The Kelvin-Helmholtz instability for relativistic particle beams - II. Flows bounded by a simple shear layer

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Abstract
The growth of the Kelvin–Helmholtz instability in a sheared beam is investigated for beams bounded by linear gradients in the flow velocity and in the square of the sound speed. The properties of pressure perturbations on the beam are qualitatively similar to those on a beam bounded by a vortex layer except for modes which can interact strongly with waves in the shear layer. As a consequence of these interactions, some previously-unstable modes may be stabilized absolutely over a moderate range of wavelengths. At all wavelengths less than the stabilized range, a large number of modes are active, the eigenfunctions have extremely frequency-dependent forms, and the small-scale flow pattern will tend to become chaotic. If it is assumed that damping mechanisms restrict the amplitudes of modes with wavelengths less than the stabilized range, the sheared layer can prevent the Kelvin–Helmholtz instability from disrupting supersonic beams with astrophysically-interesting properties until after they have propagated many beam-radii. The distorted flows that result from the gradual growth of these long-wavelength modes resemble some radio jets.

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