On the von Karman-Howarth equations for Hall MHD flows
S. Galtier
TL;DR
This paper derives the von Karman-Howarth equations for 3D Hall MHD turbulence, providing exact scaling laws that help analyze high-frequency magnetic fluctuations in plasmas like the solar wind.
Contribution
It introduces the von Karman-Howarth equations for Hall MHD and derives exact scaling laws, advancing understanding of plasma turbulence with Hall effects.
Findings
Derived exact third-order correlation tensor scaling laws.
Showed compatibility with previous numerical and heuristic results.
Provided tools for analyzing magnetic fluctuations in Hall plasmas.
Abstract
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall magnetohydrodynamics (MHD) in the case of an 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 multi-scale laws provide a relevant tool to investigate the non-linear nature of the high frequency magnetic field fluctuations in the solar wind or, more generally, in any plasma where the Hall effect is important.
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