  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 $\xi'(\Omega-\Omega_s)<0$ (or
$\xi'/(\Omega-\Omega_s)<0$) somewhere in the flow field, where $\xi$ is the
vorticitiy of profile and $\Omega_s$ is the angular velocity at the inflection
point $\xi'=0$. Second, a criterion for stability is found as
$-(\mu_1+1/r_2)<f(r)=\frac{\xi'}{\Omega-\Omega_s}<0$, 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.
