  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.
