The Relationship between the Transilient Matrix and the Green’s Function for the Advection-Diffusion Equation

Abstract

The Green?s function (or propagator) of the advection-diffusion equation is used to link the transilient matrix to the advection-diffusion equation. The Green?s function framework allows one to construct more rigorous and general derivations of various mixing properties of the transilient matrix. Unlike the transilient matrix or one-dimensional convective parameterizations, the Green?s function satisfies a composition property that allows a long-time propagator to be constructed from a series of short-time propagators.