Wave-induced instabilities in stratified fluids

The small-scale instability is studied of the flow field produced by two internal gravity waves propagating at angles + or - alpha to the vertical in a fluid with constant ambient Brunt-Vaisala frequency N. A Richardson number is defined using the superposition of the velocity fields of each of the waves (to yield a net velocity); the stability frequency is composed of the ambient N and those modifications of the ambient density structure arising from the wave motions. The analysis is extended to treat the possible Kelvin-Helmholtz instability among three interacting waves. If two of these waves are at their maximum amplitude and the third is growing from zero amplitude, the ratio of the period of this last wave to its interaction time is delta.