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

Wilczek, Michael; Daitche, A.; Friedrich, R.

doi:10.1209/0295-5075/93/34003

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

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Wilczek, Michael
Max Planck Research Group Theory of Turbulent Flows, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Wilczek, M., Daitche, A., & Friedrich, R. (2011). Theory for the single-point velocity statistics of fully developed turbulence. Europhysics Letters, 93(3): 34003. doi:10.1209/0295-5075/93/34003.

Cite as: https://hdl.handle.net/21.11116/0000-0003-E0BC-C

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.