Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow

Abstract

AbstractThis 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.