  We analyze time series stemming from experiments and direct numerical
simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are
done in periodic boxes, but with a volumetric forcing chosen to mimic the
geometry of the flow in the experiments, the von K\'arm\'an swirling flow
between two counter-rotating impellers. Parameters in the simulations are
chosen to (within computational limitations) allow comparisons between the
experiments and the numerical results. Conducting fluids are considered in all
cases. Two different configurations are considered: a case with a weak
externally imposed magnetic field, and a case with self-sustained magnetic
fields. Evidence of long-term memory and $1/f$ noise is observed in experiments
and simulations, in the case with weak magnetic field associated with the
hydrodynamic behavior of the shear layer in the von K\'arm\'an flow, and in the
dynamo case associated with slow magnetohydrodynamic behavior of the large
scale magnetic field.
