Particle mixing and reactive front motions in chaotic but closed shallow flows

A numerical study is presented of wind-induced active mixing and transport processes in closed shallow flows that are able to support chaotic advection. The wind-induced non-linear shallow water flow field is predicted using a quadtree grid based Godunov-type finite volume solver. Particles are tracked by numerically integrating the advection equations using velocity information interpolated from the predicted flow field. In complex oscillating flows, storage of all the necessary velocity information becomes problematical. Instead, we utilize the mean field and the first few dominant unsteady contributions as determined using Singular Value Decomposition. The advected particles are assumed to support autocatalytic reaction defined as A + B → 2B. Wind-induced reactive particle advection is considered in a realistic mine tailings pond with somewhat idealized bed topography. The reactive process reaches a stationary stage where reaction products occupy the whole closed flow domain. However, in the transient stage, particles undergo active advection and trace out filamentary structures that are similar to those in open flows. Because of the impossibility of particle escape and the global fine-scale chaotic mixing, the initial stages of chaotic mixing in closed flows are more efficient than in open flows. The results qualitatively validate a surface reaction theory derived by Károlyi and Tél [Károlyi G, Tél T. Chemical transients in closed chaotic flows: the role of effective dimensions. Phys Rev Lett 2005;95:264501-1-4] for closed systems.