Experiments on Convective Flows in Geophysical Fluid Systems 



Since the experiments were performed on axisymmetric types of flow only, 

 B/3(p of all quantities vanishes. Then the equation of continuity, Eq. (2), re- 

 duces to 



r 3r 



^"^T;= ° ' (5a) 



and we can introduce a stream function >/' defined by the relations 



'"" = b7 ■ ^" = ' 37 ' (5b) 



Cross-differentiating the first and third component of Eqs. (3) to eliminate 

 p, and introducing the azimuthal component of the vorticity 



^ = 37 " ?r ' (6) 



we obtain 



3<f 3 3 , 3 /v2 \ "^T , , 



-1 + — (u^) + — (w^-) = va(^) + — - — + 2nv - ag — - , •■ - ,rj) 



dt3r dz dz\' / dr ^' ' 



where we used the equation of continuity to obtain the left-hand side, and a is 

 a cylindrical diffusion operator defined by 



3 1 3 32^ "■ - ■ 



- ^ «^^^^77?77 ^^"77^- - (8) 



Furthermore, we may note that . ,. . 



. ,. ■ . ^ = a(0) . . ..; __■-, ., (9) 



We may introduce the following scaling now: 



r=(b-a)r' 

 z = d • z ' 

 Ti = (Tb-Tg) • T' = AT-T' • ' ' 



(u,v) = [agATd/2n(b- a)] • (u',v') . 

 Then, from (5a), 



(10) 



(b-a) u' 



Equations (4), (8), and the second component of Eqs. (3) may then be written 



757 



(11) 



