Experimental studies of occupation and transit times in turbulent flows

Abstract

The motion of passively advected particles is studied experimentally in approximately homogeneous and isotropic turbulent flows. The turbulence is generated in water by two moving grids. The simultaneous trajectories of many small passively advected, neutrally buoyant polystyrene particles are followed in time by a particle tracking technique. We estimate the probability distribution of the transit times of such particles in spherical volumes with given radius. A particle which is passively advected by the flow is selected to define the center of a reference sphere, with the transit time being defined as the difference between entrance and exit times of surrounding particles advected through this sphere by the turbulent motions. Simple scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. Also other formulations of the problem have been considered, by assuming, for instance, that particle positions are uniformly distributed within the reference sphere, and then determine the statistical distribution of the time they subsequently spend inside the sphere, i.e., their occupation time. These problems have Eulerian counterparts, and they were analyzed as well. In the present formulation, we find that the results of the analysis are relevant for understanding certain details in the feeding rate of microorganisms in turbulent waters, for instance.