The Lundgren-Monin-Novikov hierarchy: Kinetic equations for turbulence

Friedrich, Rudolf; Daitche, Anton; Kamps, Oliver; Lülff, Johannes; Voßkuhle, Michel; Wilczek, Michael

Research article (journal) | Peer reviewed

Abstract

We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution equations for the PDFs are derived from the basic equations of fluid motion. The closure problem arises either in terms of a coupling to multi-point PDFs or in terms of conditional averages entering the evolution equations as unknown functions. We mainly focus on the latter case and use data from direct numerical simulations (DNS) to specify the unclosed terms. Apart from giving an introduction into the basic analytical techniques, applications to two-dimensional vorticity statistics, to the single-point velocity and vorticity statistics of three-dimensional turbulence, to the temperature statistics of Rayleigh-Bénard convection and to Burgers turbulence are discussed. © 2012 Académie des sciences.

Details about the publication

JournalComptes Rendus Physique
Volume13
Issue9-10
Page range953null
StatusPublished
Release year2012 (01/11/2012)
Language in which the publication is writtenEnglish
DOI10.1016/j.crhy.2012.09.009

Authors from the University of Münster

Daitche, Anton
Institute for Theoretical Physics
Kamps, Oliver
Center for Nonlinear Science
Lülff, Johannes
Professur für Theoretische Physik (Prof. Thiele)