Probability Density Functions in Homogeneous and Isotropic Magneto-Hydrodynamic Turbulence

Abstract

We derive a hierarchy of evolution equations for multi-point probability density functions in magneto-hydrodynamic (MHD) turbulence. We discuss the relation to the moment hierarchy in MHD turbulence derived by Chandrasekhar and derive a functional equation for a joint characteristic functional which can be considered as the analogon to the Hopf functional in hydrodynamic turbulence. Furthermore, we develop a closure method for the evolution equation of the single-point magnetic field probability density function which is based on a joint Gaussian assumption for unclosed terms. It is explicitly shown that this closure, together with the assumptions of homogeneity and isotropy, leads to vanishing nonlinear terms. We discuss the implications of this finding for magnetic field generation and give a brief outlook on an axisymmetric theory which includes a mean magnetic field.

arXiv comment15 pages

References in corpus (11)

• A weak turbulence theory for incompressible MHD
• Spectrum of magnetohydrodynamic turbulence
• Observation of inertial energy cascade in interplanetary space plasma
• Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields
• On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity
• Probability Densities in Strong Turbulence
• Magnetic turbulence spectra and intermittency in the heliosheath and in the local interstellar medium
• Strong magnetohydrodynamic turbulence with cross helicity
• The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
• Nonlinear large scale flow in a precessing cylinder and its ability to drive dynamo action
• Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions