The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
arXiv:1209.6454 · doi:10.1016/j.crhy.2012.09.009
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.
arXiv commentAccepted for publication in C. R. Acad. Sci
References in corpus (26)
- Scaling in thermal convection: A unifying theory
- Burgers Turbulence
- Turbulence without pressure
- Lagrangian Tetrad Dynamics and the Phenomenology of Turbulence
- An update on the double cascade scenario in two-dimensional turbulence
- Lagrangian dynamics and statistical geometric structure of turbulence
- Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
- Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
- Fine-scale statistics of temperature and its derivatives in convective turbulence
- Lagrangian temperature, velocity and local heat flux measurement in Rayleigh-Benard convection
- On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity
- On the universality of small scale turbulence
- New relations for correlation functions in Navier-Stokes turbulence
- Probability density and scaling exponents of the moments of longitudinal velocity difference in strong turbulence
- Lagrangian Statistics and Temporal Intermittency in a Shell Model of Turbulence
- Dynamical Origins for Non-Gaussian Vorticity Distributions in Turbulent Flows
- Single-point velocity distribution in turbulence
- An exact relation between Eulerian and Lagrangian velocity increment statistics
- A note on the forced Burgers equation
- Mean- Field Approximation and Extended Self-Similarity in Turbulence
- Temperature Statistics in Turbulent Rayleigh-Bénard Convection
- Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence
- Theory for the single-point velocity statistics of fully developed turbulence
- Generalized vortex-model for the inverse cascade of two-dimensional turbulence
- Lagrangian Probability Distributions of Turbulent Flows
- Closure of two dimensional turbulence: the role of pressure gradients
Cited by in corpus (11)
- Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields
- A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows
- The Numerical Approximation of Nonlinear Functionals and Functional Differential Equations
- A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence
- On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence
- Is the log-law a first principle result from Lie-group invariance analysis?
- Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space
- Twisting vortex lines regularize Navier-Stokes turbulence
- Comment on 'Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow'
- Probability Density Functions in Homogeneous and Isotropic Magneto-Hydrodynamic Turbulence
- Probabilistic responses of dynamical systems subjected to Gaussian coloured noise excitation. Foundations of a non-Markovian theory