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Turbulent velocity fluctuations need not be Gaussian. (English) Zbl 0922.76234
Summary: It is noted that the central limit theorem does not constrain the probability distribution of the components of the turbulent velocity fluctuations to be Gaussian, if their spectral slope is steeper than $$k^{-1}$$. It is shown that, in a model of homogeneous turbulence in which each wavenumber of the energy spectrum predominantly receives contributions from eddies with roughly homogeneous amplitudes and coherence lengths, the p.d.f would be slightly sub-Gaussian. This agrees with the available experimental evidence.

##### MSC:
 76F99 Turbulence 76M35 Stochastic analysis applied to problems in fluid mechanics
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