A quadratic Reynolds stress development for the turbulent Kolmogorov flow

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