Generation of Nonlinear Internal Tides and Solitary Waves

Abstract

A set of generalized Boussinesq equations is derived for internal waves in a two-layer system; the effects of earth's rotation are included by using the f-plane approximation; a forcing mechanism due to the interaction between a tidal flow and a small finite-amplitude topography is included as well. These equations thus enable the study of the generation of nonlinear internal tides and the effects of nonhydrostatic and Coriolis dispersion on the evolution of the internal tide. Numerical solutions of the equations are presented. The three main appearances of the internal tide are considered: a linear periodic wave, a cnoidal-like wave, and a train of solitary wave sequences. In the latter case the internal tide appears in a disintegrated form. Special attention is paid to the conditions in which such a disintegration occurs, in particular to the influence of earth's rotation (Coriolis dispersion). Critical parameters of dispersion are derived in terms of the strength of the forcing; these parameters indicate whether the internal tide appears as a coherent or as a disintegrated wave.