From three-dimensional to quasi-two-dimensional: Transient growth in magnetohydrodynamic duct flows

Oliver Cassells, Tony Vo, Alban Potherat, Gregory J. Sheard

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    Abstract

    This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an external magnetic field. A particular focus is given to the question of whether at high magnetic fields purely two-dimensional mechanisms exist, and whether these can be described by a computationally inexpensive quasi-two-dimensional model. Two Reynolds numbers of 5000 and 15 000 and an extensive range of Hartmann numbers 0 ≤ Ha ≤ 800 were investigated. Three broad regimes are identified in which optimal mode topology and non-modal growth mechanisms are distinct. These regimes, corresponding to low, moderate and high magnetic field strengths, are found to be governed by the independent parameters; Hartmann number, Reynolds number based on the Hartmann layer thickness RH and Reynolds number built upon the Shercliff layer thickness RS, respectively. Transition between regimes respectively occurs at Ha~2 and no lower than RH ~ 33: P3. Notably for the high Hartmann number regime, quasi-two-dimensional magnetohydrodynamic models are shown to be excellent predictors of not only transient growth magnitudes, but also the fundamental growth mechanisms of linear disturbances. This paves the way for a precise analysis of transition to quasi-two-dimensional turbulence at much higher Hartmann numbers than is currently achievable.

    Original languageEnglish
    Pages (from-to)382-406
    Number of pages25
    JournalJournal of Fluid Mechanics
    Volume861
    Early online date19 Dec 2018
    DOIs
    Publication statusPublished - 25 Feb 2019

    Keywords

    • MHD and electrohydrodynamics
    • instability

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

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