  Turbulence in rotating Magneto-hydrodynamic systems is studied theoretically
and numerically. In the linear limit, when the velocity and magnetic
perturbations are small, the system supports two types of waves. When the
rotation effects are stronger than the ones of the external magnetic field, one
of these waves contains most of the kinetic energy (inertial wave) and the
other -- most of the magnetic energy (magnetostrophic wave). The weak wave
turbulence (WWT) theory for decoupled inertial and magnetospheric wave systems
was previously derived by Galtier (2014). In the present paper, we derive
theory of strong turbulence for such waves based on the critical balance (CB)
approach conjecturing that the linear and nonlinear timescales are of similar
magnitudes in a wide range of turbulent scales. Regimes of weak and strong wave
turbulence are simulated numerically. The results appear to be in good
agreement with the WWT and CB predictions, particularly for the exponents of
the kinetic and magnetic energy spectra.
