Evolution and breaking of internal waves under the effect of a progressive surface wave.

摘要

Evolution and breaking of internal waves are studied when they are excited by a progressive surface wave in a two-layer inviscid fluid system. A triad consisting of a single progressive surface wave and two internal waves is considered and attention is focused on subharmonic resonance in which two internal wavenumber vectors are symmetric about the surface wavenumber vector. First, multiple scales are adopted and perturbation method is carried to the second order to derive an evolution equation for internal waves. Analytic and numerical solutions are investigated respectively. Secondly, a local analysis is performed to derive the expression for critical breaking angle of internal waves and it is revealed that this angle is a function of density ratio, lower layer depth and upper layer depth. At last, the critical breaking angle is expressed in terms of wave amplitude, and study cases are conducted to demonstrate the complete evolution process of internal waves from beginning to breaking in different situations.