Experiments on Convective Flows in Geophysical Fluid Systems 



where m/r = vr is the angular momentum about the cylinder's axis and T = Tr 

 P and S are cylindrical diffusion operators defined by 



3 r B r r -^ 



32 



(18a) 



3 r 3r '" 3z ^ 



(18b) 



Finite difference versions of Eqs. (9), (13), and (17a,b) were programmed 

 for a digital computer; the appropriate numerical schemes for differencing the 

 individual terms and for iterating the resulting system of nonlinear algebraic 

 equations are discussed in the concluding section. 



The results are displayed in Figs. 1, 2, and 3, and are for the case of = 

 1.75, e = 1.0 X 10"^, \ = 2, CT = 7, and a' = a/(b-a) = .67. Figure 1 shows 

 a cross section of the annulus, Fig. 2 the streamlines, isotherms, and isolines 

 of the zonal velocity, and Fig. 3 the behavior of the temperature deviation from 

 the hot-wall temperature, as a function of height at the radial midpoint. 



HOT 



0{ 



<— 



Fie. 1 



- Cross section of 

 the annulus 



In general, the results agree with the experimental results. Figure 3 

 clearly shows the exponential behavior of the quantity st = T^, - T (r, z ) in the 

 upper region of the flow, and a comparison with the isotherms in Fig. 2(b) 

 shows that this region coincides with the large isothermal region above the 

 T = .6 line, approximately. The curved portion plots to a straight line on 



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