On the Transition to Turbulent Convection 



10' 



2 10' 



1 10^ 



10= 



TURBULENT FLOW 



TIME 

 DEPENDENT • 1 3- DIMENSIONAL 

 -j-IV • 



I °; ^ Flow j 



»— i-1 1 



STEADY^ 3- ^DIMENSIONAL FLOW '" o 



•— * 1 ii-^'^rt 00 



o o o 



5° STEADY °2-0IMENSI0NAL ° FLOW 



10-' 



NO MOTION 



10" 



10 



10^ 10' 



PRANDTL NO. 



Fig. 10. The regime diagram. The circles represent steady flows, 

 the circular dots represent time-dependent flows. The 

 stars represent transition points. The open squares are 

 Rossby's observations of time-dependent flow, the squares 

 with a dot in the centre are \Villis and Deardorff's obser- 

 vations [ 1967b] for turbulent flow. The triangle is 

 Silveston's [ 1958] point of transition to time-dependent 

 flow. 



the non-rotating case. Figure lie shows the break-down of rolls 

 and waves forming on them. The disturbance forms an angle of 

 58° ± 2° to the original roll axis, exactly as predicted by Kuppers 

 and Lortz. Figure lie is a transient state; lid is the final steady 

 state. In this state the over-all wavy pattern was not observed to 

 change with time but the internal striations representing regions of 

 strong shear were seen to change with a time scale of the order of 

 one minute. (Here d /v = 40 sec, d //f ^ 1 hr) . Figure 12 shows 

 the regime diagram for the rotating convection. The observed criti- 

 cal Taylor numbers compare only approximately with those computed 

 by Kuppers [ 1970] for finite Prandtl nunnber and rigid boundaries. 

 The observed transitions occurred at Tg = 1 . 5 X 10^ for Pr = 6.7, 

 R « Re and at T,. = 7 X 10^ for Pr = 10^, R ^ R,.. The predicted 

 values are T,. = J X 10 for Pr = 1 , Tc = 1 . 7 X 10^ for Pr = 5, 

 and 



Tc = 7 X 10 

 Tc «^ 2 X 10^ for Pr — oo. 



305 



