A Fundamental Solution for an Advection Di usion Equation in a Non Uniform Three Dimensional Flow

Abstract

We propose in this thesis an analytical solution for the three dimensional Eulerian advection diffusion equation of a scalar tracer transported by a turbulent flow where the mean flow is assumed to be linear in space relative to the center of the patch and where the effects of the small scale eddies are resolved by introducing an effective eddy diffusivity. We show how our solution is obtained by transforming it into a system of equations for the trajectories and for the concentration in the Lagrangian frame. An apparent diffusion coefficient that combines the effects of the advection and the turbulent diffusion is inferred from the solution and some asymptotic behaviors of the diffusion are explored.