A variational approach to the problem of deep-water waves forming a circular caustic

Abstract

We consider the situation where a deep-water wavetrain approaching from infinity forms a circular caustic, is glancingly reflected at the caustic, and then propagates on out to infinity. At every point in the wavefield there are two wavetrains, the incident and reflected waves. Thus the wavefield can be treated as a slowly varying field of short-crested waves. This work generalizes that of Peregrine (1981) who considered a wavefield of incident waves only. The problem is formulated using the averaged-Lagrangian variational approach of Whitham (1974). Owing to the circular symmetry of the problem, the governing differential equations can be reduced to a set of algebraic equations at each radi..