Patterns in chaotically mixing fluid flows

这个项目的目标是研究出现在混合、暂时规则流动中的模式。以下基本问题将用数值和解析方法来解决：被动平流粒子模式的演化；无序平流物质反应模式；粒子的有限尺寸对图案的影响；可压缩性的影响。主要思想是使用一种基于寻找连续或离散时间被动标量线性扩散-平流方程的领先线性模式的方法。这些模态将用于主动非线性问题的稳定性分析和非线性结构的构造。在所有阶段，将遵循与流动中粒子的拉格朗日动力学的联系，包括作用于有限大小粒子的惯性和巴塞特力的情况。该理论的可能应用在于构建有效混合的微流体构型。

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 Lagrangian dynamics of particles in the flow will be followed, including the cases of inertia and Basset forces acting on finite size particles. Possible application to the theory lies in the construction of effectively mixing microfluidic configurations.