INSTABILITY AND BREAKDOWN OF INTERNAL GRAVITY-WAVES .1. LINEAR-STABILITY ANALYSIS

We have performed three-dimensional linear stability analysis, based o n Floquet theory, to study the stability of finite amplitude internal gravity waves. This analysis has been used to compute instability grow th rates over a range of wave amplitudes and propagation angles, espec ially waves above and below overturning amplitude, and identifies seve ral new characteristics of wave instability. Computation of instabilit y eigenfunctions has allowed us to analyze the energetics of the insta bility and to clarify the paths of energy transfer from the base wave to the instability. We find that the presence of wave overturning has no qualitative effect on the wave instability, except for the limiting case when the wavenumber vector is vertical. Instabilities which are nearly two-dimensional are closely related to second-order wave-wave i nteractions. But the three-dimensional instabilities, more prominent a t higher wave amplitudes, may be caused by higher order resonance inte ractions. The energetics of the instabilities range from being shear d riven to being driven by ''density gradient'' production (the potentia l energy analog of ''shear'' production); this characteristic is stron gly dependent on wave propagation angle and the three-dimensionality o f the instability. (C) 1996 American Institute of Physics.