A quadratic Reynolds stress development for the turbulent Kolmogorov flow

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.

11 pages

References in corpus (2)

• Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
• Analysis of pseudo-spectral methods used for numerical simulation of turbulence

Cited by in corpus (3)

• Inertial range scaling of inhomogeneous turbulence
• Noise-expansion cascade: an origin of randomness of turbulence
• Clean numerical simulation (CNS) of three-dimensional turbulent Kolmogorov flow