From three-dimensional to quasi-two-dimensional

transient growth in magnetohydrodynamic duct flows

Oliver G.W. Cassells, Tony Vo, Alban Pothérat, Gregory J. Sheard

Research output: Contribution to journalArticleResearchpeer-review

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)383-406
Number of pages24
JournalJournal of Fluid Mechanics
Volume861
DOIs
Publication statusPublished - 25 Feb 2019

Keywords

  • instability
  • MHD and electrohydrodynamics

Cite this

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title = "From three-dimensional to quasi-two-dimensional: transient growth in magnetohydrodynamic duct flows",
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.",
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From three-dimensional to quasi-two-dimensional : transient growth in magnetohydrodynamic duct flows. / Cassells, Oliver G.W.; Vo, Tony; Pothérat, Alban; Sheard, Gregory J.

In: Journal of Fluid Mechanics, Vol. 861, 25.02.2019, p. 383-406.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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