How isotropic are turbulent flows generated by using periodic conditions in a cube?

In numerical simulations, "isotropic" turbulent flows are always generated by using periodic conditions. We show that these periodic conditions mathematically lead to large-scale anisotropy which can be about 10% of the mean values, and thus prevent existing post-processing results from being accurate. A decomposition method by employing spherical harmonics is then proposed to distinguish this scale-dependent anisotropy effect from others and to minimize the related post-processing error.