Theory for the single-point velocity statistics of fully developed turbulence
Institute for Theoretical Physics, Westfälische Wilhelms-Universität - Wilhelm-Klemm-Str. 9, 48149 Münster, Germany, EU
Accepted: 14 January 2011
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.
PACS: 47.27.eb – Statistical theories and models / 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 47.27.E- – Turbulence simulation and modeling
© EPLA, 2011