Random walk models of turbulent dispersion
An understanding of the dispersion of contaminants in turbulent flows is important in many fields ranging from air pollution to chemical engineering, and random walk models provide one approach to understanding and calculating aspects of dispersion. Two types of random walk model are investigated in this thesis. The first type, so-called "one-particle models", are capable of predicting only mean concentrations while the second type, "two-particle models", are able to give some information on the fluctuations in concentration as well. Many different one-particle random walk models have been proposed previously and several criteria have emerged to distinguish good models from bad. In this thesis, the relationships between the various criteria are examined and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to (i) satisfy the criteria exactly and (ii) be consistent with inertial subrange theory. Some examples of models which obey the criteria are described. The theory developed for one-particle models is then extended to the two-particle case and used to design a two-particle model suitable for modelling dispersion in high Reynolds number isotropic turbulence. The properties of this model are investigated in detail and compared with previous models. In contrast to most previous models, the new model is three-dimensional and leads to a prediction for the particle separation probability density function which is in agreement with inertial subrange theory. The values of concentration variance from the new model are compared with experimental data and show encouraging agreement.