Turbulent velocity fluctuations need not be Gaussian

Abstract

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.