Fully 3D Rayleigh-Taylor Instability in a Boussinesq Fluid

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.