THE RAYLEIGH-BENARD PROBLEM IN INTERMEDIATE BOUNDED DOMAINS

The stationary instabilities of flow patterns associated with Rayleigh -Benard convection in a 3 x 1 x 9 rectangular container are extensivel y investigated by numerical simulation. Two types of spatial instabili ties 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-ro ll instability is found at moderate Rayleigh number Ra. The results ob tained confirm the importance of this flow pattern as a continuous mec hanism for steady transition from one wavenumber to another. For Pr = 15, cross-roll instability is obtained, which at larger Ra leads to bi modal convection. For this value of Pr the soft-roll flow pattern is f ound at intermediate Ra. At higher Ra a new flow structure in which cr oss-rolls are superimposed on the soft roll is obtained. The effects o f the various flow structures on the heat transfer are given. A quanti tative comparison with previous experimental and theoretical findings is also presented and discussed.