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Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow

Published online by Cambridge University Press:  11 November 2014

Jonathan Hagan  and
Jānis Priede
Jonathan Hagan
Affiliation:
Applied Mathematics Research Centre, Coventry University, Priory Street, Coventry CV1 5FB, UK
Jānis Priede*
Affiliation:
Applied Mathematics Research Centre, Coventry University, Priory Street, Coventry CV1 5FB, UK
*
†Email address for correspondence: j.priede@coventry.ac.uk
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Abstract

This study is concerned with the stability of a flow of viscous conducting liquid driven by a pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Although the magnetic field has a strong stabilizing effect, this flow, similarly to its hydrodynamic counterpart – plane Poiseuille flow – is known to become turbulent significantly below the threshold predicted by linear stability theory. We investigate the effect of the magnetic field on two-dimensional nonlinear travelling-wave states which are found at substantially subcritical Reynolds numbers starting from $\mathit{Re}_{n}=2939$ without the magnetic field and from $\mathit{Re}_{n}\sim 6.50\times 10^{3}\mathit{Ha}$ in a sufficiently strong magnetic field defined by the Hartmann number $\mathit{Ha}$. Although the latter value is a factor of seven lower than the linear stability threshold $\mathit{Re}_{l}\sim 4.83\times 10^{4}\mathit{Ha}$, it is still more than an order of magnitude higher than the experimentally observed value for the onset of turbulence in magnetohydrodynamic (MHD) channel flow.

JFM classification

Instability: Instability Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 387 - 406
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Copyright
© 2014 Cambridge University Press 

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