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The stability of Couette flow in the presence of an axial magnetic field

Published online by Cambridge University Press:  28 March 2006

Ulrich H. Kurzweg
Ulrich H. Kurzweg
Affiliation:
United Aircraft Coporation Research Laboratories, East Hartford, Connecticut
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Abstract

The stability of Couette flow between concentric, co-rotating cylinders in an axial magnetic field is examined for fluids of arbitrary magnetic Prandtl number Pm = ν/η, where ν is the kinematic and η the magnetic viscosity of the fluid. It is assumed that the gap spacing d between the cylinders is small compared to the mean radius and that no magnetic disturbances penetrate into the cylinder walls. The critical Taylor number at which non-oscillatory disturbances are marginally stable is determined as a function of the magnetic Prandtl number and the dimensionless parameter S = (Vad/v)2, where Va is the Alfvén velocity. Asymptotic formulas relating the critical Taylor number to the magnitude of the magnetic field are derived for the limiting conditions of very small and very large magnetic Prandtl number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 1 , September 1963 , pp. 52 - 60
Copyright
© 1963 Cambridge University Press

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References

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