Experiments on Convective Flows in Geophysical Fluid Systems 



Fig. 3 - Plot of log (T]3-T) 

 vs. z at the radial mid- 

 point of the annular gap 



ordinary graph paper, and corresponds to the central "bundle" of isotherms 

 between < T < .6. For lower rotation the central "bundle" occupies a con- 

 siderably larger portion of the interior region, confining the exponential region 

 to a smaller region near the top; for higher rotation, the bundle becomes nar- 

 rower and steeper. Both the cylindrical geometry and rotation contribute to 

 this behavior of the temperature field, the former being responsible for the 

 strong asymmetry and the latter for the bundle formation. The isotherms and 

 streamlines are parallel only in certain regions of the flow, indicating that 

 thermal conduction is important throughout the gap. The isotherms display 

 clearly the "humps" found in the laboratory experiments, and even bigger humps 

 are found in the streamlines, indicating a weak reverse flow outside the bound- 

 ary layers. K we denote by dj and d^ the distances from the top and bottom, 

 respectively, at which the mean isotherm t'= crosses the radial midpoint, 

 we find that their ratio has the value dj/d2 = 3.3. This is considerably higher 

 than the ratio b/a = 2.5 that may be shown from simple geometrical arguments 

 to be the required value of dj/dj. For larger rotation rates this value is indeed 

 approached, but for lower rotation rates it becomes much higher. An inspection 

 of Fig. 2(c) shows that the zonal velocity reverses at some depth in order to 

 conserve torques about the axis. Furthermore, most of the shear in the v field 

 is concentrated at the upper part of the inner cylinder and the rigid bottom, in- 

 fluencing strongly the entrainment into the sidewall layers. 



The theory of stratification-controlled flow in a nonrotating cavity has been 

 worked out by Gill (1966), and for a rotating annulus by Mclntyre (1967). A 

 simple theory for the existence of the humps in the isotherms, their variation 

 with rotation, and the large value of the ratio dj/dj has been put forward by 



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