THREE DIMENSIONAL INSTABILITIES AND 

 VORTICES BETWEEN TWO ROTATING SPHERES 



J. Zierep and O, Sawatzki 



Universitdt Karlsruhe 

 Karlsruhe J West Germany 



We study the motion of a viscous medium between two concen- 

 tric rotating spheres. Investigating this type of flow is an extension 

 of the well-known contribution of G, I, Taylor [ l] , who studied the 

 motion between two rotating cylinders. Due to the action of the 

 centrifugal force instabilities are possible. The main difference 

 between the two flow fields is that for the spheres the centrifugal 

 force is a function of the latitude. We have here an instability in a 

 three-dimensional flow and it is possible that there exist different 

 flow regimes -- stable and unstable ones -- side by side. This prob- 

 lem is closely related to the cellular convection flow, especially to 

 those existing over nonuniformly heated surfaces [2, 3, 4] , The 

 thernnal buoyancy corresponds to the centrifugal force, the nonuniform 

 heating corresponds to the latitudinal dependence of the centrifugal 

 force. 



* 

 Now some fundamental things about the used apparatus. The 



experiments have been done primarily with the inner sphere (Aluminum) 

 rotating and the outer one (Plexiglass) fixed. The gap was filled with 

 silicon oil that contained aluminum powder as flow indicator. Measured 

 has been mainly the frictional torque that keeps the angular velocity 

 of the inner sphere constant. The temperature in the gap was con- 

 trolled by thermocouples and photographs have been taken of the 

 different flow configurations. The measurements have been done 

 by Ritter and Wimmer [ 6] as part of their master thesis. 



Figures 1 and 2 show the results for two different gap widths. 

 Plotted is the friction torque coefficient t, over a Reynolds number 

 that ranges from 10' to 10®, Covering this wide range has been 

 accomplished by 1) using silicon oils with viscosities between 3 and 

 1000 c St and 2) by varying the angular velocity from to 200 revo- 

 lutions/sec. 



In principle we have here independent of the width of the gap 

 three different donnains of fluid motion. For small Reynolds numbers 



For detailed Information see [ 5] , 



275 



