dorsal/arxiv
View SchemaInvestigation of a generalized Obukhov Model for Turbulence
| Authors | A. Baule, R. Friedrich |
|---|---|
| Categories | |
| ArXiv ID | physics/0509268 |
| URL | https://arxiv.org/abs/physics/0509268 |
| DOI | 10.1016/j.physleta.2005.10.017 |
| Journal | Physics Letters A 350 (2006) 167-173 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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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"abstract": "We introduce a generalization of Obukhov\u0027s model [A.M. Obukhov, Adv. Geophys.\n6, 113 (1959)] for the description of the joint position-velocity statistics of\na single fluid particle in fully developed turbulence. In the presented model\nthe velocity is assumed to undergo a continuous time random walk. This takes\ninto account long time correlations. As a consequence the evolution equation\nfor the joint position-velocity probability distribution is a Fokker-Planck\nequation with a fractional time derivative. We determine the solution of this\nequation in the form of an integral transform and derive a relation for\narbitrary single time moments. Analytical solutions for the joint probability\ndistribution and its moments are given.",
"arxiv_id": "physics/0509268",
"authors": [
"A. Baule",
"R. Friedrich"
],
"categories": [
"physics.flu-dyn",
"physics.data-an"
],
"doi": "10.1016/j.physleta.2005.10.017",
"journal_ref": "Physics Letters A 350 (2006) 167-173",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Investigation of a generalized Obukhov Model for Turbulence",
"url": "https://arxiv.org/abs/physics/0509268"
},
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