  A method is provided for approximating random slow manifolds of a class of
slow-fast stochastic dynamical systems. Thus approximate, low dimensional,
reduced slow systems are obtained analytically in the case of sufficiently
large time scale separation. To illustrate this dimension reduction procedure,
the impact of random environmental fluctuations on the settling motion of
inertial particles in a cellular flow field is examined. It is found that noise
delays settling for some particles but enhances settling for others. A
deterministic stable manifold is an agent to facilitate this phenomenon.
Overall, noise appears to delay the settling in an averaged sense.
