Zieve-g and Sawatzki 



mentioned full laminar flow. The Navier Stokes equations in sphericcil 

 coordinates give a very simple solution here with the velocity linear 

 in r. The analytical expressions for the three flow regions can be 

 combined and a short and simple calculation gives a torque coefficient 

 that fits surprisingly well to our experimental results, 



c. The Stuart vortices -- already mentioned in connection 

 with mode II -- all rotate in the same direction. Experiments done 

 with a rotating free sphere [ 9] have confirnned this type of vortices, 

 A simple cinematic consideration shows how one comes from the 

 Taylor-Gortler vortices that have an alternating direction of rotation 

 to the Stuart vortices. For this it is only necessary to superpose a 

 suitable flow field to the Taylor-Gortler vortices with a flow direction 

 cross to the vortex axes. With other words: to get Stuart vortices 

 it is necessary that the Taylor vortices become embedded in a suitable 

 flow field. 



We are dealing here with a real three-dimensional effect that 

 changes our vortex model. One realizes easily that for a rotating 

 free sphere or in the gap between two spheres of which one is rotating 

 the just mentioned situation exists. 



[1 



[2 

 [3 

 [4 



[5 



[6 



[7 



REFERENCES 



Taylor, G, J, , "Stability of a Viscous Liquid Contained Between 

 Two Rotating Cylinders," Phil, Trans, A 223, 289-293, 

 1923. 



Zierep, J, , "Thermokonvektiv Zellularstromiungen bei inkonstanter 

 Erwarmung der Grundflache," ZAMM41, 114-125, 1961. 



Koschmieder, E, L, , "On Convection of a Nonuniformly Heated 

 Plane," Beitr, z. Phys. d, Atmos. , 39, 208-216, 1966. 



Miiller, U, , "tJber Zellularstromungen in Horizontalen Fliissig- 

 keitsschichten Mit Ungleichmapig Erwamter Bodenflache , " 

 Beitr. z, Phys, d. Atmos., 39, 217-234, 1966, 



Sawatzki, O, , and Zierep, J. , "Das Stronnfeld Zwischen Zwei 



Konzentrischen Kugelflachen, von Denen die Innere Rotiert, " 

 Acta Mechanica, 9, 13-35, 1970, 



Wimmer, M, , and Ritter, C. F. , "Die Stromung im Spalt 



Zweier Konzentrischer Kugeln, " Diplomarbeiten, Univ. 

 Karlsruhe, Lehrstuhl fiir Strbmungslehre 1968, 1969, 



Coles, D, , "Transition in Circular Couette Flow," J. Fluid 

 Mech. 21, 385-425, 1965. 



286 



