Asymptotic analysis of Rayleigh–Taylor flow for Newtonian miscible fluids

Abstract

Asymptotic analysis is used to derive anelastic, quasi-isobaric, and Boussinesq approximations for Rayleigh–Taylor induced flow between Newtonian fluids. The anelastic approximation appears to be valid for slightly stratified equilibrium states, but the analysis does not provide bounds on the Atwood number. The quasi-isobaric model is valid for unstratified equilibrium states without bounds on the Atwood number, while the Boussinesq approximation is a restriction of the quasi-isobaric model for vanishing Atwood numbers. These three models are consistently derived from first principles within the same framework, and they greatly facilitate investigations – including some compressibility effects – of Rayleigh–Taylor flow.