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

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Abstract
In this paper we discuss Kelvin–Helmholtz instabilities in pressure-confined two-dimensional flows (slabs) delimited by boundary layers with velocity and density gradients. It is found that the fastest growing modes in supersonic flows are produced by perturbations reflecting at the boundaries and have wavelengths of the order of the slab width; this peak of instability is even more evident than in the case of vortex-sheet cylindrical flows, discussed in a previous paper. From a comparison of the results for the two-dimensional slab and three-dimensional cylinder we conclude that a two-dimensional treatment provides an adequate description of instabilities in fluid flows. In this analogy, symmetric and antisymmetric modes in the slab correspond to pinching and helical modes in the cylinder. In the final section we attempt a comparison of the results obtained with morphologies in collimated jets in extragalactic radio sources; general characteristics appear to be classifiable in terms of scale-lengths of the velocity and density gradients in the boundary layers.

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