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 R λ 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.

Oscillating grid mesocosm for studying oxygen dynamics under controlled unsteady turbulence

“…In presence of cores, exponent values for the power law varied from 0.58 to 1.83, averaging at 1.08 (Table ), thus deviating by 8% from the exponent of 1 found by Hopfinger and Toly () in an empty tank, without cores. Deviation from the exponent of 1 is likely due to the turbulence intermittency produced by unsteady vortex shedding in the near grid field (Chien et al ) as the power law fitting was performed closer from grid mid‐position (between 0.5 and 1.5 mesh size, due to the constrained space between grid and cores) than in previous experimental studies (Hannoun and List ; Redondo ; Fernando ) which validated the exponent of 1 beyond at least one mesh size away from the grid. Spatial heterogeneity of the flow statistics due to turbulence intermittency within or between cores was estimated by the residual error of the power law fitting and averaged at 16% for motor frequencies ranging from 0.5 Hz to 3.5 Hz among the four profiles.…”

Mixing in modulated turbulence. Analytical results

“…Their variations also become important only for large amplitude ratios. A recent related study of a similar effect can be found in [19]. They exploited experimentally the idea by Monin and Yaglom [20], section 25.1, who introduced a model to illustrate the influence of a fluctuating dissipation rate, or energy injection rate, on the Kolmogorov constant.…”

Extracting turbulent spectral transfer from under-resolved velocity fields

“…In the inertial range, 1 D LL = C 2 ( r) 2/3 , where C 2 ≈ 2.13 is expected to be a universal constant, although with some uncertainty. [23][24][25] Thus, the dissipation rate is often estimated in experiments by measuring D LL and scaling it appropriately. In Fig.…”