Longitudinal and transverse structure functions in high Reynolds-number magneto-hydrodynamic turbulence

TL;DR

This study examines the scaling behavior of structure functions in high Reynolds-number MHD turbulence, revealing no significant differences between longitudinal and transverse functions, contrasting with hydrodynamic turbulence.

Contribution

It introduces an exact hierarchy and numerical simulations to compare structure functions in MHD turbulence, highlighting the role of pressure in scaling differences.

Findings

No substantial differences between longitudinal and transverse structure functions in MHD turbulence.

Pressure contributions are reduced in MHD, explaining the absence of differences.

Contrasts with hydrodynamic turbulence where differences persist.

Abstract

We investigate the scaling behavior of longitudinal and transverse structure functions in homogeneous and isotropic magneto-hydrodynamic (MHD) turbulence by means of an exact hierarchy of structure function equations as well as by direct numerical simulations of two- and three-dimensional MHD turbulence. In particular, rescaling relations between longitudinal and transverse structure functions are derived and utilized in order to compare different scaling behavior in the inertial range. It is found that there are no substantial differences between longitudinal and transverse structure functions in MHD turbulence. This finding stands in contrast to the case of hydrodynamic turbulence which shows persistent differences even at high Reynolds numbers. We propose a physical picture that is based on an effective reduction of pressure contributions due to local regions of same magnitude and alignment of velocity and magnetic field fluctuations. Finally, our findings underline the importance of the pressure term for the actually observed scaling differences in hydrodynamic turbulence.