Extended Scaling Laws in Numerical Simulations of MHD Turbulence
  Magnetised turbulence is ubiquitous in astrophysical systems, where it
notoriously spans a broad range of spatial scales. Phenomenological theories of
MHD turbulence describe the self-similar dynamics of turbulent fluctuations in
the inertial range of scales. Numerical simulations serve to guide and test
these theories. However, the computational power that is currently available
restricts the simulations to Reynolds numbers that are significantly smaller
than those in astrophysical settings. In order to increase computational
efficiency and, therefore, probe a larger range of scales, one often takes into
account the fundamental anisotropy of field-guided MHD turbulence, with
gradients being much slower in the field-parallel direction. The simulations
are then optimised by employing the reduced MHD equations and relaxing the
field-parallel numerical resolution. In this work we explore a different
possibility. We propose that there exist certain quantities that are remarkably
stable with respect to the Reynolds number. As an illustration, we study the
alignment angle between the magnetic and velocity fluctuations in MHD
turbulence, measured as the ratio of two specially constructed structure
functions. We find that the scaling of this ratio can be extended surprisingly
well into the regime of relatively low Reynolds number. However, the extended
scaling becomes easily spoiled when the dissipation range in the simulations is
under-resolved. Thus, taking the numerical optimisation methods too far can
lead to spurious numerical effects and erroneous representation of the physics
of MHD turbulence, which in turn can affect our ability to correctly identify
the physical mechanisms that are operating astrophysical systems.
