Multipoint concentration statistics for transport in stratified random velocity fields

Abstract : We determine the full multipoint concentration statistics for superdiffusive transport in a steady stratified random velocity field. Using a Lagrangian approach, we derive explicit analytical expressions for the multipoint moments of concentration and specifically for the concentration variance, which is a measure for concentration uncertainty. The multipoint concentration moments are fully characterized by the Lagrangian mean velocity and by the one and two particle velocity correlations. While the relative variance at the center of mass of the mean concentration is constant, it increases exponentially with time and distance from the center of mass. This implies that small concentration values are particularly uncertain, which can pose a serious practical concern as these are typically the earliest and latest to arrive at a point.