# Rotating magnetohydrodynamic turbulence

## TL;DR

This paper investigates rotating magnetohydrodynamic turbulence through theoretical derivations and numerical simulations, focusing on weak and strong wave turbulence regimes, and confirms predictions with spectral exponent results.

## Contribution

It develops a theory of strong turbulence based on the critical balance approach for rotating MHD systems, extending previous weak turbulence models.

## Key findings

- Numerical simulations agree with weak wave turbulence theory predictions.
- Spectral exponents match theoretical predictions for both weak and strong turbulence.
- The study confirms the applicability of the critical balance approach in rotating MHD turbulence.

## Abstract

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.