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

TLDR

Random‑walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed, and several criteria have emerged to distinguish good from poor models. This paper examines the relationships among these criteria for a general class of models, showing that most of them are equivalent. The authors describe models that satisfy the criteria and illustrate them with calculations of dispersion in free‑convective conditions. They demonstrate that the criteria are largely equivalent and that a model can be constructed to satisfy them exactly while remaining consistent with inertial‑subrange theory.

Abstract

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.