Numerical simulation of the return to isotropy of homogeneous turbulence

Direct numerical simulation of the return to isotropy of homogeneous turbulence is carried out for the various initial anisotropic turbulent fields. Navier-Stokes equation is calculated with the spectral method using 32 to the 3rd Fourier components of velocity. The numerical results show that the two rotational invariants 2 and 3 of the anisotropy tensor which describes the departure of the Reynolds stress from isotrophy characterize well the process of the return to isotrophy of homogeneous turbulence. The values of the constant in the Rotta's turbulence model are calculated for the tensor components of the pressure-strain correlation and the mean Rotta's constant is evaluated from the least squares mean of these tensor components for each anisotropic turbulence. The mean Rotta's constants of the various anisotropic turbulence show a nearly identical variation in time in the range from 0.5 to 4.0, which roughly coincides with the dispersive range of the experimental results. The variation of the Rotta's constant implies its dependence on variants 2, 3, and Reynolds number.