Scattering of shelf waves by a spatially varying mean current

Abstract

A linearized shallow water model is used to investigate the scattering of barotropic shelf waves by spatial variations of a sheared mean current flowing in the same direction as free‐wave phase propagation. The mean current is specified to follow smooth changes in the bottom topography through a scattering region of finite length. The mean current scatters the shelf waves by changing the background potential vorticity, as well as reducing the number of propagating modes available to carry energy downstream of the scattering region. Scattering increases as the strength of the mean current increases, and large‐amplitude evanescent modes may be generated which decay slowly downstream of the scattering region. When combined with the mean current, the evanescent modes appear as compact, mesoscale flows between the mean current and the coast. In some cases, energy is extracted from the mean current and transferred to the shelf waves within the scattering region, such that the scattering process becomes a source of energy for the propagating shelf waves rather than a sink.