University of Colorado & National Center for Atmospheric Research

**Abstract**: The range of scales encountered in MHD problems of astrophysical interest is well beyond expected computer resolutions in the
next decades. For this reason, closure schemes are often employed to model the
effect of the unresolved scales. One such closure is Lagrangian-averaged
magnetohydrodynamics (LAMHD) or the "alpha model."v This model is an extension
of the smoothing procedure in fluid dynamics which filters velocity fields
locally while leaving their associated vorticities unsmoothed, and has proven
useful for high Reynolds number turbulence computations. It differs from large
eddy simulations in that it preserves the invariants of a given flow. We
present DNS and LAMHD simulations of forced and free decaying two-dimensional
magnetohydrodynamic turbulence. The exponents of structure functions of the
velocity, the magnetic field, and the Els\"asser variables are studied. LAMHD
is found to have the same intermittent behavior as the DNS. The statistics of
sign cancellations of the current (and vorticity) at small scales are also
studied using both the cancellation exponent and the fractal dimension of the
structures. LAMHD is found to have the same scaling behavior between positive
and negative contributions as the DNS. At large Reynolds numbers, an
independence of the cancellation exponent with the Reynolds numbers is
observed.