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

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. Several formulations of the 2D advection-diffusion equations are being used by different authors in the literatureSeveral formulations and coefficient values of the diffusivity tensor are employedThe number and quality of the available validation data sets are too weak, which limits the validation processes performed by the authors

Automated summary

This article reviews the mathematical formulations of the depth-integrated advection-diffusion equation used 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. The fragmentation of existing methodologies highlights a lack of scientific consensus, but promising approaches and possible paths for improvement are outlined.