von Kármán-Howarth equations for Hall magnetohydrodynamic flows

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1 Pt 2):015302. doi: 10.1103/PhysRevE.77.015302. Epub 2008 Jan 11.

Abstract

The von Kármán-Howarth equations are derived for three-dimensional Hall magnetohydrodynamics in the case of a homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multiscale laws provide a relevant tool to investigate the nonlinear nature of the high-frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.