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

作者：Ren, Jian; Duan, Jinqiao; Jones, Christopher K R T^*

来源：Journal of Dynamics and Differential Equations, 2015, 27(3-4): 961-979.

DOI：10.1007/s10884-015-9452-z

• Random slow manifolds
• Dimension reduction
• Stochastic differential equations (SDEs)
• Approximation under big scale-separation
• Inertial particles in flows

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.

• 出版日期2015-12
• 单位华中科技大学; 广州大学