Direct numerical simulation of anisotropic turbulent flow for incompressible fluid

Equation for small-scale velocity or pulsation is a starting point to build almost all models of turbulence. Transport equation for Reynolds stresses, dissipation rate, kinetic energy are derived from this equation, adding some assumptions about structure of terms, including in these equations. Equation for small-scale velocity can be simplified, if we assume that large – scale velocity and its gradients are constants instead of linear profile for large-scale velocity. We implemented the direct numerical simulation of this equation under the simple shear, leading to anisotropy. The nonlinear helicity terms were computed in spectral space, using the three-dimensional Fast Fourier transformation, then, the inverse Fast Fourier transformation was used to return in physical space. Aliasing terms were not removed. Four – order Runge- Kutta method was used for integration in time. Evolution of Reynolds stresses in time were computed.