Distribution functions in the statistical theory of convective MHD turbulence of an incompressible fluid

Abstract

In this paper, we define a hierarchy of distribution functions for simultaneous velocity, magnetic, and temperature fields. Some properties of the constructed distribution functions such as reduction, separation, and coincidence are discussed. Equations for the evolution of one- and two-point distribution functions have been derived. Finally, a comparison of the equation for the single-point distribution function in case of zero viscosity, negligible diffusivity, and infinite electrical conductivity is made with first equation of BBGKY hierarchy in the kinetic theory of gases.