Anisotropy of third-order structure functions in MHD turbulence

TL;DR

This study uses numerical simulations to analyze the anisotropy of third-order structure functions in MHD turbulence, revealing how guide field strength influences turbulence anisotropy and cascade rate measurements.

Contribution

It provides a detailed characterization of the anisotropy of Y in MHD turbulence through DNS, highlighting the effects of guide field strength and polarization components.

Findings

Anisotropy of Y depends on guide field strength and polarization.

Inertial range anisotropy affects cascade rate measurements.

Simulated cascade rates differ from solar wind observations, indicating weaker anisotropy in the solar wind.

Abstract

The measure of the third-order structure function, Y, is employed in the solar wind to compute the cascade rate of turbulence. In the absence of a mean field B0=0, Y is expected to be isotropic (radial) and independent of the direction of increments, so its measure yields directly the cascade rate. For turbulence with mean field, as in the solar wind, Y is expected to become more two dimensional (2D), that is, to have larger perpendicular components, loosing the above simple symmetry. To get the cascade rate one should compute the flux of Y, which is not feasible with single-spacecraft data, thus measurements rely upon assumptions about the unknown symmetry. We use direct numerical simulations (DNS) of magneto-hydrodynamic (MHD) turbulence to characterize the anisotropy of Y. We find that for strong guide field B0=5 the degree of two-dimensionalization depends on the relative importance of shear and pseudo polarizations (the two components of an Alfv\'en mode in incompressible MHD). The anisotropy also shows up in the inertial range. The more Y is 2D, the more the inertial range extent differs along parallel and perpendicular directions. We finally test the two methods employed in observations and find that the so-obtained cascade rate may depend on the angle between B0 and the direction of increments. Both methods yield a vanishing cascade rate along the parallel direction, contrary to observations, suggesting a weaker anisotropy of solar wind turbulence compared to our DNS. This could be due to a weaker mean field and/or to solar wind expansion.