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.