On the Transition to Turbulent Convection 



The plexiglass tank containing the fluid also contains four blocks of 

 alunninum 6061 T 651. Two of the blocks are 4 in. thick, two are 

 i in. thick, each is 20 in. by 20 in. wide. The electrical heater, 

 which is a fine mesh of resistance material embedded in silicon 

 rubber, is attached to the bottom of the lowest block, which is 4 in. 

 thick. The heat input is controlled by a variable transformer backed 

 by a constant voltage transformer of the line voltage. Above this 

 lowest aluminum block is a low- conductivity layer of methyl metha- 

 crylate, A layer of liquid sufficiently thin that it never convects 

 for the temperature gradients occurring in these experiments effects 

 constant thermal contact between the layers. Above this low con- 

 ductivity layer is a block of aluminum 1 in. thick; above this is the 

 convecting fluid, whose depth is defined by plexiglass spacers. The 

 arrangement of blocks above the convecting layer is symmetric to 

 that below except that the cooling is accomplished by cooling fluid 

 from a constant-temperature circulator flowing in channels in the 

 uppermost aluminum block. The channels for incoming and outgoing 

 flows are side by side in order to minimize horizontal temperature 

 gradients. The channels were cut in a complicated pattern and 

 spaced so that the separation of channels was not close to an integral 

 multiple of the expected convection cell size. The maximum flow 

 rate of the cooling fluid is 2 • 5 gcil/min. This apparatus was used 

 in the studies which will be described with air, water, and silicone 

 oils. For convection in mercury, the aluminum blocks were replaced 

 by copper blocks of which two are 2 in. thick, two are 1 in. thick 

 and each is 20 in. by 20 in. wide. 



The thermal conductivity of the aluminum is about three orders 

 of magnitude larger than that of the oils. The thermal conductivity 

 of copper is 50 times as large as that of mercury. This is, of course, 

 an attempt to approach the ideal condition of perfectly conducting 

 boundaries. With poorly conducting boundaries a horizontal tempera- 

 ture ripple corresponding to the cellular structure in the convecting 

 fluid penetrates into the boundaries and may control transitions to 

 different cellular structures. Also the metal acts as a diffuser of 

 any horizontal temperature variations arising from the discrete 

 nature of the cooling channels. The large mass of metal (approxi- 

 mately 400 lb of aluminum or 700 lb of copper) acts as a large heat 

 capacity so that temperatures in the blocks are very stable. 



The heat transported by the convecting liquid is measured by 

 concentrating the temperature gradient across the poor conductor in 

 the manner devised by Malkus [ 1954] . In the steady state the heat H 

 transported by the fluid is the average of the heat conducted across 

 the two poor conductors: 



" " ^P 2dp ^P 2dp 



where kp and ki are the molecular conductivities of the low con- 

 ductivity layers, dp is the depth of the layer, and T, , Tg, T3 and 



291 



