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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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