  We present an extension of the Karman-Howarth theorem to the Lagrangian
averaged magnetohydrodynamic (LAMHD-alpha) 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 MHD turbulence, solving directly the MHD equations, and employing
the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the
third-order structure function with length is observed. The LAMHD-alpha
equations also capture the anomalous scaling of the longitudinal structure
function exponents up to order 8.
