STABILITY OF NONLINEAR PERIODIC INTERNAL WAVES IN A DEEP STRATIFIED FLUID

Stability of the nonlinear periodic solutions of the Benjamin-Ono equa tion with respect to one-dimensional perturbations and taking into acc ount transverse modulations is analytically studied. The full set of e igenfrequencies and of small perturbations is found in the one-dimensi onal case. The dispersion equation for long-wave oblique perturbations is obtained. These perturbations are shown to be unstable under eithe r sign of the dispersion of the linear dispersion relation. The instab ility limits and the maximum growth rates are determined in the extrem e cases of strongly and weakly nonlinear waves.