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A large-deviation approach to passive scalar advection, diffusion and reaction

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Mathematics for the Fluid Earth

Co-authors: Peter H. Haynes (University of Cambridge), Alexandra Tzella (University of Birmingham)

The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion can often be described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value. This description fails to capture the tails of the scalar concentration in initial-value problems, however. This talk addresses this issue and shows how the theory of large deviation can be applied to capture the concentration tails by solving a family of eigenvalue problems. Two types of flows are considered: shear flows and cellular flows. In both cases, large deviation is shown to generalise classical results (Taylor dispersion for shear flows, homogenisation results for cellular flows). Explicit asymptotic results are obtained in the limit of large Pclet number corresponding to small molecular diffusivity. The implications of the results for the problem of front propagation in reacting flows are also discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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