Formulations and Diffusivity Coefficients of the 2D Depth-Averaged Advection-Diffusion Models: A Literature Review

Abstract

This article reviews the mathematical formulations of the depth-integrated advection-diffusion equation used so far for modeling scalar transport and mixing in shallow environmental flows. It also summarizes the main approaches developed to evaluate the diffusivity tensor in such models. Remarkably, seven different formulations were found for the depth-averaged advection-diffusion equation, and eight distinct approaches have been used for determining the coefficients of the diffusivity tensor. Besides, only a minority of the reviewed studies report calibration of the diffusivity tensor against experimental or field observations. The fragmentation of existing methodologies exhibits a lack of scientific consensus. Promising approaches are highlighted and possible paths for improving the calibration, validation and transferability of the diffusivity coefficients are outlined.