Numerical study of the return of axisymmetric turbulence to isotropy

The spectral method of Orszag and Patterson (1972) is used here to study pressure and velocity fluctuations in axisymmetric, homogeneous, incompressible, decaying turbulence at Reynolds numbers not greater than about 40. In real space 32 x 32 x 32 points are treated. The return to isotropy is simulated for several different sets of anisotropic Gaussian initial conditions. All contributions to the spectral energy balance for the different velocity components are shown as a function of time and wave number. The return to isotropy is effected by the pressure-strain correlation. The rate of return is larger at high than at low wave numbers. The inertial energy transfer tends to create anisotropy at high wave numbers. This explains the overrelaxation found by Herring (1974). The pressure and the inertial energy transfer are zero initially as the triple correlations are zero for the Gaussian initial values. The pressure-strain correlation becomes small for extremely large anisotropies. This can be explained kinematically. Rotta's (1951) model is approximately valid if the anisotropy is small and if the time scale of the mean flow is much larger than the time scale of the triple correlations. The effect of strain is studied