Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow

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 Ren=2939 without the magnetic field and from Ren? 6.50× 103Ha 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 Rel? 4.83× 104Ha, 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. NOTE: some mathematical symbols do not display correctly on this abstract - please see the abstract at the publisher's site http://dx.doi.org/10.1017/jfm.2014.612 to read these.