Refraction of finite-amplitude water waves obliquely incident on a uniform beach

Abstract

The behaviour of a periodic wavetrain propagating obliquely over water of slowly varying depth is studied. The depth contours are taken to be straight and parallel. The wave properties used are those of ‘numerically exact’ solutions for waves on water of uniform depth. Comparison is made with linear theory which proves to be quite accurate for predicting wave direction unless the waves are propagating in a direction within about 25° of the contours. The results give a direct indication of where waves may break, but do not include dissipation.Examples are given which correspond to waves ‘trapped’ within a region of limited depth. They are related to edge waves and to caustics of the linear theory. The behaviour of solutions is consistent with earlier work on deep-water waves. This includes behaviour we term ‘anomalous refraction’, which is to be discussed in another paper.