## 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 language | English (US) |
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Pages (from-to) | 170-175 |

Number of pages | 6 |

Journal | AIP Conference Proceedings |

Volume | 1084 |

State | Published - 2009 |

Event | 26th International Symposium on Rarefied Gas Dynamics, RGD26 - Kyoto, Japan Duration: Jul 20 2008 → Jul 25 2008 |

## Keywords

- Kinetic theory
- Navier-Stokes equations
- Turbulence theory

## ASJC Scopus subject areas

- General Physics and Astronomy