Dynamic Alignment and Exact Scaling Laws in Magnetohydrodynamic Turbulence

Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent highresolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is E(k⊥) ∝ k ⊥ . 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. Subject headings: MHD — turbulence—solar wind—ISM: magnetic fields