328 Mr Taylor, Experiments with Rotating Fluids 



One consequence of the fact that the velocity of the fluid at 

 tHe surface of the sphere is zero, relative to fixed axes, is that as 

 a sphere moves up the axis of a rotating fluid the hquid streaming 

 past It vnll not tend to rotate it. This is found to be true It 

 IS shown experimentally that a hght sphere initially rotating with 

 tne liqmd m a tall rotating jar of water, stops rotating directly 

 It IS moved along the axis of the jar, but that it starts rotating 

 again as soon as the motion along the axis ceases. ° 



3. Stability of fluid jnotion between two concentric cylinders. 



The late Lord Rayleigh has stated, though without formal 

 proot, tJiat tor three dimensional symmetrical disturbances the 

 steady motion of a perfect hquid between two cyhnders which 

 rotate with different speeds is stable if the square of the circulation 

 round circular paths concentric with the cyhnders increases on 

 passing from the inner cyhnder to the outer one. But that it is 

 unstable otherwise. This conclusion is now proved to be correct 

 by ca culatmg the actual motion in a normal disturbance 



All calculations about the stabihty of liquid between two 

 rotating cyhnders have assumed two dimensional motion In the 

 case of two dimensional motion a rotation of the whole system 

 makes no difference to the type of motion. Its stability or in- 

 stability are determined only by the relative motion of the two 

 cyhnders. 



Experiments made by Mallock* and Conettef showed that if 

 the inner cyhnder is fixed while the outer one rotates the motion 

 only becomes unstable at a very much higher relative velocity 

 than if the inner one is fixed and the outer one rotates. This 

 evidently suggests that the instabihty observed is not two dimen- 

 sional. Accordmg to Rayleigh's criterion for the stabihty of the 

 symmetrical disturbance of an inviscid fluid between rotating 

 cyhnders the case when the outer cyhnder is fixed and the inner 

 one rotates should always be unstable. If it is observed to be 

 stable this must be some effect due to viscosity 



In the case when the inner cyhnder is fixed and the outer one 

 rotates symmetrical disturbances should be on the limit between 

 stabihty and mstabihty. The shghtest rotation of the inner cyhnder 

 m tlie same direction as the outer one should make the disturbances 

 stable while the shghtest rotation in the opposite direction should 

 make them unstable. 



It appears therefore that the method adopted by previous 

 experimenters m which one or other of the cyhnders was fixed 

 IS unfortunate. 



* Mallock. Phil. Trans. A, 1896. p. 41. 



t Conette. Annales de Chitnie etde Physique, [6], xxi, p. 433. 



