Modeling the turbulent cross-helicity evolution: Production, dissipation, and transport rates

TL;DR

This paper develops a model for the dissipation rate of turbulent cross helicity in MHD turbulence, introduces an evolution equation for it, and applies the model to solar wind turbulence, comparing results with satellite data.

Contribution

It proposes a new evolution equation for the dissipation rate of turbulent cross helicity based on statistical turbulence theory.

Findings

The algebraic model suffices for large-scale solar wind evolution.

Cross-helicity evolution depends on velocity shear and flow expansion.

Model results agree with satellite observations.

Abstract

It has been recognized that the turbulent cross helicity (correlation between the velocity and magnetic-field fluctuations) can play an important role in several magnetohydrodynamic (MHD) plasma phenomena such as the global magnetic-field generation, turbulence suppression, etc. Despite its relevance to the cross-helicity evolution, little attention has been paid to the dissipation rate of the turbulent cross helicity, $\epsilon_W$. In this paper, we consider the model expression for the dissipation rate of the turbulent cross helicity. In addition to the algebraic model, an evolution equation of $\epsilon_W$ is proposed on the basis of the statistical analytical theory of inhomogeneous turbulence. A turbulence model with the modeling of $\epsilon_W$ is applied to the solar-wind turbulence. Numerical results on the large-scale evolution of the cross helicity is compared with the satellite observations. It is shown that, as far as the solar-wind application is concerned, the simplest possible algebraic model for $\epsilon_W$ is sufficient for elucidating the large-scale spatial evolution of the solar-wind turbulence. Dependence of the cross-helicity evolution on the large-scale velocity structures such as velocity shear and flow expansion is also discussed.