Lagrangian statistics and transilient matrix measurements by PTV in a convective boundary layer

The most common velocity measurement techniques, based on image analysis, calculate the velocity by cross-correlation of a portion of the digitized images, and give a Eulerian description of the investigated field. Particle tracking velocimetry (PTV), based on the recognition of trajectories of seeding particles, only furnishes a Eulerian description provided the trajectories are shorter than the characteristic scale of the phenomenon. If particles are tracked for a longer time, a Lagrangian description is obtained. Consequently, in order to successfully evaluate Lagrangian statistics, a long series of single-exposed images has to be acquired. PTV has been used to examine the pollutant dispersion in a laboratory simulation of the convective boundary layer of the atmosphere. The convective layer has been simulated by a water tank heated from below, where the atmospheric thermal stratification has been reproduced. Though the phenomenon was observed to be steady in the Eulerian reference frame, the same did not occur in the Lagrangian reference frame. From the analysis of particle motion, it is possible to determine the characteristic time scale of the turbulence and to describe the different behaviour of hot updraughts and cold downdraughts. The pollutant dispersion is described in detail by the transilient matrix representing the probability of transition of a particle from one level to another of the convective layer. From the information given by this matrix, it is possible, in principle, to estimate the concentration fields, due to a variety of concentrated and distributed pollutant sources.