On the fundamentals of Rayleigh-Taylor dynamics with variable acceleration

TL;DR

This paper develops a theoretical framework for Rayleigh-Taylor instability driven by variable, power-law acceleration, revealing new invariance properties and linking interface dynamics to interfacial shear, with implications for natural and technological processes.

Contribution

It introduces a novel group theory approach to analyze nonlinear RTI with variable acceleration, providing solutions and invariance properties that extend understanding beyond constant acceleration models.

Findings

RTI growth-rate depends on acceleration parameters and initial conditions.

Identifies a family of asymptotic solutions for late-time RTI dynamics.

Reveals invariance properties and multi-scale structure of nonlinear RTI.

Abstract

Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing studies have considered constant acceleration. This work focuses on RTI driven by acceleration with power-law time-dependence, and applies group theory to solve the classical problem. For early time dynamics, we find dependence of RTI growth-rate on acceleration parameters and initial conditions. For late time dynamics, we directly link interface dynamics to interfacial shear, find continuous family of regular asymptotic solutions, and discover invariance properties of nonlinear RTI. Our results reveal the interfacial and multi-scale character of RTI with variable acceleration. The former is exhibited in structure of flow fields with intense fluid motion near the interface and effectively no motion in the bulk; the latter follows from the invariance properties of nonlinear dynamics defined by the interplay of two macroscopic length-scales - the wavelength and the amplitude. Our theory resolves the long-standing problem of RTI nonlinear dynamics, achieves excellent agreement with observations, and elaborates diagnostic benchmarks for future experiments and simulations.