General stability criteria for inviscid rotating flow

Details General stability criteria for inviscid rotating flow General stability criteria for inviscid rotating flow

2006-03-22

arxiv.org/abs/physics/0603177v3

Physics

Fluid Dynamics

3 pages, physics/0512208, physics/0601043, physics/0601112, physics/0605167, physics/0702037, arXiv:0905.3317 , arXiv:1004.345

Scientific paper

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)

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