The weak version of universality in turbulence refers to the independence of the scaling exponents of the n-th order structure functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced-stationary and freely decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is the case also for the case of Navier-Stokes turbulence.
VS L\'vov, RA Pasmanter, A Pomyalov, I Procaccia. Strong universality in forced and decaying turbulence in a shell model
published, Phys. Rev. E., 2003, 67