Patterns in chaotically mixing fluid flows

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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.