A phase-resolving, coupled-mode model for wave-current-seabed interaction over steep 3D bottom topography. Parallel architecture implementation

摘要

A phase-resolving, coupled-mode model is developed for the wavecurrent- seabed interaction problem, with application to wave scattering by steady currents over steep three-dimensional bottom topography. The vertical distribution of the wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus an additional term accounting for the bottom boundary condition when the bottom slope is not negligible. Using the above representation, in conjunction with a variational principle, the problem is reduced to a coupled system of differential equations on the horizontal plane. If only the propagating mode is retained in the vertical expansion of the wave potential, and after additional simplifications, the above coupled-mode system is reduced to the mild-slope model derived by Kirby (1984) with application to the problem of wavecurrent interaction over slowly varying topography. The present system is discretized by using a second-order finite difference scheme and numerically solved by means of a parallel implementation, developed using the message passing programming paradigm on a commodity computer cluster. Thus, direct numerical solution is made feasible for realistic domains corresponding to areas with size of the order of several kilometers. The analytical structure of the present model facilitates its extension to treat non-linear waves, and it can be further elaborated to study wave propagation over random bottom topography and currents.