Temporal large-scale intermittency and its impact on flow statistics

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 in 1944, sufficiently slow variations of the large scales should nonetheless be expected to impact small-scale statistics. Such variations, often termed large-scale intermittency, are almost inevitable in experiments and even in simulations, while differing from flow to flow. Here we evaluate the impact of temporal large-scale fluctuations on velocity, velocity gradient, and acceleration statistics by introducing controlled 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, amplifying the tails of the measured distributions. We also show that the stronger tails can be accounted for by superposing an ensemble of stationary flows such that the temporal variations of an appropriate flow measure such as the energy dissipation rate are matched. Overall, our work demonstrates that in order to ensure comparability of statistical results in turbulence, large-scale intermittency needs to be taken into account.