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Spectral Analysis of Optimal Disturbances of Stratified Turbulent Couette Flow

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Abstract

For a stratified turbulent Couette flow, the eigenmodes and optimal disturbances of corresponding simplified equations linearized around a steady state are considered. It is shown that the spectrum of these equations is symmetric with respect to the real axis and lies strictly in the left half-plane, i.e., all eigenmodes are stable, and the main part of an optimal disturbance is a linear combination of a large number of modes corresponding to eigenvalues with largest real parts. The number of the most significant modes in this linear combination grows with increasing Reynolds number.

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ACKNOWLEDGMENTS

We are grateful to A.V. Glazunov and E.V. Mortikov for providing direct numerical simulation data, showing interest in this work, and participating in helpful discussions of the results.

Funding

This work was supported by the Moscow Center of Fundamental and Applied Mathematics, contract no. 075-15-2019-1624 with the Ministry of Education and Science of the Russian Federation.

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Authors and Affiliations

  1. Department of the Moscow Center of Fundamental and Applied Mathematics, Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    G. V. Zasko & Yu. M. Nechepurenko

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

    Yu. M. Nechepurenko

Authors
  1. G. V. Zasko
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  2. Yu. M. Nechepurenko
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Correspondence to G. V. Zasko or Yu. M. Nechepurenko.

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Translated by I. Ruzanova

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Zasko, G.V., Nechepurenko, Y.M. Spectral Analysis of Optimal Disturbances of Stratified Turbulent Couette Flow. Comput. Math. and Math. Phys. 61, 129–141 (2021). https://doi.org/10.1134/S0965542521010103

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  • DOI: https://doi.org/10.1134/S0965542521010103

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