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Decomposition methods for wave scattering by topography with application to ripple beds. (English) Zbl 0968.76520
Summary: A method is described for determining those approximations to wave scattering by bed topography which are based on second-order ordinary differential 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 matrix for a ripple bed, consisting of an arbitrary number of periodic undulations, is expressed in terms of the scattering properties of a single ripple. The structure obtained reveals the main features of ripple bed scattering, including resonant reflection at certain frequencies. The analysis is allied to numerical calculations to compare five different models of ripple bed scattering.

##### MSC:
 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 86A05 Hydrology, hydrography, oceanography
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##### References:
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