Krishnamurti 



perature record at a point within the fluid showed a temperature 

 anomaly each time a bright region moved pass the point. It is an 

 oscillation in the sense that the temperature and flow show a time 

 periodicity at a fixed point in the fluid. This oscillatory miode is 

 illustrated in the following movie which shows convection in a 

 Hele-Shaw cell having dimensions 24 in, wide, 2 in, tall, and 1/16 

 in. thick (that is i/i6 in. in the direction of the line of sight). It 

 shows hot spots and cold spots (bright regions) forming and being 

 advected by the mean circulation of the cell. 



As the Rayleigh number is increased transition to turbulence 

 appears to result from the increased number and frequency of these 

 oscillations. 



in. TRANSITION TO TURBULENT CONVECTION IN A ROTATING 

 FLUID LAYER 



This topic will be discussed very briefly. A horizontal layer 

 of fluid heated below and cooled above is rotated about a direction 

 parallel to the force of gravity. The linear stability theory has been 

 treated by Chajidrasekhar [ 1961 J . The finite amplitude theory with 

 very clear physical explanations is given by Veronis [ 1959] . Notable 

 experiments have been performed by Fultz and Nakagawa [ 1955] , 

 by Rossby [ 1966] , and others. 



Recently, Kvippers and Lortz [ 1969] have shown that for 

 infinite Prandtl number there exists a critical Taylor number Tc 

 beyond which there can be no stable steady convection in the vicinity 

 of R,;. The Taylor number T is defined as 



T =^f^ 



where Q is the rotation rate, d the layer depth, and v is the kine- 

 matic viscosity. For T < T^. they show that the only stable finite 

 amplitude solution is the two-dimensional roll solution. For T > Tg 

 there must be a transition from the conduction state to a time de- 

 pendent flow as the Rayleigh niamber is increased beyond the critical. 



The apparatus consisted of a fluid layer i or 2 cm in depth, 

 18 inches in diameter in the horizontal direction. The fluid was 

 bounded below by a 2 in, thick aluminum block containing an electri- 

 cal heater which is a fine mesh of resistance material. Above the 

 fluid layer was bounded by a glass plate over which the cooling fluid 

 circulated. 



Photographs taken from above by a camera rotating with the 

 fluid are shown in Fig. 11. Figure Ua shows rolls. Fig. lib shows 

 the cross instability forming on the rolls, of the same kind found in 



304 



