On the Rayleigh-Taylor unstable dynamics of 3D interfacial coherent structures with time-dependent acceleration

Abstract

Rayleigh-Taylor instability (RTI) occurs in a range of industrial and natural processes. Whereas the vast majority of existing studies have considered constant acceleration, RTI is in most instances driven by variable acceleration. Here we focus on RTI driven by acceleration with a power-law time-dependence, and by applying a group theoretic method find solutions to this classical nonlinear boundary value problem. We deduce that the dynamics is dominated by the acceleration term and that the solutions depend critically on the time dependence for values of the acceleration exponent greater than $-2$. We find that in the early-time dynamics, the RTI growth-rate depends on the acceleration parameters and initial conditions. For the later-time dynamics, we link the interface dynamics with an interfacial shear function, and find a continuous family of regular asymptotic solutions and invariant properties of nonlinear RTI. The essentially interfacial and multi-scale character of the dynamics is also demonstrated. The velocity field is potential in the bulk, and vortical structures appear at the interface due to interfacial shear. The multi-scale character becomes clear from the invariance properties of the dynamics. We also achieve excellent agreement with existing observations and elaborate new benchmarks for future experimental work.