Sur la nature de la transition à l'instationnaire d'un écoulement de convection naturelle en cavité différentiellement chauffée à grands écarts de température

Abstract

Natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients, is considered. The low Mach approximation equations are those obtained by Paolucci allowing for filtering of sound waves. Transition to unsteadiness is studied with numerical simulation, with a finite volume code based on a fractional time step method derived from projection methods used for incompressible flows. When the fluid physical properties are prescribed constants, transition to unsteadiness follows the classical scheme of a Hopf bifurcation. The transition is quite different when viscosity obeys Sutherland's law while the Prandtl number is kept constant. There is evidence of hysteresis, therefore the transition seems to be subcritical. In the vicinity of the transition, on the large amplitude branch, an intermittent solution is observed, with periodic bursts separating quasi-steady states.