Generalized scaling in fully developed turbulence

Abstract

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About Generalized Scaling for Passive Scalars in Fully Developed Turbulence

“…By contrast, a similar form of scaling does not seem to hold for the structure function of a passive scalar transported by turbulence [2]. This indicates that General Scaling is representative of a fundamental property of velocity increments.…”

“…Recent studies, however, have raised up doubts about the validity of such scaling: for example, it is shown in [1] that the true scaling could rather be exp(ζ(n)a −1 a ) where a is inversely proportional to the Reynolds number. Given such controversy, the discovery by [2] of a new form of scaling is very interesting. This general form of scaling, named General Scaling, extends down to the smallest resolvable scale.…”

Multiscale Velocity Correlations in Turbulence

“…0, by a simple uncorrelated random cascade (5) and that their subleading contribution, r R ϳ O͑1͒, is fully captured by the geometrical constraint previously discussed, namely, the Ward identities.…”

“…In [5] it has been discussed in detail whether the refined Kolmogorov hypothesis (RKH) for the energy dissipation is consistent with a random multiplicative process for the velocity increments. It has been shown that, at least on the synthetic signal, RKH is satisfied.…”

“…Stochastic cascade processes are simple and well known useful tools to describe the leading phenomenology of the intermittent energy transfer in the inertial range. Both anomalous scaling exponents and viscous effects [1,5] can be reproduced by choosing a suitable random process for the multiplier, W ͑r, R͒, which connects velocity fluctuations at two different scales, R . r.…”