Fully 3D Rayleigh-Taylor instability in a Boussinesq fluid

Stephen John Walters, Lawrence K. Forbes

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 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

Keywords


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



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



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.