Probability and dispersion theory

Abstract

In this study the authors consider a very old branch of fluid mechanics, namely that of Taylor dispersion, in a new light, using up-to-date techniques from the theory of stochastic processes. The aim is to show how these techniques not only help in deepening our understanding of dispersion, but are in fact very useful for every-day calculations. Some old and not-so-old problems in dispersion theory are considered in order to demonstrate the new techniques, and so far as possible any hidden calculations are avoided, so a reader new to the probabilistic techniques can judge their effectiveness. A wider knowledge of probabilistic techniques would be useful in many traditional areas of applied mathematics, but dispersion theory is probably the most natural field for their introduction into fluid mechanics.