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We present direct numerical simulations and Lagrangian averaged (also knownas alpha-model) simulations of forced and free decaying magnetohydrodynamicturbulence in two dimensions. The statistics of sign cancellations of thecurrent at small scales is studied using both the cancellation exponent and thefractal dimension of the structures. The alpha-model is found to have the samescaling behavior between positive and negative contributions as the directnumerical simulations. The alpha-model is also able to reproduce the timeevolution of these quantities in free decaying turbulence. At large Reynoldsnumbers, an independence of the cancellation exponent with the Reynolds numbersis observed.Comment: Finite size box effects have been taken into account in the  definition of the partition function. This has resulted in a more clear  scaling in all figures. Several points are clarified in the tex

physical review. e, statistical, nonlinear and soft matter physics

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: Direct numerical simulations and Lagrangian averaged modeling