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arXiv · 1102.2776

Theory for the single-point velocity statistics of fully developed turbulence

Michael Wilczek·Anton Daitche·Rudolf Friedrich
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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.

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Michael Wilczek, Anton Daitche, Rudolf Friedrich. 2011-02-17. Theory for the single-point velocity statistics of fully developed turbulence. https://doi.org/10.1209/0295-5075%2F93%2F34003

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