The invariant theory of isotropic turbulence in magneto-hydrodynamics. II

Abstract

In this paper the invariant theory of isotropic turbulence in magneto-hydrodynamics developed by the writer in a recent paper is extended to include the correlations {Pu_i'u_j'} and {Ph_i'h_j'}, of the total pressure, P (= p + ½ρ|h|²), with two components either of the velocity, (u_i), or of the magnetic field, (h_i). It is shown how the scalars defining these tensors can be expressed in terms of the scalars defining the second-order correlations {u_iu_j'}, {u_ih_j'} and {h_ih_j'} if the fourth-order correlations of two components of velocity (respectively, magnetic field) at one point, with two components of velocity or magnetic field at another point, can be assumed to be related to the second-order correlations in the same manner as if they were jointly, normally, distributed.