The nonlinear stability of the conduction-diffusion solution of a fluid mixture heated and salted from below (and of a homogeneous fluid heated from below) and saturating a porous medium is studied with the Lyapunov direct method. Both Darcy and Brinkman models have been used. The porous medium is bounded by two horizontal parallel planes and is rotating about a vertical axis. Necessary and sufficient conditions of unconditional stability are proved (i.e., the critical linear and nonlinear stability Rayleigh numbers coincide). Our results generalize those given by Straughan [21] for a homogeneous fluid in the Darcy regime. In the case of a mixture two stabilizing effects act: that of the rotation and of the concentration of the solute.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received March 05, 2002 / Published online June 4, 2002
RID="a"
ID="a" e-mail: lombardo@dmi.unict.it
RID="b"
ID="b" e-mail: mulone@dmi.unict.it
Communicated by Brian Straugham, Durham
Rights and permissions
About this article
Cite this article
Lombardo, S., Mulone, G. Necessary and sufficient conditions of global nonlinear stability for rotating double-diffusive convection in a porous medium. Continuum Mech Thermodyn 14, 527–540 (2002). https://doi.org/10.1007/s001610200091
Issue Date:
DOI: https://doi.org/10.1007/s001610200091