Inter-scale transfer of the large-scale background anisotropy under periodic conditions

In numerical simulations of three-dimensional isotropy turbulence, low-wave-number truncation leads to large-scale anisotropy, but little anisotropy is generated at small scales. As the generally accepted energy cascade theory suggests an energy transfer from large to small scale, we phenomenally guess that an inter-scale anisotropy evolution might occur in the energy transfer process. With analyses in Kolmogorov’s equation and DNS validations, we demonstrate that the large-scale anisotropy is effectively transferred by convective effect, but this anisotropy is then diminished at small scales by viscous dissipation. The inter-scale anisotropy transfer process is synchronised with the inter-scale energy transfer. Time evolution of anisotropy distribution is then investigated in free-decaying, forced and non-equilibrium isotropic turbulence. It is shown that the anisotropy distribution remains stationary if the shape of energy spectrum does not change. The objective of this work is to provide a theoretical and numerical support for the further study on anisotropy correction in post-processing results.