  In this paper, the author investigates the impact of external sources on the
pattern formation and long-time behavior of concentration profiles of passive
tracers in a two-dimensional shear flow. It is shown that a time-periodic
concentration profile exists for time-periodic external source, while for
random source, the distribution functions of all concentration profiles weakly
converge to a unique invariant measure (like a stationary state in
deterministic systems) as time goes to infinity
