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=R_t= 2·4 × 10³. ForR>R_t, 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 thanR_c, 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 atR_IIis investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering ofR_II. 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.