Triply Resonant Double Diffusive Convection in a Fluid Layer

Abstract

We study the problem of double-diffusive convection in a horizontal plane fluid layer when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

Keywords:

• double-diffusive
• three layer
• resonance
• thermal insulation

AMS Subject Classification:

• 76E06
• 76M22