14 research outputs found
The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
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-B\'enard convection and to Burgers turbulence are
discussed.Comment: Accepted for publication in C. R. Acad. Sc
Two-point vorticity statistics in the inverse cascade of two-dimensional turbulence
A statistical analysis of the two-point vorticity statistics in the inverse energy cascade of two-dimensional turbulence is presented in terms of probability density functions (PDFs). Evolution equations for the PDFs are derived in the framework of the Lundgren–Monin–Novikov hierarchy, and the unclosed terms are studied with the help of direct numerical simulations (DNS). Furthermore, the unclosed terms are evaluated in a Gaussian approximation and compared to the DNS results. It turns out that the statistical equations can be interpreted in terms of the dynamics of screened vortices. The two-point statistics is related to the dynamics of two point vortices with screened velocity field, where an effective relative motion of the two point vortices originating from the turbulent surroundings is identified to be a major characteristics of the dynamics underlying the inverse cascade