A Nonlinear Model of the Shoaling and Refraction of Interfacial Solitary Waves in the Ocean. Part II: Oblique Refraction across a Continental Slope and Propagation over a Seamount

Abstract

The refraction of internal solitary waves can be due to variations in water depth, nonlinearity, stratification, or shear. This paper addresses the effects of the first two of these effects. Part I of this paper investigated how the amplitude and phase speed of an interfacial solitary wave varied as the wave propagated across a one-dimensional slope. Important differences between the predictions of Korteweg–de Vries (KdV) and extended KdV (EKdV) theory were found. In particular the EKdV limited the amplitude growth seen in KdV as the wave passed into shallow water, leading to an associated strong retardation in speed. In this second part of the paper these results are applied to two-dimensional bathymetry. The propagation of an oblique planar wave across a wedge-shaped slope is first studied. Whereas the linear internal-wave theory predicts small refraction of the wave front, the nonlinear EKdV model shows that the refraction of large amplitude internal waves is significantly greater. This is explained by the stronger retardation seen in the shoaling experiments. Second, the propagation of a planar internal wave across a seamount is investigated. Here significant differences are found between the KdV and EKdV theory. Linear theory and nonlinear EKdV theory predict a focusing of rays past the seamount, and an eventual caustic. The EKdV predicts that the focusing occurs at shorter ranges than in the linear case, with the range dependent on the wave amplitude. In contrast KdV theory predicts that the focusing and consequent amplitude increase leads to such an increase in speed that the rays start to spread again and the caustic is avoided. It is concluded that nonlinearity has a significant effect on the refraction of interfacial solitary waves. Further, as the strongest refraction occurs in water depths where the EKdV appears to be the more appropriate theory, the EKdV results are considered to be more reliable.