Pia-csek 



Fig. 7 - Variation of horizon- 

 tally averaged temperature 

 with depth for experiment C 



C. Wave-Number Selection in Finite Amplitude 

 Benard Convection 



This problem considers the convection flow that arises in a thin horizontal 

 layer of fluid when a steady and uniform temperature contrast is maintained 

 across it. In particular, a determination of the horizontal cell dimensions is 

 sought when the motions may be considered to be two-dimensional. Both the 

 experimental results of Rossby (1966), Koschmieder (1966), and Chen and White- 

 head (1968), and the theoretical results of Schluter, Lortz, and Busse (1965), 

 have indicated that in the case of rigid-rigid boundaries almost all the laminar 

 flow range exhibits two-dimensional behavior in the form of "rolls." The object 

 of the present study was to determine the preferred horizontal length of such 

 rolls and the mechanisms or principles that are responsible for the selection. 



Equations (19) through (22) are also applicable here. They may be put in 

 nondimensional form, by choosing 



t = l 



T = AT • T' 



(24) 



to obtain (dropping the primes) 

 1 



di d , B ^ 



T7+ — (uO +— (wO 



ot ox oz 



V2<f - Ra • ^ 

 Bx 



(25) 



^T 3 ^ ^ ^ 



— + — (uT) + — (wT) 

 3t 3x 3z 



V^T 



(26) 



770 



