The structure of Kelvin-Helmholtz vortices with super-sonic flow

We have done two-dimensional simulations of the Kelvin-Helmholtz instability (KHI) with super-sonic flow using the CIP method. The linear analyses of a simple uniform density case show that the KHI cannot grow vigorously when the velocity jump is more than twice the sound speed (when the flow speed relative to the vortex is super-sonic). In this study, by situating a high density contrast across the shear layer, we set the flow in only one of the sides to be super-sonic and then show that the KHI does grow and rolls up a vortex. The formation of a shock is essential for the KHI vigorous growth and the structure of the vortex is strongly influenced by the shock geometry. The results should have substantial implications to velocity shear layer dynamics involving large density jump, such as planetary magnetospheric boundary layers.