Patterns in chaotically mixing fluid flows

这个项目的目标是调查的模式出现在混合，时间规则流。以下基本问题将解决与数值和分析方法：被动平流粒子的图案的演变;图案反应混沌平流物种;的影响，与有限尺寸的粒子图案;压缩性的影响。其主要思想是使用一种方法的基础上寻找领先的线性扩散平流方程的线性模式的被动标量，无论是在连续或离散时间。然后，这些模式将用于主动非线性问题的稳定性分析和非线性结构的建设。在所有阶段的连接到拉格朗日动力学的粒子在流动中，将遵循，包括惯性和巴塞力的情况下，作用在有限尺寸的颗粒。该理论的可能应用在于构建有效混合的微流体配置。

The goal of this project is the investigation of patterns which appear in mixing, temporally regular flows. The following basic questions will be addressed with numerical and analytical methods: evolution of patterns of passively advected particles; patterns for reacting chaotically advected species; the influence of the effects related to the finite size of particles on the patterns; the effect of compressibility. The main idea is to use an approach based on finding leading linear modes of the linear diffusion-advection equation for a passive scalar, either in continuous or in discrete time. These modes will be then used for stability analysis of active nonlinear problems and for construction of nonlinear structures. On all stages a connection to the Lagraingian dynamics of particles in the flow will be followed, including the cases of inertia and Basset forces acting on finite size particles. Possible application of the theory lies in the construction of effectively mixing microfluidic configurations.