The effect of Kolmogorov (1962) scaling on the universality of turbulence energy spectra

Abstract: It has long been established that turbulence energy spectra scale on the Kolmogorov (1941) variables over a wide range of Reynolds numbers and in vastly different physical systems, depending only on the dissipation rate, the kinematic viscosity and the wavenumber. On the other hand, the analogous study of structure functions in real space is strongly influenced by the Kolmogorov (1962) refined theory, which introduced a dependence on a large length scale Lext, characteristic of the system size. If such a dependence exists it is surprising that it does not show up in the study of wavenumber spectra, where the different physical systems suggest that Lext can vary by up to five orders of magnitude. Here we use an order of magnitude calculation to suggest that scaling according to Kolmogorov (1962) would destroy the observed asymptotic universality of energy spectra at large wavenumbers.