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Instability of an inviscid flow between porous cylinders with radial flow

Published online by Cambridge University Press:  30 July 2013

Konstantin Ilin  and
Andrey Morgulis
Konstantin Ilin*
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK
Andrey Morgulis
Affiliation:
Department of Mathematics, Mechanics and Computer Science, The Southern Federal University, 344090 Rostov-on-Don, Russian Federation South Mathematical Institute, Vladikavkaz Center of RAS, 362027 Vladikavkaz, Russian Federation
*
†Email address for correspondence: konstantin.ilin@york.ac.uk
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Abstract

The stability of a two-dimensional inviscid flow in an annulus between two permeable cylinders is examined. The basic flow is irrotational, and both radial and azimuthal components of the velocity are non-zero. The direction of the radial flow can be from the inner cylinder to the outer one (the diverging flow) or from the outer cylinder to the inner one (the converging flow). It is shown that, independent of the direction of the radial flow, the basic flow is unstable to small two-dimensional perturbations provided that the ratio of the azimuthal component of the velocity to the radial one is sufficiently large. The instability is oscillatory and persists if the viscosity of the fluid is taken into consideration.

JFM classification

Instability: Absolute/convective instability Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 364 - 378
Copyright
©2013 Cambridge University Press 

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