A new representation of energy spectra in fully developed turbulence

It is well known that the Kolmogorov 1941 theory is based on global invariance, in the limit of Reynolds number tending to infinity. Experimentally, it is well verified only for very high Reynolds numbers, namelyR2000 (Monin and Yaglom 1975).We propose a new experimental representation for energy spectra. Using the Kolmogorov scales, a compilation of dimensionless spectra (E= (k)/(v⁵)^1/4 andK=k(v³/)^1/4) shows that log(0.154E)/log(R/R*) is a universal function of log(5.42K)/log(R/R*) withR*=75. This new representation is not compatible with neither local nor global scaling invariance. The constant 5.42 takes into account the small scale intermittency. Similar results have been obtained for velocity structure functions of order 2, 3 and 6. In particular the wavenumber constant 5.42 is independent on the order of the moments.