Abstract
This article deals with the stability of incompressible inviscid 2D planar flows in a rotating frame. We give a sufficient condition for such flows to undergo 3D short-wave centrifugal-type instabilities. This criterion states that a steady 2D planar flow subject to rotation Ω is unstable if there exists a streamline for which at each point \( 2\left( {V/\mathcal{R}{\text{ + }}\Omega } \right)\left( {\omega + 2\Omega } \right) < 0 \) where ω is the vorticity of the streamline, R is the local algebraic radius of curvature of the streamline and V is the local norm of the velocity. If this condition is satisfied then the flow is unstable to short-wavelength perturbations. When the streamlines are closed, it is further shown that a localized unstable normal mode can be constructed in the vicinity of a streamline.
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© 2000 Springer-Verlag Berlin Heidelber
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Sipp, D., Jacquin, L. (2000). A Criterion of Centrifugal Instabilities in Rotating Systems. In: Maurel, A., Petitjeans, P. (eds) Vortex Structure and Dynamics. Lecture Notes in Physics, vol 555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44535-8_21
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DOI: https://doi.org/10.1007/3-540-44535-8_21
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