On the Transition to Turbulent Convection 



VJSL\ 



(a) 



(b) 



(c) 



Fig. 9. Streak line photographs of tracers in a vertical slice through 

 the convecting fluid. The Prandtl number is 860. (a) a ver- 

 tical slice through steady two-dimensional rolls at R = 6 Rg. 

 (b) Showing a pair of cells with a tilt relative to the vertical. 

 R = 74 Rp. (c) Showing a tilted cell at R = 89 Re- 



In case of the tilted cells, however, ( uw) over one cell is non-zero 

 and is always in the sense of transporting positive x-component of 

 monnentum to regions where the flow is in the positive x-direction, 

 transporting negative x-component to regions where the flow is In 

 the negative x-direction. Again one might rationalize the increased 

 slope of the heat fliox curve by the following argument. As the exter- 

 nally imposed heat flux is increased more and more, the fluid must 

 move faster and faster. Then, to accomplish the heat exchange at 

 the boundaries, the cells must become wider and wider. The tilting 

 of the cells can help to maintain this flow against the increased viscous 

 dissipation along the boundaries. The tilting of cumulus convection 

 cells in the earth's atmosphere has often been related with a vertical 

 wind shear. The tilted cell is believed to be important in transporting 

 momentum in the vertical direction, thus maintaining the wind aloft. 

 It is interesting to note that in this laboratory situation convection 

 cells tilt even in the absence of a mean wind shear. 



The second mode of time dependence is an oscillatory mode 

 with a much shorter time scale. Figure 7 shows (x,t) photographs 

 taken with the light beam near the bottom of the layer of fluid. 

 Figure 7b shows a bright region, which is a region of strong shear, 

 move from one cell boundary to another. This process is repeated 

 periodically in time, (x,t) photographs synchronized with a tem- 



303 



