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On the nature of the transition to unsteadiness of natural convection solutions in a differentially heated cavity under large temperature gradients. (Sur la nature de la transition à l’instationnaire d’un écoulement de convection naturelle en cavité différentiellement chauffée à grands écarts de température.) (French. Abridged English version) Zbl 1056.76032

Summary: We consider natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients. The low Mach approximation equations allow 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 physical properties of the fluid 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 a vicinity of the transition, on the large amplitude branch, an intermittent solution is observed, with periodic bursts separating the quasi-steady states.

MSC:

76E06 Convection in hydrodynamic stability
76R10 Free convection
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
80A20 Heat and mass transfer, heat flow (MSC2010)
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