Inertial range scaling, Karman-Howarth theorem, and intermittency for forced and decaying Lagrangian averaged magnetohydrodynamic equations in two dimensions

We present an extension of the Kármán-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-α) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two-dimensional magnetohydrodynamic (MHD) turbulence, solving the MHD equations directly, and employing the LAMHD-α equations at 1∕2 and 1∕4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-α equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.