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The rapid-rotation limit of the neutral curve for Taylor–Couette flow

Published online by Cambridge University Press:  27 October 2016

Kengo Deguchi
Kengo Deguchi*
Affiliation:
School of Mathematical Sciences, Monash University, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

An asymptotic theory is developed for the linear stability curve of rapidly rotating Taylor–Couette flow. The analytic curve obtained by the theory excellently explains the limiting Navier–Stokes stability result for general disturbances. When the cylinders are corotating, the asymptotic theory describes the gap between the neutral curve and the Rayleigh stability criterion. For the case when the cylinders are counter-rotating, it is found that, along the stability boundary, the Reynolds number based on the inner cylinder speed is proportional to that based on the outer cylinder speed to the power of $3/5$.

JFM classification

Aerodynamics: High-speed flow
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , R2
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Copyright
© 2016 Cambridge University Press 

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