## Abstract

A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a major open issue is whether a purely Markovian statistical description of hydrodynamic turbulence actually can be achieved. Based on the formulation of a deterministic inverse kinetic theory (IKT) for the 3D incompressible Navier-Stokes equations, here we claim that such a Markovian statistical description actually exists. The approach, which involves the introduction of the local velocity probability density for the fluid (local pdf) - rather than the velocity-difference pdf adopted in customary approaches to homogeneous turbulence - relies exclusively on first principles. These include - in particular - the exact validity of the stochastic Navier-Stokes equations, the principle of entropy maximization and a constant H-theorem for the Shannon statistical entropy. As a result, the new approach affords an exact equivalence between Lagrangian and Eulerian formulations which permit local pdf's which are generally non-Maxwellian (i.e., non-Gaussian). The theory developed is quite general and applies in principle even to turbulence regimes which are non-stationary and non-uniform in a statistical sense.

Original language | English (US) |
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Pages (from-to) | 230-235 |

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

- Physics and Astronomy(all)