The Rayleigh–Bénard problem in intermediate bounded domains

Abstract

The stationary instabilities of flow patterns associated with Rayleigh–Bénard convection in a 3 × 1 × 9 rectangular container are extensively investigated by numerical simulation. Two types of spatial instabilities of the base convection rolls are predicted in the transition from steady two-dimensional flow to the unsteady oscillatory regime; these instabilities depend on the Prandtl number. For Pr = 0.71 the soft-roll instability is found at moderate Rayleigh number Ra. The results obtained confirm the importance of this flow pattern as a continuous mechanism for steady transition from one wavenumber to another. For Pr = 15, cross-roll instability is obtained, which at larger Ra leads to bimodal convection. For this value of Pr the soft-roll flow pattern is found at intermediate Ra. At higher Ra a new flow structure in which cross-rolls are superimposed on the soft roll is obtained. The effects of the various flow structures on the heat transfer are given. A quantitative comparison with previous experimental and theoretical findings is also presented and discussed.