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 epsilon is equal to one. For other values of epsilon 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 (C) 2001 John Wiley & Sons, Ltd.
Nonlinear stability in the Bénard problem for a double-diffusive mixture in a porous medium
LOMBARDO, SEBASTIANO;MULONE, Giuseppe;
2001-01-01
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 epsilon is equal to one. For other values of epsilon 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 (C) 2001 John Wiley & Sons, Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
