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Rayleigh-Taylor interfacial mixing has critical importance in a broad rangeof processes in nature and technology. In most instances Rayleigh-Taylordynamics is induced by variable acceleration, whereas the bulk of existingstudies is focused on the cases of constant and impulsive accelerationsreferred respectively as classical Rayleigh-Taylor and classicalRichtmyer-Meshkov dynamics. In this work we consider Rayleigh-Taylor mixinginduced by variable acceleration with power-law dependence on the spatialcoordinate in the acceleration direction. We apply group theory and momentummodel to find deterministic asymptotic solutions for self-similar RT mixing. Wefurther augment momentum model with a stochastic process to study numericallythe effect of fluctuations on statistical properties of self-similar mixing ina broad parameter regime. We reveal that self-similar mixing can beRayleigh-Taylor-type and Richtmyer-Meshkov type depending on the accelerationexponent. We further find the value of critical exponent separatingRayleigh-Taylor-type mixing and Richtmyer-Meshkov-type mixing, and identifyinvariant quantities characterizing Rayleigh-Taylor-type mixing andRichtmyer-Meshkov-type mixing.

Deterministic and stochastic properties of self-similar Rayleigh-Taylor mixing induced by space-varying acceleration