Spectra of decaying two-dimensional magnetohydrodynamic turbulence on a $\beta$-plane

The formation of the Iroshnikov-Kraichnan spectrum in the inertial interval has been shown for two-dimensional $\beta$-plane decaying homogeneous magnetohydrodynamic turbulence. An expression for the wavenum-ber that characterizes the boundary between the inertial interval of the Iroshnikov-Kraichnan spectrum and the region of existence of Rossby waves has been obtained. The self-similar decay of the Iroshnikov-Kraichnan spectrum in time has been investigated. The violation of the self-similar decay of the total energy spectrum and the formation of the Kolmogorov spectrum in the inertial range of the kinetic energy have been found at large time intervals. The inverse cascade of the kinetic energy characteristic of the detected Kolmogorov spectrum provides the origin of zonal flows.