3-DIMENSIONAL INSTABILITIES OF STANDING WAVES IN ROTATING FLUIDS

Standing plane waves in a rigidly rotating ideal fluid are considered. It is shown that all of them are unstable with respect to three-dimen sional perturbations. When the amplitude of standing waves is small, t he growth rate of the instabilities increases as their wavenumber incr eases. It approaches the value predicted by a WKB analysis (Lifschitz & Fabijonas 1996) from below. The most dangerous modes are concentrate d near the node-planes of the basic flow field. For long wavelength di sturbances of small amplitude inertial waves resonant triad instabilit ies are observed.