Investigation of a generalized Obukhov Model for Turbulence
Fluid Dynamics
2009-11-11 v2 Data Analysis, Statistics and Probability
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.
Keywords
Cite
@article{arxiv.physics/0509268,
title = {Investigation of a generalized Obukhov Model for Turbulence},
author = {A. Baule and R. Friedrich},
journal= {arXiv preprint arXiv:physics/0509268},
year = {2009}
}
Comments
10 pages