The effect of topography on the stability of a barotropic coastal current

We consider small non-divergent perturbations to a barotropic current flowing parallel to a straight coastline. Sufficient conditions for stability and a semi-circle theorem are established for general current profiles and topography. An asymptotic expansion for long waves is described. Some analytic solutions are obtained when the topography is piece-wise constant and the current is piece-wise linear. Two kinds of instability, a shear instability and a topographic instability, are identified. Our results are applied to a model of the East Australian current.