Criteria for the selection of stochastic models of particle trajectories in turbulent flows

Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory. Some examples of models that obey the criteria are described. As an illustration some calculations of dispersion in free-convective conditions are presented.