Anisotropy of Third-order Structure Functions in MHD Turbulence
Abstract
The measure of the third-order structure function, {\boldsymbol{Y}} , is employed in the solar wind to compute the cascade rate of turbulence. In the absence of a mean field {{B}0}=0, {\boldsymbol{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, {\boldsymbol{Y}} is expected to become more two-dimensional (2D), that is, to have larger perpendicular components, losing the above simple symmetry. To get the cascade rate, one should compute the flux of {\boldsymbol{Y}} , which is not feasible with single-spacecraft data thus, measurements rely on assumptions about the unknown symmetry. We use direct numerical simulations (DNSs) of magnetohydrodynamic (MHD) turbulence to characterize the anisotropy of {\boldsymbol{Y}} . We find that for strong guide field {{B}0}=5 the degree of two-dimensionalization depends on the relative importance of shear-Alfvén and pseudo-Alfvén polarizations (the two components of an Alfvén mode in incompressible MHD). The anisotropy also shows up in the inertial range. The more {\boldsymbol{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 DNSs. This could be due to a weaker mean field and/or to solar wind expansion.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- May 2015
- DOI:
- 10.1088/0004-637X/804/2/119
- arXiv:
- arXiv:1502.04705
- Bibcode:
- 2015ApJ...804..119V
- Keywords:
-
- magnetohydrodynamics: MHD;
- solar wind;
- turbulence;
- Astrophysics - Solar and Stellar Astrophysics;
- Physics - Plasma Physics;
- Physics - Space Physics
- E-Print:
- Some text editing and typos corrected, 13 pages, 6 figures, to be published in ApJ