Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration

Desmond L. Hill, Aklant K. Bhowmick, Dan Ilyin, Snezhana Abarzhi

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We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

Original languageEnglish
Article number063905
Number of pages18
JournalPhysical Review Fluids
Issue number6
Publication statusPublished - 21 Jun 2019

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