Capillary–gravity waves against a vertical cliff

Abstract

In considering the problem of waves on a sloping beach, little regard seems to have been given to the effect of surface tension. Wehausen and Laitone (7) tend to attribute this to the fact that the additional force is small. This does not, of course, preclude the possibility that the effect may be appreciable in certain regions, and Longuet-Higgins (3), for example, has shown this to be the case near the crests for waves on the point of breaking. They also add, which is probably rather more pertinent, that difficulties arise when a solid boundary pierces the surface, since an additional boundary condition is required at the intersection, but give no indication as to what the boundary condition should be.