Fokker-Planck kinetic description of small-scale fluid turbulence for classical incompressible fluids

M. Tessarotto, M. Ellero, D. Sarmah, P. Nicolini

Research output: Contribution to journalConference articlepeer-review

Abstract

Extending the statistical approach proposed in a parallel paper [1], purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a suitable local phase-space probability density function (pdf). In particular, we pose the problem of the construction of Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here adopted is based on the so-called IKT approach (inverse kinetic theory), developed by Tessarotto et al. (2004-2008) which permits an exact phase-space description of incompressible fluids based on the adoption of a local pdf. We intend to show that for prescribed models of stochasticity the present approach permits to determine uniquely the time evolution of the stochastic fluid fields. The stochastic-averaged local pdf is shown to obey a kinetic equation which, although generally non-Markovian, locally in velocity-space can be approximated by means of a suitable Fokker-planck kinetic equation. As a side result, the same pdf is proven to have generally a non-Gaussian behavior.

Original languageEnglish (US)
Pages (from-to)170-175
Number of pages6
JournalAIP Conference Proceedings
Volume1084
StatePublished - 2009
Event26th International Symposium on Rarefied Gas Dynamics, RGD26 - Kyoto, Japan
Duration: Jul 20 2008Jul 25 2008

Keywords

  • Kinetic theory
  • Navier-Stokes equations
  • Turbulence theory

ASJC Scopus subject areas

  • General Physics and Astronomy

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