THE STABILITY OF NONLINEAR INERTIO-INTERNAL GRAVITY WAVES FOR STRATIFIED SHEAR FLOW

In this paper, starting from the equations of the nonlinear inertio-internal gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase plane with Cartesian axes u, v.On the du/dz (the velocity shear), L2-L02(L is the horizontal scale, L0 is the Rossby radius of deformation) plane, the integral curves divide the plane into some domains of different stability.