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Non-linear stability in the Bénard problem for a double-diffusive mixture in a porous medium

✍ Scribed by S. Lombardo; G. Mulone; B. Straughan

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
141 KB
Volume
24
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The linear and non‐linear stability of a horizontal layer of a binary fluid mixture in a porous medium heated and salted from below is studied, in the Oberbeck–Boussinesq–Darcy scheme, through the Lyapunov direct method. This is an interesting geophysical case because the salt gradient is stabilizing while heating from below provides a destabilizing effect. The competing effects make an instability analysis difficult. Unconditional non‐linear exponential stability is found in the case where the normalized porosity ϵ is equal to one. For other values of ϵ a conditional stability theorem is proved. In both cases we demonstrate the optimum result that the linear and non‐linear critical stability parameters are the same whenever the Principle of Exchange of Stabilities holds. Copyright © 2001 John Wiley & Sons, Ltd.

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