A quadratic Reynolds stress development for the turbulent Kolmogorov flow

Wenwei Wu (1, 2) , François Schmitt , Enrico Calzavarini (3) , Lipo Wang

1 LOG - Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187
2 ULCO - Université du Littoral Côte d'Opale
3 UML - Unité de Mécanique de Lille - ULR 7512

We study the three-dimensional turbulent Kolmogorov flow, i.e. the Navier-Stokes equations forced by a single-low-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 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 sinusoidalforcing are emphasized.

Domaines: Dynamique des Fluides [physics.flu-dyn]

Wenwei Wu, François Schmitt, Enrico Calzavarini, Lipo Wang. A quadratic Reynolds stress development for the turbulent Kolmogorov flow. Physics of Fluids, 2021, 33 (12), pp.125129. ⟨10.1063/5.0069688⟩. ⟨hal-03610033⟩