Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow

Abstract

The present study is concerned with the stability of a flow of viscous conducting liquid driven by 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 2D nonlinear travelling-wave states which are found at substantially subcritical Reynolds numbers starting from $R{e}_n=2939$ without the magnetic field and from $R{e}_n\sim 6.50\times 10^{3}Ha$ in a sufficiently strong magnetic field defined by the Hartmann number $Ha.$ Although the latter value is by a factor of seven lower than the linear stability threshold $R{e}_l\sim 4.83\times 10^{4}Ha$,it is still more by an order of magnitude higher than the experimentally observed value for the onset of turbulence in the MHD channel flow.

19 pages, 8 figures; final version

References in corpus (4)

• An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar
• Quasi-two dimensional perturbations in duct flows under transverse magnetic field
• Capacitance matrix technique for avoiding spurious eigenmodes in the solution of hydrodynamic stability problems by Chebyshev collocation method
• Weakly nonlinear stability analysis of MHD channel flow using an efficient numerical approach

Cited by in corpus (1)

• Linear stability of magnetohydrodynamic flow in a square duct with thin conducting walls