On the nature of the transition to unsteadiness of natural convection solutions in a differentially heated cavity under large temperature gradients

Natural convection of ail inside a rectangular cavity, differentially heate d under large temperature gradients, is considered. The low Mach approximat ion equations al e those obtained by Paolucci allowing for filtering of sou nd waves. Transition to unsteadiness is studied with numerical simulation w ith a finite volume code based on a fractional time step method derived fro m projection methods used for incompressible flows. When the fluid physical properties are prescribed constants, transition to unsteadiness follows th e classical scheme of a Hopf bifurcation. The transition is quite different when viscosity obeys Sutherland's law while the Prandtl number is kept con stant. There is evidence of hysteresis, therefore the transition seems to b e subcritical. In the vicinity of the transition, on the large amplitude br anch, an intermittent solution is observed, with periodic bursts separating quasi-steady states. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.