Cancellation exponent and multifractal structure in two-dimensional   magnetohydrodynamics: direct numerical simulations and Lagrangian averaged   modeling
  We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha-model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha-model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed. 
Jonathan Pietarila-Graham, Pablo D. Mininni, and Annick Pouquet