Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow. (11th November 2014) - Hagan, Jonathan; Priede, Jānis
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 $Re_{n}=2939$ without the magnetic field and from $Re_{n}\sim 6.50× 10^{3}Ha$ in a sufficiently strong magnetic field defined by the Hartmann number $Ha$ . Although the latter value is a factor of seven lower than the linear stability threshold $Re_{l}\sim 4.83× 10^{4}Ha$, 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.