The focusing of surface waves by internal waves

Abstract

The surface current generated by internal waves in the ocean affects surface gravity waves. The propagation of short surface waves is studied using both simple ray theory for linear waves and a fully nonlinear numerical potential solver. Attention is directed to the case of short waves with initially uniform wavenumber, as may be generated by a strong gust of wind. In general, some of the waves are focused by the surface current and in these regions the waves steepen and may break. Comparisons are made between ray theory and the more accurate solutions. For ray theory, the occurrence of focusing is examined in some detail and exact analytic solutions are found for rays on currents with linear and quadratic spatial variation – only the latter giving focusing for our initial conditions. With regard to interpretation of remote sensing of the sea surface, we find that enhanced wave steepness is not necessarily associated with a particular phase of the internal wave, and simplistic interpretations may sometimes be misleading.