Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow

Jonathan Paul Hagan, Janis Priede

    Research output: Contribution to journalArticle

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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 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.
    Original languageEnglish
    Pages (from-to)387-406
    Number of pages20
    JournalJournal of Fluid Mechanics
    Volume760
    Early online date11 Nov 2014
    DOIs
    Publication statusPublished - 10 Dec 2014

    Fingerprint

    channel flow
    Channel flow
    Magnetohydrodynamics
    traveling waves
    magnetohydrodynamics
    Magnetic fields
    magnetic fields
    Hartmann number
    thresholds
    Pressure gradient
    laminar flow
    pressure gradients
    Reynolds number
    Turbulence
    Hydrodynamics
    turbulence
    hydrodynamics
    conduction
    Liquids
    liquids

    Keywords

    • instability
    • magnetohydrodynamics
    • nonlinear instability

    Cite this

    Two-dimensional nonlinear travelling waves in magnetohydrodynamic channel flow. / Hagan, Jonathan Paul; Priede, Janis.

    In: Journal of Fluid Mechanics, Vol. 760, 10.12.2014, p. 387-406.

    Research output: Contribution to journalArticle

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