Wave shoaling

Abstract

The transformation of progressive waves as they travel from deep water to the shore is analyzed using the Stokes theory at a fifth order of approximation and the method of conservation of energy flux. The approximation is not uniformly valid because the wave is traveling from deep to shallow water. The first, third, and fifth orders of approximation are compared with each other and with experiments. The differences between the predictions based on the three orders of approximation are small—of the order of 5%. For most practical purposes the third-order theory would probably give the most reliable results.