Spatiotemporal statistics of the dissipation rate at the boundary of a turbulent flow using Diffusing-Wave Spectroscopy

We use Diffusing Wave Spectroscopy (DWS) to perform the first direct space- and time-resolved measurement of the dissipation rate~$ε$ at the boundary of a turbulent flow. We have shown in a previous publication that this technique provides maps of the dissipation rate of Newtonian fluids~{Francisco}. Here, we apply the technique at the boundary of a turbulent flow generated in a square box by an impeller stirring the fluids. Although the measurement is made on a small region near the boundary, we show that the dissipation remains proportional to the injected power and follows the turbulent scaling ε∝ Re³, with Re being the Reynolds number ranging from 1.5 × 10⁴ to 6 × 10⁵. With this flow, there is no need for logarithmic corrections to reproduce the dissipation near the flat boundary. In addition, our setup allows us to measure the spatio-temporal fluctuations of the dissipation near the boundary. These fluctuations are quite large (the relative fluctuations are about 50%) and are well described by a log-normal distribution, as expected for the dissipation rate in the bulk of homogeneous and isotropic turbulence (HIT) but Power Density Spectra (PDS) do not correspond to those expected for HIT {Li07,Graham16,K62}