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

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