Oceanic internal waves - their run-up on a sloping seabed

Abstract

This is a study of the nonlinear geophysical phenomenon of the run-up of two-dimensional oceanic internal waves on a submerged seabed of uniform slope. An internal-wave run-up model is developed for nonlinear and nondispersive long waves propagating along the interface of a two-layered inviscid fluid and incident upon the sloping seabed, with the elevation of the top free surface assumed negligible for the baroclinic mode of interest. Explicit solutions of the nonlinear equations are obtained for several classes of wave forms, which are matched, when necessary for achieving uniformly valid results, with the outer solution based on linear theory for the outer region in which the lower layer is no longer shallow compared to the top one. Under specific criteria, these waves can maintain progressing without breaking.

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