Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty

TL;DR

This paper introduces a method to approximate random slow manifolds in stochastic systems, enabling analytical reduction of complex models, and investigates how environmental noise influences the settling behavior of inertial particles.

Contribution

It provides a novel analytical approach for approximating random slow manifolds and applies it to study noise effects on particle settling in fluid flows.

Findings

Noise delays particle settling in some cases

Noise can enhance settling for other particles

Overall, noise tends to delay settling on average

Abstract

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.