Modelling Transverse Anomalous Solute Transport in Highly Heterogeneous Porous Media

We study the intermittent transverse dynamics of solute transport through highly heterogeneous porous media.  Considering a Lagrangian framework focused on the equidistantly analysis of the particles motion, we identify two fundamental mechanisms that determine large scale particle motion, amely, the relaxation towards an (non-zero) average transverse particle position and the short-scale correlated behavior of the transverse particles motion. Based on these mechanisms, we derive a theory that jointly predicts anomalous transverse and longitudinal dispersion in terms of Eulerian velocity distribution, key statistics of the system heterogeneity and two additional parameters related to the particles relaxation process with a clear physical meaning.