Obliquely incident surface waves in shallow water of slowly varying depth

Abstract

The propagation properties of obliquely incident, weakly nonlinear surface waves in shallow water of slowly varying depth are studied analytically. The depth changes slowly in a direction that makes a constant angle with the propagation direction of the incident wave, initially travelling in a region of uniform depth. In the adjacent inhomogeneous region, the depth variations occur on a scale shorter than that on which the wave evolves. It is shown that the problem then reduces to an evolution equation with constant coefficients. Since weak three-dimensional effects are also taken into account, this equation is related to the KP equation. The effect of oblique incidence on mass transfer is studied in detail. In addition, it is shown that the conditions for fission of an incident solitary wave differ from the case of normal incidence.