# Comparison of forcing functions in magnetohydrodynamic turbulence

## TL;DR

This study compares different mechanical forcing functions in magnetohydrodynamic turbulence simulations, revealing that while energy and magnetic helicity reach similar steady states, cross helicity behavior varies significantly, affecting ergodicity assumptions.

## Contribution

It systematically analyzes the effects of three common forcing functions on MHD turbulence, highlighting differences in cross helicity evolution and implications for simulation validity.

## Key findings

- All forcing functions produce similar energy and magnetic helicity states.
- Cross helicity varies significantly with sinusoidal forcing.
- Ergodicity assumptions may not hold due to uncontrolled helicity injection.

## Abstract

Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different mechanical forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale velocity field as a forcing function), a nonhelical random force, and a nonhelical static sinusoidal force (analogous to helical ABC forcing). The time evolution of the three ideal invariants (energy, magnetic helicity and cross helicity), the time-averaged energy spectra, the energy ratios and the dissipation ratios are examined. All three forcing functions produce qualitatively similar steady states with regards to the time evolution of the energy and magnetic helicity. However, differences in the cross helicity evolution are observed, particularly in the case of the static sinusoidal method of energy injection. Indeed, an ensemble of sinusoidally-forced simulations with identical parameters shows significant variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems in which the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored.