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Investigation of a generalized Obukhov Model for Turbulence

A. Baule·R. Friedrich
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Abstract

We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6, 113 (1959)] 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.

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BibTeXRIS

A. Baule, R. Friedrich. 2008-07-31. Investigation of a generalized Obukhov Model for Turbulence. https://doi.org/10.1016/j.physleta.2005.10.017

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