The flow around planetary scale islands is examined when the island possesses a topographic skirt representing a steep continental shelf. The model is barotropic and governed by the shallow water equations and the motion is driven by a wind stress with a constant curl. The presence of the strong topographic "skirt" around the island vitiates the elegant Island Rule of Godfrey and the closed potential vorticity contours around the island produced by the topography allow a geostrophic, stationary mode to resonate with an amplitude that is limited only by dissipation. In the limit of weak forcing the outline of the outermost closed potential vorticity isoline essentially replaces the island shape and determines the flow beyond that contour. Stronger nonlinearity produces substantial changes in the flow pattern as well as the transports trapped on the closed contours and the transport between the island and the basin boundary. Laboratory experiments, numerical calculations and analytical results are presented describing the structure of the flow.
A western standing meander at the edge of the island's topography involves a rapid change in the direction of flow and this feature, predicted by analytical and numerical calculations is confirmed in laboratory experiments.
As the measure of nonlinearity is increased beyond a threshold that depends on the ratio of the inertial boundary layer thickness to the Munk layer thickness the flow becomes time dependent and a strong eddy field emerges.
The transports on the closed contours and the inter-basin exchange outside the closed potential vorticity contours show an enhancement over the linear analytical approximation as nonlinearity increases.