Are the energy and magnetic potential cascades direct or inverse in 2D MHD turbulence?

Transfer of energy and magnetic potential is studied in 2D MHD turbulence in the presence of a background shear flow and magnetic field. The energy is injected into both fluid and magnetic field by external forcing. By using a two-scale analysis and the Gabor transform, the direction of the cascade of energy and magnetic vector potential is found to depend on the properties of forcings. In particular, in the case of a magnetic forcing that is isotropic, the magnetic vector potential cascades from small to large-scales whereas the energy from large to small-scales.