  Magnetohydrodynamic (MHD) turbulence in the majority of natural systems,
including the interstellar medium, the solar corona, and the solar wind, has
Reynolds numbers far exceeding the Reynolds numbers achievable in numerical
experiments. Much attention is therefore drawn to the universal scaling
properties of small-scale fluctuations, which can be reliably measured in the
simulations and then extrapolated to astrophysical scales. However, in contrast
with hydrodynamic turbulence, where the universal structure of the inertial and
dissipation intervals is described by the Kolmogorov self-similarity, the
scaling for MHD turbulence cannot be established based solely on dimensional
arguments due to the presence of an intrinsic velocity scale -- the Alfven
velocity. In this Letter, we demonstrate that the Kolmogorov first
self-similarity hypothesis cannot be formulated for MHD turbulence in the same
way it is formulated for the hydrodynamic case. Besides profound consequences
for the analytical consideration, this also imposes stringent conditions on
numerical studies of MHD turbulence. In contrast with the hydrodynamic case,
the discretization scale in numerical simulations of MHD turbulence should
decrease faster than the dissipation scale, in order for the simulations to
remain resolved as the Reynolds number increases.
