DYNAMIC ALIGNMENT AND EXACT SCALING LAWS IN MAGNETOHYDRODYNAMIC TURBULENCE

Abstract

Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent high-resolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is E(k ⊥) ∝ k –3/2 ⊥. So far, there has been no phenomenological theory that simultaneously explains this spectrum and satisfies the exact analytic relations for MHD turbulence due to Politano & Pouquet. Indeed, the Politano-Pouquet relations are often invoked to suggest that the spectrum of MHD turbulence instead has the Kolmogorov scaling –5/3. Using geometrical arguments and numerical tests, here we analyze this seeming contradiction and demonstrate that the –3/2 scaling and the Politano-Pouquet relations are reconciled by the phenomenon of scale-dependent dynamic alignment that was recently discovered in MHD turbulence.