Rayleigh-Taylor instability with variable acceleration

TL;DR

This paper analyzes the early-time behavior of Rayleigh-Taylor instability under variable acceleration, revealing two distinct regimes based on the acceleration's power-law exponent and providing explicit growth-rate formulas.

Contribution

It introduces a group-theoretic and scaling approach to characterize early-time dynamics under variable acceleration, identifying a transition point at exponent -2.

Findings

Two regimes of early-time dynamics depending on acceleration exponent

Explicit formulas for instability growth-rate across parameter ranges

Identification of a transition at exponent -2

Abstract

We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time 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 threedimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct sub-regimes 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 regime 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.