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The Malkus theory applied to magnetohydrodynamic turbulent channel flow

Published online by Cambridge University Press:  28 March 2006

Jacques C. J. Nihoul
Jacques C. J. Nihoul
Affiliation:
Institut de Mathématique, Université de Liège.
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Abstract

The turbulent flow of a weakly conducting liquid between parallel plates in the presence of a transverse magnetic field is investigated. The form of the mean velocity profile is determined by a series of constraints resulting from the boundary conditions and the Navier–Stokes equations and by the Malkus postulates on the spectrum of the mean vorticity gradient. The width of the transition regions near the walls is derived in terms of the governing dimensionless numbers and this expression is checked, in the asymptotic laminar case, against the well-known Hartmann result. A graphical method, exploiting the relation between the boundary region thickness and the smallest scale of motion defined by the Malkus theory is proposed to determine the scale of the velocity profile, i.e. the flow rate in terms of the pressure gradient and the magnetic field strength.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 1 , May 1966 , pp. 1 - 16
Copyright
© 1966 Cambridge University Press

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