Investigation of a generalized Obukhov Model for Turbulence

Details Investigation of a generalized Obukhov Model for Turbulence Investigation of a generalized Obukhov Model for Turbulence

2005-09-30

arxiv.org/abs/physics/0509268v2

Physics Letters A 350 (2006) 167-173

Physics

Fluid Dynamics

10 pages

Scientific paper

10.1016/j.physleta.2005.10.017

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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