Coastal imbalance: generation of oceanic Kelvin waves by atmospheric perturbations

The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number ε≪1. Using matched asymptotics we show that a long Kelvin wave, with O(ε−1) length scale and O(ε) amplitude relative to quasigeostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass which is violated in the quasigeostrophic approximation.