Localised instability in a bénard layer

Abstract

Linear stability in a Bénard layer with a non-uniform temperature profile is considered. Instability sets in at a level where a local destabilising steady-state temperature gradient sufficiently exceeds the adiabatic gradient. Two boundary value problems arise depending on whether this level is at a boundary, or within the fluid. In this paper the former is solved asymptotically, and the eigenvalue estimates confirmed numerically using the compound matrix method.

AMS (MOS):

• 41A60
• 76E15
• 65L15