Piacsek 



(a) 



StP^Hf f UNCTION 



If.t^PtBCiTUflE 



Cb) 



,[HFAH f IKCTIjh 



TEflPEHRT'JRE 









m 



^ iiiv m 



u) 





rPHPF«^flTuP^ 



Fig. 9 - Steady-state streamlines (left) and isotherms (right) for 

 Benard convection with y = 1.68: (a) stretching of a y = 1.00 cell; 

 (b) initial perturbation cos Zttx; and (c) initial perturbation sin Z-tx 



of aspect ratio > . The curious result found was that a perturbation of form 

 cos 27TX (run (b))will lead to a 2-roll steady state, whereas a sin 2ttx (run (c)) 

 will lead to a 3-roll behavior. Run (c) corresponds to the y = 1.00 cell adia- 

 batically "stretched" to a y = 1.68 cell. The answer appears to lie in the fact 

 that the sin 2ttx mode does not naturally satisfy the temperature boundary con- 

 ditions, but is forced to do so at the gridpoints adjacent to the boundary, by the 

 numerical procedure. This causes the temperature profile to have a point of 

 inflection near the boundary and to develop regions of buoyancy opposite to that 

 of the interior region adjacent to it. These appear to be the cause of the forma- 

 tion of the smaller cells on the sides. The highest heat transfer is associated 

 with mode (c), i.e., the one exhibiting the largest number of upward-moving 

 columns per unit area. This agrees with the Nusselt number's dependence on 

 7, where the largest heat transfer occurs for the smallest width-to-depth ratio. 



774 



