeal is made to a laboratory model, consisting of a rotating annulus with a sloping bottom to simulate the beta effect. Dynamic similarity is achieved through the nondimensional Island number. The resulting flow pattern reveals a uniform flow field upstream from the island with the formation of a stationary disturbance downstream that agrees qualitatively with the theoretical results.