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 range 2·5 × 10 −2 [les ] Pr [les ] 0·85 × 10 4 . 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 = R t = 2·4 × 10 3 . For R > R t , 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 R 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 at R II is investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering of R 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 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.