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Abstract

Both the consistent coupled-mode system (CCMS) and the eigenfunction matching method (EMM) are well-known models for simulating the propagation of small-amplitude water waves over variable bathymetry. In this study, a thorough comparison is performed through numerical experiments. For the CCMS, a bottom-sloping mode is coupled in the mildslope equation with evanescent modes, then the CCMS are discretized by the finite-element method with high-order shape functions. For the EMM, the bottom profile is approximated in terms of successive flat shelves separated by abrupt steps, and then eigensolutions on the shelves are matched by the conservation of mass and momentum. To perform error analysis, numerical solutions are compared with Roseau’s analytical solution and the semi-analytical solutions of the integral equation method. Numerical results indicate that the CCMS and EMM are accurate up to six and four decimal places, respectively. On the other hand, the EMM is more efficient for short waves because multiple waves can be approximated by few shelves. In addition, improvements in their accuracy over the mild-slope system without bottomsloping mode are shown to be significant.

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