Integral OnePoint Statistical Characteristics of Vector Fields in Stochastic Magnetohydrodynamic Flows

摘要

We study integral statistical characteristics of a vector passive tracer (homogeneous at the initial time) in a velocity field that is assumed to be a Gaussian random field homogeneous in space and deltacor related in time. Such statistical characteristics describe the dynamical system as a whole in the entire space, separating out the field generation processes, which allows us to not digress into details of the dynamics related to the advection of these quantities. The density field gradient (in the general case of a compressible fluid) and the magnetic field vector with its spatial derivatives (in an incompressible fluid) are such a tracer. We study the isotropization in time, helicity, and dissipation of these fields in the absence of molecular diffu sion effects. We formulate a method of successive approximations for the variance of the density field and the mean magnetic field energy that allows the solutions valid in the entire time interval to be obtained in the first order in molecular diffusion coefficients.