Paidoussis 



while at the tail it is - fJvIU^Sy/Bx) , producing a moment tending to 

 exaggerate the original inclination. However, there are Coriolis 

 forces proportional to MU(8y/9x 8t) which always oppose rotation 

 [cf. Eq. (10)]. 



To understand this action of the Coriolis forces we consider 

 the related physical system of a hinged-free tube containing flowing 

 fluid (as mentioned in §2), depicted in Fig, i8(a), which was first 

 considered by Benjamin [ 3 2] , We see that if the system rotates 

 about A without bending, the fluid suffers a Coriolis acceleration 

 which has a reaction on the tube always opposing the motion. This 

 is clearly a stabilizing effect, as energy has to be expended by the 

 tube to keep the motion going; as further elaborated by Benjamin, 

 this represents the action of a pump from the energy-transfer point 

 of view. 



Fig. 18 Rudimentary representation of a pump and a 

 radial-flow turbine 



We next consider flexural instabilities. Clearly everything 

 mentioned so far applies here also. But we also have another force 

 coming into play. Once again we consider the hinged-free tube con- 

 taining flowing fluid, as shown in Fig. 18(b), where the tube is 

 momentarily 'frozen' in the bent shape shown. The centrifugal force 

 of the fluid acts to increase the curvature further. This is clearly 

 a destabilizing force, energy flowing from the fluid to the tube; it is 

 the action of a radial-flow turbine. In flexural oscillations we have 

 a play between these 'centrifugal' forces and the Coriolis forces; 

 •'-hen the former prevail, then instabilities may develop. 



1012 



