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The Rayleigh-Taylor instability in a porous medium

Citation

Forbes, LK and Browne, CA and Walters, SJ, The Rayleigh-Taylor instability in a porous medium, SN Applied Sciences, 3, (2) pp. 1-14. ISSN 2523-3963 (2021) [Refereed Article]


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DOI: doi:10.1007/s42452-021-04160-z

Abstract

The classical Rayleigh-Taylor instability occurs when a heavy fuid overlies a lighter one, and the two fuids are separated by a horizontal interface. The confguration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar fow, but in a porous medium governed by Darcy's law. First, the fully saturated situation is considered, where the two horizontal fuids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely difuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding fow for two free fuids.

Item Details

Item Type:Refereed Article
Keywords:porous medium; Rayleigh-Taylor instability; spectral methods; boussinesq fow; nonlinear effectf
Research Division:Physical Sciences
Research Group:Condensed matter physics
Research Field:Electronic and magnetic properties of condensed matter; superconductivity
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Forbes, LK (Professor Larry Forbes)
UTAS Author:Browne, CA (Miss Catherine Browne)
UTAS Author:Walters, SJ (Mr Stephen Walters)
ID Code:152553
Year Published:2021
Web of Science® Times Cited:4
Deposited By:Mathematics
Deposited On:2022-08-22
Last Modified:2022-09-15
Downloads:0

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