Energy transfer and third-order law in forced anisotropic MHD turbulence with hyperviscosity

TL;DR

This study uses direct numerical simulations to analyze the third-order law in anisotropic MHD turbulence with hyperviscosity, revealing how anisotropy and hyperviscosity influence energy transfer rate estimations.

Contribution

It introduces a systematic analysis of anisotropic effects on third-order structure functions and demonstrates the advantages of hyper-viscosity in inertial range separation.

Findings

Peak transfer rate aligns with B0 direction and shifts with B0 strength.

Hyper-viscosity improves inertial range separation.

Spherical surface averaging accurately predicts energy transfer rates.

Abstract

The Kolmogorov-Yaglom (third-order) law, links energy transfer rates in the inertial range of magneto-hydrodynamic (MHD) turbulence with third-order structure functions. Anisotropy, a typical property in the solar wind, largely challenges the applicability of the third-order law with isotropic assumption. To shed light on the energy transfer process in the presence of anisotropy, the present study conducted direct numerical simulations (DNSs) on forced MHD turbulence with normal and hyper-viscosity under various strengths of the external magnetic field ($B_0$), and calculated three forms of third-order structure function with or without averaging azimuthal or polar angles to $B_0$ direction. Correspondingly, three forms of estimated energy transfer rates were studied systematically with various $B_0$. The result shows that the peak of the estimated longitudinal transfer rate occurs at larger scales as closer to the $B_0$ direction, and its maximum shifts away from the $B_0$ direction at larger $B_0$. Compared with normal viscous cases, hyper-viscous cases can attain better separation of the inertial range from the dissipation range, thus facilitating the analyses of the inertial range properties and the estimation of the energy cascade rates. The direction-averaged third-order structure function over a spherical surface proposed in literature predicts the energy transfer rates and inertial range accurately, even at very high $B_0$. With limited statistics, the calculation of the third-order structure function shows a stronger dependence on averaging of azimuthal angles than the time, especially at high $B_0$ cases. These findings provide insights into the anisotropic effect on the estimation of energy transfer rates.