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.
Highlights
The question whether longitudinal and transverse structure functions posses different scaling behavior in highly turbulent flows is still an open and unsolved problem
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
We argued that rescaling relations of the form (28) apply for all even order velocity and magnetic structure functions. We have examined these relations in direct numerical simulations of 3D MHD turbulence
Summary
The question whether longitudinal and transverse structure functions posses different scaling behavior in highly turbulent flows is still an open and unsolved problem. The result of this paper is that there is no substantial difference longitudinal and transverse structure functions in the inertial range of high Reynolds number MHD flows This observation can be attributed to regions of preferential alignment of the magnetic and the velocity field which result in an effective depletion of pressure contributions. In reverse, these results open up the way for a better understanding of the problem in hydrodynamic turbulence. The paper concludes with a simple examination of local regions of same magnitude and alignment of velocity and magnetic field contributions and their depleting effect on the total pressure
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