Fully 3D Rayleigh-Taylor Instability in a Boussinesq Fluid

TL;DR

This paper develops a linearized theory and a novel spectral method for analyzing the fully 3D Rayleigh-Taylor instability in Boussinesq fluids, providing insights into early-time growth and nonlinear interface evolution.

Contribution

It introduces a new spectral method for fully 3D nonlinear analysis and compares it with linear theory for Rayleigh-Taylor instability in Boussinesq fluids.

Findings

Linearized theory describes early-time interface evolution.

Spectral method enables large-scale 3D nonlinear simulations.

Results highlight differences between linear and nonlinear growth phases.

Abstract

Rayleigh-Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present linearized theory for arbitrary 3D initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D non-linear problem in a Boussinesq fluid, where the interface between the light and heavy fluid is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, compared and contrasted with the early-time linearized theory.