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Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Stratified Medium

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Abstract

To study the flow in a far plane turbulent wake in a passively stratified medium, we use a mathematical model that includes differential equations for the balance of turbulence energy, the transfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and the vertical component of the mass flux vector. Algebraic truncation of the last equation leads to a well-known gradient relation for the vertical component of the mass flux vector. It is established that under a certain constraint on the values of empirical constants in the mathematical model and the law of time scale growth consistent with the mathematical model, this relation is a differential constraint for the model. The equivalence of the local equilibrium approach for the vertical component of the mass flux vector and the zero Poisson bracket for the dimensionless turbulent diffusion coefficient and the averaged density is shown. The results of numerical experiments illustrating the theoretical results are presented.

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Funding

The presented results were obtained as part of the work on the topic “Development and research of computer technologies for solving fundamental and applied problems of aero-, hydro-, and wave dynamics” of the state assignment for the Federal Research Center for Information and Computational Technologies. Numerical experiments were carried out within the framework of the state assignment for Kutateladze Institute of Thermophysics of the Siberian Branch of the Russian Academy of Sciences, project no. 122041400020-6. The formulation of the problem and the results of calculations were discussed jointly by the coauthors. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Federal Research Center for Information and Computational Technologies, Novosibirsk, 630090, Russia

    V. N. Grebenev & G. G. Chernykh

  2. Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. G. Demenkov

  3. Novosibirsk State Technical University, Novosibirsk, 630073, Russia

    A. G. Demenkov

Authors
  1. V. N. Grebenev
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  2. A. G. Demenkov
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  3. G. G. Chernykh
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Corresponding authors

Correspondence to V. N. Grebenev, A. G. Demenkov or G. G. Chernykh.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Grebenev, V.N., Demenkov, A.G. & Chernykh, G.G. Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Stratified Medium. J. Appl. Ind. Math. 18, 36–46 (2024). https://doi.org/10.1134/S1990478924010046

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