  Turbulent flows in three dimensions are characterized by the transport of
energy from large to small scales through the energy cascade. Since the small
scales are the result of the nonlinear dynamics across the scales, they are
often thought of as universal and independent of the large scales. However, as
famously remarked by Landau, sufficiently slow variations of the large scales
should nonetheless be expected to impact small-scale statistics. Such
variations, often termed large-scale intermittency, are pervasive in
experiments and even in simulations, while differing from flow to flow. Here we
evaluate the impact of temporal large-scale fluctuations on velocity,
vorticity, and acceleration statistics by introducing controlled sinusoidal
variations of the energy injection rate into direct numerical simulations of
turbulence. We find that slow variations can have a strong impact on flow
statistics, raising the flatness of the considered quantities. We discern three
contributions to the increased flatness, which we model by superpositions of
statistically stationary flows. Overall, our work demonstrates how large-scale
intermittency needs to be taken into account in order to ensure comparability
of statistical results in turbulence.
