Magnetohydrodynamic Kelvin-Helmholtz instabilities in astrophysics. III - Hydrodynamic flows with shear layers

A study of Kelvin-Helmholtz instabilities in pressure-confined, two-dimensional flows or slabs, delimited by boundary layers and possessing both velocity and density gradients, has shown that the fastest-growing modes in supersonic flows are produced by perturbations which reflect at the boundaries and have wavelengths on the order of the slab width. It is concluded, from a comparison of results for the two-dimensional slab and previously-published results for a three-dimensional cylinder, that a two-dimensional treatment provides an adequate description of instabilities in fluid flows, where the analogy invoked has symmetric and antisymmetric modes in the slab correspond to the pinching and helical modes in the cylinder.