On nonlinear sea waves and the induced mean flow

The nonlinear modulation of water wave groups is investigated and the interaction equations with induced flows are obtained. The analysis is performed up to the third order of the wave steepness a by treating it as a small parameter in the singular perturbation technique by means of the Krylov-Bogoliubov-Mitropolski method. The equation which governs the development of the wave envelope is found by a modification of the ordinary nonlinear Schroedinger equation for the case of uniform depth. The equations governing the behavior of the induced mean flow are examined by deriving the second order flow when the form of the modulated wave train is prescribed. The present theory can describe the mean flow caused by the radiation stress. Some applications containing the monochromatic wave instability are given to confirm the theoretical results.An outline of this paper was presented at The Ocean Surface Symposium (Sendai, 1984).