LOG-SIMILARITY FOR TURBULENT FLOWS

We critically examine a recently proposed representation for turbulent energy spectra (called here log-similarity) which is predicted both by the multifractal model and the variational approach of the small scale intermittency. Within this representation, spectra are homothetic in the log-log plot, the homothety factor depending on the Taylor scale based Reynolds number R(lambda). Experimental results on energy spectra and velocity structure functions of order 2, 3 and 6 measured in different flows at several R(lambda) show that this factor is beta(R(lambda)), a measurable exponent which characterises intermittency in the inertial range. Experimentally, beta displays the existence of a transition in the neighbourhood of R(lambda) congruent-to 400 and for R(lambda) tending to infinity, beta behaves as 1/ln(R(lambda)/R*).