Analytical and experimental study of the oblique passing of a solitary wave over a shelf in a two-layer fluid

Abstract

A surface or internal solitary wave passing over a shelf is partially reflected and there are at least two transmitted waves. When the incident wave is oblique relative to the shelf, there is a refraction phenomenon as for optical waves. The refraction angle of the transmitted wave is a function of the incident angle as well as of the relative height of the shelf. Within the framework of the slowly time-varying long waves in shallow water, we compute both the refraction angle of the transmitted waves, and the amplitudes of the reflected and transmitted waves far from the shelf, in non-rotating fluid. The method also allows for the computations of the local perturbations in the shelf-slope region thus providing a complete description of the phenomena at the first order approximation. The experiments performed in the 14 m diameter rotating platform support the conclusions of the analysis regarding the refraction angle. However, when rotation is introduced, the refraction angle almost doubles, probably because of double-Kelvin wave generation along the shelf break.