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PHYSICS LETTERS A
Volume 350, Issue 3-4, Pages 167-173Publisher
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DOI: 10.1016/j.physleta.2005.10.017
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We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6 (1959) 113] for the description of the joint position-velocity statistics of a single fluid particle in fully developed turbulence. In the presented model the velocity is assumed to undergo a continuous time random walk. This takes into account long time correlations. As a consequence the evolution equation for the joint position-velocity probability distribution is a Fokker-Planck equation with a fractional time derivative. We determine the solution of this equation in the form of an integral transform and derive a relation for arbitrary single time moments. Analytical solutions for the joint probability distribution and its moments are given. (c) 2005 Published by Elsevier B.V.
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