Nonlinear periodic capillary-gravity waves on a fluid of finite depth

Abstract

Periodic capillary-gravity waves on a fluid of finite depth are studied theoretically by using various perturbation schemes. The classical perturbation scheme is utilized to obtain the wave profile up to and including the fourth order of approximation. The classical perturbation scheme possesses singularities for certain wave numbers, and Wilton's analysis for this situation is generalized to include finite depth. In the vicinity of the singular wave numbers, the method of strained coordinates as initiated by Pierson and Fife for infinite depth is extended to finite depth. Finally, short-crested waves are studied for the nonsingular case.