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Ring vortices generated electromagnetically

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, University of Michigan
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Abstract

If an electric current of uniform density j0 is passed axially through a stationary fluid between concentric cylinders of radii r1 and r2 (> r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line current J along the axis, sufficient conditions for stability being $J \le -\pi j _0(r^2_2 - r^2_1)$, or $\ge J\; \pi j _0r^2_1$

The values of J needed to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the case r2-r1 [Lt ] r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders if J and j0 have the same sign, and if J is not very small compared with πj0r2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 5 , Issue 3 , April 1959 , pp. 436 - 444
Copyright
© 1959 Cambridge University Press

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