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 #approx# 0.4 -- 0.6. We furthermore measure the distance-neighbourfunction, 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 resultswe 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 ofabout 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 experimentalmethods 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 oflocal homogeneity. Finally, we measure the full velocity structure tensor.