Instabilities and Vortioes Between Two Rotating Spheres 



the end of the vortices up to the poles the laminar flow remains 

 stable. With increasing Reynolds number, the axes of the vortices 

 become wavy (Fig, 6) and the flow turns turbulent after passing some 

 intermediate states (Figs. 7, 8). In this case photographs still show 

 a remarkable distinct structure of the flow. 



Fig, 6 The vortex axes become wavy for very large 

 Reynolds number, s = 2 mm. Re = 16,800, 

 Ta = 68.8 



For the larger relative width of the gap this matter is much 

 more complicated. In the transition from laminar to turbulent flow 

 we found that altogether five basically different but reproducible 

 main modes are possible. In the torque diagram all these modes 

 are noticeable and they are remarkably stable as soon as they have 

 become existent. For this reason we called them "stable instabilities, " 

 In the experiment these different modes can be established by apply- 

 ing a suitable acceleration of the angular velocity. In analogy to the 

 rotating cylinders [ 7] we have here a case of nonuniqueness. The 

 mode of instability that is finally realized depends on the initial con- 

 dition given by the exper indent ator. Now the main modes I - V shall 

 be discussed briefly. 



I, In spite of having an overcritical state no vortices become 

 visible. The transition to the turbulent flow occurs by passing through 

 mode II, that is described below. Mode I is characterized by the fact 



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