Fully  3D  Rayleigh-Taylor instability in a Boussinesq fluid

Stephen John Walters; Lawrence K. Forbes

doi:10.21914/anziamj.v61i0.13700

Authors

Stephen John Walters University of Tasmania
Lawrence K. Forbes University of Tasmania

DOI:

https://doi.org/10.21914/anziamj.v61i0.13700

Keywords:

viscous flow, Rayleigh-Taylor instability, linearization, spectral method.

Abstract

Rayleighâ€“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 a linearized theory for arbitrary three-dimensional (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 nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids 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, and compared and contrasted with the early-time linearized theory. doi:10.1017/S1446181119000087

Author Biographies

Stephen John Walters, University of Tasmania

Researcher, School of Mathematics and Physics, University of Tasmania,Hobart, 7001, Tasmania.

Lawrence K. Forbes, University of Tasmania

Professor, School of Mathematics and Physics, University of Tasmania, Hobart, 7001, Tasmania.

Fully 3D Rayleigh-Taylor instability in a Boussinesq fluid