A comparison of two models for surface-wave propagation over rapidly varying topography

Abstract

Comparisons are made between the predictions of two models for surface-wave propagation over rapidly-varying bottom topography, one based on the extended-mild-slope equation derived by Kirby (Kirby, J.T. J. Fluid Mechanics, 162 (1986) 171–186), 1 and the other on the successive-application-matrix model described by O'Hare & Davies (O'Hare, T. J. & Davies A. G. Coastal Engineering, 18 (1992) 251–266). 2 The models are applied to two types of undulating topography, namely sinusoidal and doubly-sinusoidal beds, and comparisons are made with existing laboratory data. Both models provide similar, accurate, predictions for the first-order resonant reflection of surface waves having wavelength equal to approximately twice that of the sinusoidal bed components. Agreement between the models and data is less good for higher-order resonances, due to the (different) formulations of the bottom boundary condition used in the models. In particular, some disagreement arises both when the surface wavelength is approximately equal to that of a bed component, and also when it corresponds to the sub-harmonic ‘difference’ wavelength. Generally, the successive-application-matrix model, which provides a more explicit formulation of the wave propagation problem than the extended-mild-slope equation model, gives better predictions of the data, but is computationally more demanding.