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Hydromagnetic stability of dissipative flow between rotating permeable cylinders. Part 2. Oscillatory critical modes and asymptotic results

Published online by Cambridge University Press:  29 March 2006

Tien Sun Chang  and
Walter K. Sartory
Tien Sun Chang
Affiliation:
North Carolina State University, Raleigh, N.C. and Oak Ridge National Laboratory, Oak Ridge, Tennessee
Walter K. Sartory
Affiliation:
Oak Ridge National Laboratory, Oak Ridge, Tennessee
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Abstract

In considering the onset of instability of an electrically conducting fluid between rotating permeable perfectly conducting cylinders in an applied axial magnetic field, it is found that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes. Results are presented showing the effect of the oscillatory modes on the criterion of onset of instability.

The asymptotic behaviour of the stability criterion is considered in the limit of very large radial Reynolds number, and also in the limit where both the radial Reynolds number and the Hartmann number are large.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 1 , 27 March 1969 , pp. 193 - 206
Copyright
© 1969 Cambridge University Press

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References

Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability Oxford: Clarendon.
Chang, T. S. & Sartory, W. K. 1967a Hydromagnetic stability of dissipative flow between rotating permeable cylinders. Part 1. Stationary critical modes J. Fluid Mech. 27, 65.Google Scholar
Chang, T. S. & Sartory, W. K. 1967b On the onset of instability by oscillatory modes in hydromagnetic Couette flow. Proc. Roy. Soc. A 301, 451.Google Scholar