Abstract
Oblique flexural gravity wave scattering due to abrupt change in bottom topography is investigated under the assumption of linearized theory of water waves. The problem is studied first for single step in case of finite water depth whose solution is obtained based on the expansion formulae for flexural gravity wavemaker problem and corresponding orthogonal mode-coupling relation. The results for the multiple step topography are obtained from the result of single step using the method of wide-spacing approximation. Energy relation for oblique flexural gravity wave scattering due to change in bottom topography is used to check the accuracy of the computation. Using shallow water approximation the wave scattering due to multiple step topography is derived considering the continuity of mass and energy flux. In this case also the result for single step topography is obtained and then using the wide-spacing approximation the result for multiple steps are derived. Numerical results for reflection and transmission coefficients and deflection of ice sheet are obtained to analyze the effect of multiple step topography on the propagation of flexural gravity waves.
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