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

• We show that periodic conditions mathematically lead to large-scale anisotropy in turbulent flows.
• This anisotropy index can be about 10% of the mean values.
• A decomposition method by employing spherical harmonics is proposed to remove this anisotropy.

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%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.