The general stability criteria of inviscid Taylor-Couette flows with angular velocity \Omega ( r ) are obtained analytically .
First , a necessary instability criterion for centrifugal flows is derived as \xi ^ { \prime } ( \Omega - \Omega _ { s } ) < 0 ( or \xi ^ { \prime } / ( \Omega - \Omega _ { s } ) < 0 ) somewhere in the flow field , where \xi is the vorticitiy of profile and \Omega _ { s } is the angular velocity at the inflection point \xi ^ { \prime } = 0 .
Second , a criterion for stability is found as - ( \mu _ { 1 } +1 / r _ { 2 } ) < f ( r ) = \frac { \xi ^ { \prime } } { \Omega - \Omega _ { s } } < 0 , where \mu _ { 1 } is the smallest eigenvalue .
The new criteria are the analogues of the criteria for parallel flows , which are special cases of Arnol ’ d ’ s nonlinear criteria .
Specifically , Pedley ’ s cirterion is proved to be an special case of Rayleigh ’ s criterion .
Moreover , the criteria for parallel flows can also be derived from those for the rotating flows .
These results extend the previous theorems and would intrigue future research on the mechanism of hydrodynamic instability .