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FULLY 3D RAYLEIGH–TAYLOR INSTABILITY IN A BOUSSINESQ FLUID

Part of: Hydrodynamic stability Basic methods in fluid mechanics

Published online by Cambridge University Press:  01 July 2019

S. J. WALTERS Open the ORCID record for S. J. WALTERS [Opens in a new window]  and
L. K. FORBES Open the ORCID record for L. K. FORBES [Opens in a new window]
S. J. WALTERS*
Affiliation:
School of Mathematics and Physics, University of Tasmania, P.O. Box 37, Hobart, 7001, Tasmania, Australia email stephen.walters@utas.edu.au, larry.forbes@utas.edu.au
L. K. FORBES
Affiliation:
School of Mathematics and Physics, University of Tasmania, P.O. Box 37, Hobart, 7001, Tasmania, Australia email stephen.walters@utas.edu.au, larry.forbes@utas.edu.au
*
✉stephen.walters@utas.edu.au
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Abstract

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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.

Keywords

viscous flowRayleigh–Taylor instabilitylinearizationspectral method

MSC classification

Primary: 76E17: Interfacial stability and instability
Secondary: 76M22: Spectral methods
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 3 , July 2019 , pp. 286 - 304
Copyright
© 2019 Australian Mathematical Society 

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