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Optimal Energy Growth in Stably Stratified Turbulent Couette Flow

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Abstract

Optimal disturbances of a turbulent stably stratified plane Couette flow in a wide range of Reynolds and Richardson numbers are studied. These disturbances are computed based on a simplified system of equations in which turbulent Reynolds stresses and heat fluxes are approximated by isotropic viscosity and diffusivity with the coefficients obtained from results of direct numerical simulation. Three types of disturbances are considered: large-scale streamwise-elongated rolls converting into streamwise streaks; large-scale vortical structures, inclined in the vertical plane, changing the inclination to the opposite in process of their evolution; near-wall rolls converting into streaks. Large-scale rolls and streaks predominate at neutral or weakly stable stratification while the inclined structures begin to dominate at moderately stable stratification. Near-wall rolls and streaks appear at any stratification and their spanwise size in wall length units does not depend on the values of Reynolds and Richardson numbers. It is shown that the development of inclined optimal disturbances is due to the coupled action of the lift-up effect and the inviscid Orr mechanism. The energetics of the optimal disturbances is discussed. It is shown that inclined optimal disturbances dissipate rapidly after reaching maximum energy amplification.

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Data availibility

The results of DNS used during the current study are available from E.V. Mortikov (evgeny.mortikov@gmail.com) on reasonable request.

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Acknowledgements

Numerical analysis of the optimal disturbances and mathematical justification of the results were supported by Russian Science Foundation (Grant No. 17-71-20149). Direct numerical simulation and physical justification of the results were supported by Russian Foundation for Basic Research (Grant No. 20-05-00776). Direct numerical simulations were carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University. We express our gratitude to the two anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya sq., 4, Moscow, Russia, 125047

    Grigory V. Zasko & Yuri M. Nechepurenko

  2. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkin str., 8, Moscow, Russia, 119333

    Grigory V. Zasko, Andrey V. Glazunov, Evgeny V. Mortikov, Yuri M. Nechepurenko & Pavel A. Perezhogin

  3. Research Computing Center of Lomonosov Moscow State University, Leninskie Gory str., 1, p. 4, Moscow, Russia, 119991

    Evgeny V. Mortikov

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  1. Grigory V. Zasko
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Correspondence to Grigory V. Zasko.

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Zasko, G.V., Glazunov, A.V., Mortikov, E.V. et al. Optimal Energy Growth in Stably Stratified Turbulent Couette Flow. Boundary-Layer Meteorol 187, 395–421 (2023). https://doi.org/10.1007/s10546-022-00744-3

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