Second-harmonic wave diffraction at large depths

Publisher Website
Google Scholar
Abstract
An approximation of the second-order diffraction potential is derived, for water waves of small amplitude incident upon a fixed body in a fluid of large depth. Attention is focused on the second-harmonic component of this potential, in terms of the fundamental incident-wave frequency, and on the particular solution of the inhomogeneous free-surface boundary condition with quadratic forcing by the first-order solution. By considering only the far-field approximation of the forcing function, a simple solution is derived in the near field of the body which is dominant when the submergence of the field point is large. The validity of this approach is confirmed by comparisons with two-dimensional experiments and three-dimensional computations.