A formulation of the theory of isotropic hydromagnetic turbulence in an incompressible fluid

Abstract

The theory of hydromagnetic isotropic turbulence in incompressible fluids is formulated using methods similar to those of quantum field theory. The present formulation is a generalization of Wyld's formulation of ordinary istropic turbulence in incompressible fluids. Solutions for the velocity and magnetic field in the form of perturbation series are set up. Terms in the series are then represented by a one-to-one correspondence by diagrams similar to Feynman diagrams. A study of these diagrams reveals that they may be rearranged to give integral equations governing the second order correlation functions for the velocity and the magnetic field. These integral equations contain an infinite number of terms. To obtain manageable results, the equations are truncated at finite orders, yielding approximate equations. An approximation at the lowest order gives Chandrasekhar's equations; while a “second approximation” gives a more complicated set of equations.