Some further studies on the transition to turbulent convection

Abstract

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbersR, for a given Prandtl numberPr.The regime diagram has been extended to include the Prandtl-number range2·5 × 10−2[les ]Pr[les ] 0·85 × 104.In particular it is found that distinct changes in the slope of the heat-flux curve occur even forPr= 2·5 × 10−2. The flow is steady up toR=Rt= 2·4 × 103. ForR>Rt, the period of oscillation is compared with the theoretical values of Busse. ForPr= 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.ForRjust greater thanRc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition atRIIis investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering ofRII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at largeRand high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.