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On the stability of plane Poiseuille flow with a finite conductivity in an aligned magnetic field

Published online by Cambridge University Press:  28 March 2006

Sung-Hwan Ko
Sung-Hwan Ko
Affiliation:
General Dynamics Corporation Electronics Division, Rochester, New York
Also, Rochester Institute of Technology, Rochester, New York.
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Abstract

A study is made of the stability of a viscous, incompressible fluid with a finite conductivity flowing between parallel planes in a parallel magnetic field. The general form of the magnetohydrodynamic stability equation is a sixth-order differential equation. The complete sixth-order differential equation is solved numerically as an eigenvalue problem. Stability curves are obtained for a range of values of the magnetic Reynolds number Rm and the Alfvé n number A based on two-dimensional disturbances. It is found that the minimum critical Reynolds number is raised as Rm increases for a given A2 and as A2 increases for a given Rm, respectively. The stability curve closes and finally degenerates to a point which gives the critical value for Rm or A2. Results obtained for two-dimensional disturbances are modified to take into account three-dimensional disturbances. Then the minimum critical Reynolds number where three-dimensional disturbances become apparent is obtained, below which two-dimensional disturbances are the most unstable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 3 , 2 September 1968 , pp. 433 - 443
Copyright
© 1968 Cambridge University Press

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References

Drazin, P. G. 1960 J. Fluid Mech. 8, 130.
Hains, F. D. 1965 Phys. Fluids, 8, 2014.
Hunt, J. C. R. 1966 Proc. Roy. Soc. A, 293, 342.
Lin, C. C. 1955 Theory of Hydrodynamic Stability. Cambridge University Press.
Michael, D. H. 1953 Proc. Camb. Phil. Soc. 49, 166.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.
Stuart, J. T. 1954 Proc. Roy. Soc. A, 221, 189.
Tarasov, YU. A. 1960 Soviet Phys. JETP 10, 1209 (in English).
Thomas, L. H. 1953 Phys. Review, 91, 780.
Tollmien, W. 1936 NACA TM, 792.
Velikhov, E. P. 1959 Soviet Phys. JETP 9, 848 (in English).
Wooler, P. T. 1961 Phys. Fluids, 4, 24.