The linear dispersion relation for the Rayleigh–Taylor instability is derived for fluids under plausible astrophysical conditions, and asymptotic limits of this relation are presented both for extremely relativistic and non-relativistic fluids to show the effects of relativity and compressibility on the growth of instabilities. Whereas earlier analyses have considered isothermal fluctuations, we consider the more appropriate adiabatic case. The general astrophysical implications are discussed, but specific applications are left to later papers. In general it is shown that compressibility stabilizes, and ‘saturates’ on large scales at large accelerations, but that it may be neglected for most applications. Plasmas with a relativistic equation of state are stabilized through the inertia of the pressure term. The importance of anomalous viscosity in determining mixing morphology is also discussed.
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Allen et al. (1984) studied this question.