Analysis of the time behaviour of a diffusive transport in a stratified medium

The paper presents a study of the diffusive transport of passive solute plu mes in a two-dimensional non-homogeneous depth stratified flow domain. All the properties of the process are expressed by depth dependent deterministi c functions. The method of moments, combined with the method of Green funct ions are chosen to determine the relevant characteristics of the flow (mass , center of mass, variance, etc.) used to describe the behaviour of the tra nsient motion. General relationships for the n-order concentration moments are proved. Further, it is derived that the transient motion defined by tim e-dependent parameters tends asymptotically at large time to a stable regim e whose characteristics are determined, Consequently, under certain hypothe ses, an equivalence between the mean original process and a Fickian diffusi ve transport at large time may be established. The time required by the pro cess to reach its asymptotic behaviour is also calculated.