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| Coherent structures are ubiquitous in environmental and geophysical flows. Recent advances in the identification of finite-time transport barriers have enabled the extraction of organizing templates for passive scalars in the limit of infinitesimal diffusion. In this presentation, we show, by using example of an autocatalytic reaction, that reaction processes can also be tied to finite-time Lagrangian measures, which varies quite significantly in different types of flow topologies. In particular, we consider the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation embedded in a flow with two oscillating gyres. We show that a model based on finite-time Lagrangian stretching rates represents the variabilities from the actual simulations well. Some recent efforts to extend the theory to more complicated reaction processes will also be discussed. |
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