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Magnetohydrodynamic (MHD) turbulence in the majority of natural systems,including the interstellar medium, the solar corona, and the solar wind, hasReynolds numbers far exceeding the Reynolds numbers achievable in numericalexperiments. Much attention is therefore drawn to the universal scalingproperties of small-scale fluctuations, which can be reliably measured in thesimulations and then extrapolated to astrophysical scales. However, in contrastwith hydrodynamic turbulence, where the universal structure of the inertial anddissipation intervals is described by the Kolmogorov self-similarity, thescaling for MHD turbulence cannot be established based solely on dimensionalarguments due to the presence of an intrinsic velocity scale -- the Alfvenvelocity. In this Letter, we demonstrate that the Kolmogorov firstself-similarity hypothesis cannot be formulated for MHD turbulence in the sameway it is formulated for the hydrodynamic case. Besides profound consequencesfor the analytical consideration, this also imposes stringent conditions onnumerical studies of MHD turbulence. In contrast with the hydrodynamic case,the discretization scale in numerical simulations of MHD turbulence shoulddecrease faster than the dissipation scale, in order for the simulations toremain resolved as the Reynolds number increases.

Scaling properties of small-scale fluctuations in magnetohydrodynamic turbulence