Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades

Details Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades Theoretical Model for the Kramers-Moyal Description of Turbulence Cascades

1999-07-05

arxiv.org/abs/cond-mat/9907063v1

Physical Review Letters, vol 82, 1680, (1999)

Physics

Condensed Matter

4 pages, revtex, two postscript figures

Scientific paper

10.1103/PhysRevLett.82.1680

We derive the Kramers-Moyal equation for the conditional probability density of velocity increments from the theoretical model recently proposed by V.Yakhot [Phys.Rev.E {\bf 57}, 1737 (1998)] in the limit of high Reynolds number limit. We show that the higher order (n>=3) Kramers-Moyal coefficients tends to zero and the velocity increments are evolved by the Fokker-Planck operator. Our result is compatible with the phenomenological descriptions by R.Friedrich and J.Peinke [Phys.Rev.Lett. {\bf 78}, 863 (1997)].

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