Theory for the single-point velocity statistics of fully developed turbulence
arXiv:1102.2776 · doi:10.1209/0295-5075/93/34003
Abstract
We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint analytical and numerical analysis shows that these deviations may be quantified studying correlations of dynamical quantities like pressure gradient, external forcing and energy dissipation with the velocity. A stationary solution for the PDF equation in terms of these quantities is presented, and the theory is validated with the help of direct numerical simulations indicating sub-Gaussian tails of the PDF.
6 pages, 4 figures, corrected typo in eq. (4)