Transport equation for the homogeneous mean energy dissipation rate in decaying grid turbulence
Résumé
Grid turbulence is, from an academic viewpoint, a flow which permits various relations based on the assumption of local isotropy to be tested with a good deal of confidence if not rigour. However, in an experimental context, and for rather low Reynolds numbers, this flow does exhibit non-negligible departures from isotropy. This is why general relations based on weakly restrictive assumptions are required to provide a better description of the mechanisms involved in turbulence. The present paper presents an analytical work on the evolution behind the grid of the mean dissipation rate of the turbulent kinetic energy. More specifically, and for the sake of generality, we will consider the homogeneous form of this quantity, hom. The decay of hom mainly depends on two parameters, one representing the generation of vorticity by the action of the turbulent strain rate, and the other its destruction through molecular viscosity. Our equation is evaluated through the use of experimental data obtained in a low-Reynolds number grid turbulence, 32