SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW

In this paper a simple current system which consists of two stratified incompressible layers is examined. For the basic equations of the motion of fluid a lower order spectrum model is established by means of Galerkin method. Adopting the difference of wind velocity between the upper and lower layers, As =as a control parameter, the bifurcation and stability of the solution of the dynamical systemare discussed. It is found that the flow states in the lower layer will have a catastrophe, when where Cg is the phase velocity of the internal inertio-gravitational wave in a geostrophic current.These results may give a reasonable explanation for the mechanism of the catastrophe phenomena, including the "pressure-jump" in the atmosphere.