Experimental Study of Relative, Turbulent Diffusion

The purpose is to study relative turbulent diffusion under controlled, reproducible conditions in the laboratory in order to estimate the constant C in Richardson-Obukhov’s law. We get C ≈ 0.4 – 0.6. We furthermore measure the distance-neighbour function, which is the probability density function of the separation of two fluid particles that are initially close to each other. We find that the model proposed by Richardson is far superior to the one suggested by Batchelor. To obtain these results we use the Particle Tracking (PT) technique to measure trajectories of fluid particles in a water tank with two oscillating grids generating turbulence. In the experiments reported here we have obtained Reynolds numbers based on Taylor’s microscale of about one hundred. The PT system, which is also described in this report, consists of four CCD cameras, a synchronous light source and a recording system with two computers each equipped with a frame grabber card. In the search for the best experimental methods we have revised the concept of local homogeneity and derived a law for the velocity–acceleration structure function. A second by-product of this effort is a relatively simple derivation of Kolmogorov’s four-fifth law based on the assumption of local homogeneity. Finally, we measure the full velocity structure tensor. The Particle Tracking Project was sponsored by the Danish Technical Research Council under contract 9601244 “Eksperimentelt studium af relativ, turbulent diffusion” (Experimental study of relative, tubulent diffusion). ISBN 87–550–2370–3; 87–550–2603–6 (Internet) ISSN 0106–2840 Information Service Department · Risø · 1999