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arXiv · 2101.05176

A quadratic Reynolds stress development for the turbulent Kolmogorov flow

Wenwei Wu·Francois G. Schmitt·Enrico Calzavarini·Lipo Wang
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Abstract

We study the three-dimensional turbulent Kolmogorov flow, i.e. the Navier-Stokes equations forced by a low-single-wave-number sinusoidal force in a periodic domain, by means of direct numerical simulations. This classical model system is a realization of anisotropic and non-homogeneous hydrodynamic turbulence. Boussinesq's eddy viscosity linear relation is checked and found to be approximately valid over half of the system volume. A more general nonlinear quadratic Reynolds stress development is proposed and its parameters estimated at varying the Taylor scale-based Reynolds number in the flow up to the value 200. The case of a forcing with a different shape, here chosen Gaussian, is considered and the differences with the sinusoidal forcing are emphasized.

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Wenwei Wu, Francois G. Schmitt, Enrico Calzavarini, Lipo Wang. 2021-09-02. A quadratic Reynolds stress development for the turbulent Kolmogorov flow. https://doi.org/10.1063/5.0069688

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