Implications of Reynolds Averaging for Reactive Tracers

This talk will examine the application of Reynolds averaging on advection-diffusion-reaction equations, focusing on the implications for the reaction terms. Mathematical theory will be briefly presented for reactions that can be described or approximated by polynomials. Fisher’s equation will be used as an illustrative example in which the interaction of fluctuations acts as a sink in the mean advection-diffusion-reaction equation. Statistics from an ensemble of numerical simulations describing the transport of active (Fisher’s equation) and passive tracers by Rayleigh-Taylor instabilities will be presented. The scalar variances of the two tracers will be compared and eddy fluxes will be contrasted with corresponding eddy diffusivities.