Statistics of Lagrangian velocities in turbulent flows.
We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling v approximately t(1/2). However, the statistics need not be Gaussian.
Friedrich
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Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.