The effect of evanescent wave modes on scattering and near-trapping

Abstract

The effect of evanescent modes on the scattering and near‐trapping of small‐amplitude waves over axisymmetric topography is investigated. A two‐stage numerical implementation, which facilitates an examination of the resonant frequencies associated with near‐trapping, is developed. This is achieved in the latter stage of the procedure by dealing with the progressing and decaying waves separately. Numerical results are given for a selection of bed shapes, and it is found that the evanescent waves can have a significant effect on scattering. Numerical evidence is found that, for the selection of bed profiles considered, no new resonant frequencies are introduced by the inclusion of the decaying wave components, but that the inclusion of these decaying waves does improve previous approximations to resonant frequencies.