Statistical mechanics and large-scale velocity fluctuations of turbulence

Details Statistical mechanics and large-scale velocity fluctuations of turbulence Statistical mechanics and large-scale velocity fluctuations of turbulence

2010-10-26

arxiv.org/abs/1010.5368v4

PoF, 23, 125110 [2011]

Physics

Fluid Dynamics

7 pages, accepted by Physics of Fluids (see http://pof.aip.org/)

Scientific paper

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.

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