Effects of fluctuating energy input on the small scales in turbulence

In the standard cascade picture of three-dimensional turbulent fluid flows, energy is input at a constant rate at large scales. Energy is then transferred to smaller scales by an intermittent process that has been the focus of a vast literature. However, the energy input at large scales is not constant in most real turbulent flows. We explore the signatures of these fluctuations of large-scale energy input on small-scale turbulence statistics. Measurements were made in a flow between oscillating grids, with ${R}_{\lambda } $ up to 262, in which temporal variations in the large-scale energy input can be introduced by modulating the oscillating grid frequency. We find that the Kolmogorov constant for second-order longitudinal structure functions depends on the magnitude of the fluctuations in the large-scale energy input. We can quantitatively predict the measured change with a model based on Kolmogorov’s refined similarity theory. The effects of fluctuations of the energy input can also be observed using structure functions conditioned on the instantaneous large-scale velocity. A linear parametrization using the curvature of the conditional structure functions provides a fairly good match with the measured changes in the Kolmogorov constant. Conditional structure functions are found to provide a more sensitive measure of the presence of fluctuations in the large-scale energy input than inertial range scaling coefficients.