Dispersion and front propagation in networks and cellular vortex flows: the role of large deviations

We discuss the dispersion of a diffusive scalar released inside a periodic fluid environment. Motivated by environmental applications, the particular focus is on fluid-filled rectangular networks and steady cellular vortex flows. We describe how large-deviation theory can be used to provide an approximation for the long-time concentration that remains valid for large distances from the center of mass, much beyond the range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. The same theory can be used to describe the speed of propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) type reactions. We discuss asymptotic regimes corresponding to distinguished limits of reaction rate (Damköhler number) in the limit of small molecular diffusivity (large Péclet number).

Joint work with J Vanneste (University of Edinburgh)