Instabilities and Vortices Between Two Rotating Spheres 



is directed inward (Figs. 10, 11). This can be explained by a cellular 

 motion in the field between the pole and the vortex that forces the 

 vortex to rotate in the mentioned direction. The result is the sink 

 flow at the equator, 



IV. Two pairs of Taylor vortices develop symmetrical to the 

 equator but now with an outward motion at the equator (Figs, 12, 13). 

 Mode III is a limit case of IV reached by increasing angular velocity. 

 The cell close to the equator becomes smaller and smaller and in the 

 limit the flow reverses at the equator. 



V. This is an unsteady version of mode III. Vortices, 

 generated at the equator, leave the equator under a snniall angle of 

 about 10 (Fig, 14) and move on spiral trajectories to the pole. 



It is interesting to see that the critical Taylor number increases 

 with increasing gap width. Corresponding calculations for rotating 

 cylinders with arbitrary gap width, done by Kirchga^ner [ ll] , agree 

 very well with our experimental results for spheres having the same 

 direction (Fig. 15). The explanation for this is that in our case the 

 instability first begins at the equator and we have there locally a 

 similar situation as in the case of the two cylinders. 



Sink 



Source 



Pole 



Pole 



Fig. 12 Sketch of Mode IV 



283 



