Comparison of forcing functions in magnetohydrodynamics

Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different kinetic forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale 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. The effect of the number of grid points and Reynolds number on the performance of the forces is also considered. All three forces produce qualitatively similar steady states with some differences. In particular, the magnetic helicity is well-conserved in all cases but the sinusoidal method of energy injection has a tendency to introduce cross helicity into the system. Indeed, an ensemble of sinusoidally-forced simulations with identical parameters shows large variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems where the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored. N.B. a description of the software which ran the simulations can be found in the PhD theses of the two people who designed and implemented the majority of it: Sam Yoffe ( https://arxiv.org/abs/1306.3408 ) and Moritz Linkmann respectively ( https://www.era.lib.ed.ac.uk/handle/1842/19572).