Instabilities of Kelvin-Helmholtz type for Relativistic streaming

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Abstract
Some models of extragalactic radio sources require that energy is transferred from the nucleus to the radio components by relativistic streams, and it is pertinent to ask how much such streams would be spread out laterally and slowed down by entrainment of surrounding material. As a preliminary to attempting to understand such a situation we here investigate the Kelvin–Helmholtz instability at a tangential velocity discontinuity when the relative motion is relativistic, for values of the sound speed in the two fluids which may or may not be relativistic. We also consider the case where one half space is occupied by a collisionless gas of particles or photons, which therefore cannot be treated as a fluid. The principal result is that growing modes exist in all these cases; the growth rates of small perturbations have been calculated for a wide variety of parameters.

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