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

Abstract

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~\cite{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 $ε\propto \mathrm{Re}^3$, with Re being the Reynolds number ranging from $1.5 \times 10^4$ to $6 \times 10^5$. 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 \cite{Li07,Graham16,K62}