DECOMPOSITION METHODS FOR WAVE SCATTERING BY TOPOGRAPHY WITH APPLICATION TO RIPPLE BEDS

A method is described for determining those approximations to wave sca ttering by bed topography which are based on second-order ordinary dif ferential equations. The development of a decomposition method allows the scattering matrix for an extended section of varying topography to be assembled in a piecemeal fashion, In particular, the scattering ma trix for a ripple bed, consisting of an arbitrary number of periodic u ndulations, is expressed in terms of the scattering properties of a si ngle ripple, The structure obtained reveals the main features of rippl e bed scattering, including resonant reflection at certain frequencies . The analysis is allied to numerical calculations to compare five dif ferent models of ripple bed scattering.