Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

Details Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

2001-10-20

arxiv.org/abs/cond-mat/0110436v2

Physica D 165, 94-125 (2002)

Physics

Condensed Matter

Statistical Mechanics

Latex document of 40 pages, including 18 eps figures

Scientific paper

10.1016/S0167-2789(02)00390-1

We present the results of a search of log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (2500) of three-dimensional fully developed turbulence. A simple dynamical representation of the Richardson-Kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log-periodic corrections to scaling associated with a discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical'' averaging that we test extensively on synthetic examples constructed to mimick the interplay between a weak log-periodic component and rather strong multiplicative and phase noises. Our extensive tests confirm the remarkable observation of statistically significant log-periodic corrections to scaling, with a prefered scaling ratio for length scales compatible with the value gamma = 2. A strong confirmation of this result is provided by the identification of up to 5 harmonics of the fundamental log-periodic undulations, associated with up to 5 levels of the underlying hierarchical dynamical structure. A natural interpretation of our results is that the Richardson-Kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales.

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