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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1576–1586 (Mi zvmmf11135)  

Modeling of the turbulent Poiseuille–Couette flow in a flat channel by asymptotic methods

V. B. Zametaevabc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141701 Russia
b Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119333 Russia
c Central Aerohydrodynamic Institute (TsAGI), National Research Center "Zhukovsky Institute", Zhukovskii, Moscow oblast, 140180 Russia

Abstract: Developed turbulent flow of a viscous incompressible fluid in a channel of small width at high Reynolds numbers is considered. The instantaneous flow velocity is represented as the sum of a stationary component and small perturbations, which are generally different from the traditional averaged velocity and fluctuations. The study is restricted to the search for and consideration of stationary solution components. To analyze the problem, an asymptotic multiscale method is applied to the Navier–Stokes equations, rather than to the RANS equations. As a result, a steady flow in the channel is found and investigated without using any closure hypotheses. The basic phenomenon in the Poiseuille flow turns out to be a self-induced fluid flow from the channel center to the walls, which ensures that kinetic energy is transferred from the maximum-velocity zone to the turbulence generation zone near the walls, although the total averaged normal velocity is, of course, zero. The stationary solutions for the normal and streamwise velocities turn out to be viscous over the entire width of the channel, which confirms the well-known physical concept of large-scale “turbulent viscosity”.

Key words: turbulence, channel flow, mathematical modeling, asymptotic methods.

Funding Agency
This work was performed at the Moscow Institute of Physics and Technology and was supported by the Russian Science Foundation, project no. 20-11-20006. Computer support was provided by the Central Aerohydrodynamic Institute and the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences.

DOI: https://doi.org/10.31857/S0044466920090185

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1528–1538

Bibliographic databases:

UDC: 517.95
Received: 17.05.2020
Revised: 20.05.2020

Citation: V. B. Zametaev, “Modeling of the turbulent Poiseuille–Couette flow in a flat channel by asymptotic methods”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1576–1586; Comput. Math. Math. Phys., 60:9 (2020), 1528–1538

Citation in format AMSBIB
\by V.~B.~Zametaev
\paper Modeling of the turbulent Poiseuille--Couette flow in a flat channel by asymptotic methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1576--1586
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 9
\pages 1528--1538

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