Kinematic regimes of convection at high Prandtl number in a shallow cavity

Overview & Synopsis

We consider free convection in a horizontal shallow cavity with different end temperatures, filled with a high Prandtl number fluid. From scaling analysis, we find two kinematic regimes resulting from the competition of heat transfer by conduction and by convection. Numerical simulations realized for a large range of Rayleigh number and aspect ratio confirm the phenomenological analysis and provide the threshold between the two regimes. The conductive and convective regimes occur at RaA^2 smaller and larger than 443 respectively, where Ra is the Rayleigh number and A is the aspect ratio. In the convective regime, the characteristic velocity is independent of depth of the cavity.