Two-dimensional magnetohydrodynamic turbulence in the small magnetic Prandtl number limit

In this paper we introduce a new method for computations oftwo-dimensional magnetohydrodynamic (MHD) turbulence at low magneticPrandtl number $\Pra=\nu/\eta$. When $\Pra \ll 1$, the magnetic fielddissipates at a scale much larger than the velocity field. The methodwe utilise is a novel hybrid contour--spectral method, the ``Combined Lagrangian Advection Method'', formally to integrate the equationswith zero viscous dissipation. The method is compared with a standardpseudo-spectral method for decreasing $\Pra$ for the problem ofdecaying two-dimensional MHD turbulence. The method is shown to agreewell for a wide range of imposed magnetic field strengths. Examples ofproblems for which such a method may prove invaluable are also given