Passive tracer dispersion with random or periodic source

In this paper, the author investigates the impact of external sources on th e pattern formation and long-time behavior of concentration profiles of pas sive tracers in a two-dimensional shear flow. It is shown that a time-perio dic concentration profile exists for time-periodic external source, while f or random source, the distribution functions of all concentration profiles weakly converge to a unique invariant measure (like a stationary state in d eterministic systems) as time goes to infinity. (C) 1998 Elsevier Science L td. All rights reserved.