On the Transition to Turbulent Convection 





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Fig. 5b. Photographs showing the plan fornn within circular side 

 walls. The transition is the same as in Fig. 5a. The 

 Prandtl number is 860. 



definite Prandtl number dependence in the range 10 < Pr < 10 , 

 There was a marked hysteresis both in the heat flux and plan form 

 as the Rayleigh number was increased then decreased past Rjj . 

 This transition is shown by the curve labelled II in the regime dia- 

 gram (Fig. 10). 



The Third Transition 



The third transition in order of increasing R occurs at a 

 Rayleigh number which will be labelled Rjjj . It marks a change 

 from steady three-dimensional to time-dependent flow, and has 

 associated with it a discrete change in slope of the heat flux curve 

 (Fig. 6) [Krishnamurti, i970b] . The change in slope was measured 

 for each of the fluids shown in Fig. 10, with 10'^ < Pr < 10^ The 

 transition point is labelled as curve III. For Rayleigh numbers 

 above this curve the flow showed two modes of time dependence. 

 The one is a slow time dependence with time scale of the order of 

 the thermal diffusion time d^//C. An (x,t) photograph showing 

 this mode is seen in Fig. 8. The light beam was near the bottom 

 of the fluid. It is a slow tilting of the cell with height. Below Rjj^ 

 there was never a noticeable tilt observed. Above Rjjj some cells 

 would be tilted for times of the order of d^//C. Fig. 9 shows streak 

 photographs of tracer particles in a vertical slice through the con- 

 vecting fluid. Figure 9a shows steady flow in cells of rectangular 

 cross section at Rayleigh number Re and Pr = 860. Figures 9b and 

 9c show tilted cells at Rayleigh number 74 R^. and 89 Re, respectively, 

 and Pr = 860. The tilted cells often occurred in pairs with the tilt 

 always such that two rising particles were close together near the 

 bottom boundary, flaring apart near the top. Two sinking particles 

 were close together near the top, flaring apart near the bottom. 

 Untilted cells, as in Fig. 9a are symmetrical about a horizontal 

 line at m.id- depth in the fluid. When integrated over the cell, the 

 net vertical transport of the x-component of velocity, ( uw) is zero. 



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