Anomalous refraction and conjugate solutions of finite-amplitude water waves

Abstract

Calculations of the refraction of water waves obliquely incident on a beach indicate that in certain circumstances finite-amplitude waves are refracted to turn in a sense opposite to the refraction of linear waves. This is termed ‘anomalous refraction’. It is demonstrated that similar solutions exist for a wide class of weakly nonlinear dispersive waves. When anomalous refraction solutions exist there are two ‘conjugate’ solutions satisfying the slowly varying wave equations. Properties of the conjugate solutions are given here. Discussion of the possibility of jumps in wave properties between conjugate solutions and their relevance to refraction is in another paper (Peregrine 1983), which shows that the anomalous-refraction solution is not normally relevant on a beach.