Exact coherent structures in stably stratified plane Couette flow

D. Olvera, R. R. Kerswell

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number .Pr D 1/using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge tracking-EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (J. Fluid Mech., vol. 745, 2014, pp. 25-61)-and found to connect with two-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-Bénard problem with shear). Both these states and Nagata's (J. Fluid Mech., vol. 217, 1990, pp. 519-527) original exact solution feel the presence of stable stratification when Rib DO.Re..2/or equivalently when the Rayleigh number Ra VD ..RibRe2Pr D O.1/. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib D O.Re..2=3/. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58-85). Increasing the stratification further appears to lead to a third, ultimate regime where Rib D O.1/in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar-turbulent boundary in the (Re-Rib) plane are briefly discussed.

    Original languageEnglish
    Pages (from-to)583-614
    Number of pages32
    JournalJournal of Fluid Mechanics
    Volume826
    Early online date8 Aug 2017
    DOIs
    Publication statusPublished - 10 Sep 2017

    Fingerprint

    Couette flow
    stratification
    Fluids
    fluids
    Richardson number
    Reynolds number
    Prandtl number
    wave interaction
    Rayleigh number
    Terminology
    Gravitation
    Vortex flow
    vortices
    gravitation
    shear

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

    Cite this

    Exact coherent structures in stably stratified plane Couette flow. / Olvera, D.; Kerswell, R. R.

    In: Journal of Fluid Mechanics, Vol. 826, 10.09.2017, p. 583-614.

    Research output: Contribution to journalArticle

    Olvera, D. ; Kerswell, R. R. / Exact coherent structures in stably stratified plane Couette flow. In: Journal of Fluid Mechanics. 2017 ; Vol. 826. pp. 583-614.
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    abstract = "The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds-Richardson number (Re-Rib) space for a fluid of unit Prandtl number .Pr D 1/using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge tracking-EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (J. Fluid Mech., vol. 745, 2014, pp. 25-61)-and found to connect with two-dimensional convective roll solutions when tracked to negative Rib (the Rayleigh-B{\'e}nard problem with shear). Both these states and Nagata's (J. Fluid Mech., vol. 217, 1990, pp. 519-527) original exact solution feel the presence of stable stratification when Rib DO.Re..2/or equivalently when the Rayleigh number Ra VD ..RibRe2Pr D O.1/. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at Rib D O.Re..2=3/. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58-85). Increasing the stratification further appears to lead to a third, ultimate regime where Rib D O.1/in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar-turbulent boundary in the (Re-Rib) plane are briefly discussed.",
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