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 numbers R, for a given Prandtl number Pr. 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 for Pr = 2·5 × 10−2. The flow is steady up to R = Rt = 2·4 × 103. For R > Rt, the period of oscillation is compared with the theoretical values of Busse. For Pr = 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.For R just greater than Rc, 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 at RII is investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering of RII. 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 large R and 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.