Effects of Fluctuating Energy Input on the Small Scales in Turbulence

Abstract

In the standard cascade picture of 3D 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 Re up to 271, 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 parameterization using the curvature of the iconditional 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.