Using the potential energy anomaly equation to investigate tidal straining and advection of stratification in a region of freshwater influence

Abstract

In this paper we derive the potential energy anomaly equation suitable for the analysis of three-dimensional numerical models. We apply this equation to the results of an idealised numerical model simulation of the Rhine River Plume and demonstrate how we can use the potential energy anomaly equation to analyse the physical processes affecting stratification, in this region of freshwater influence (ROFI). For this test case, we use the 10 terms from the potential energy anomaly equation that dominate the evolution of stratification in the Rhine ROFI. The principal terms are the cross-shore and along-shore straining and cross-shore and along-shore advection of horizontal density gradients. In addition non-linear shear dispersion terms representing correlations between density and velocity perturbations over the vertical control horizontal exchange and mixing in the cross-shore and along-shore directions. Moreover, in the vertical direction two terms dominate the vertical exchange processes: a term describing the effect of vertical mixing on the density profile, and a term related to up and downwelling. Analysis of the model results using the potential energy anomaly equation allows us to present a detailed overview of the spatial distribution of the terms affecting the evolution of stratification in the Rhine ROFI. The results highlight the important role of cross-shore tidal straining in the downstream coastal current region of the plume. In addition, the roles of along-shore straining, as well as along-shore and cross-shore advection in the Rhine ROFI, in particular in the region of the bulge near the river mouth, are also of importance. The results for the Rhine ROFI show that the potential energy anomaly equation provides a powerful tool with which to analyse the mechanisms contributing to mixing and stratification in coastal seas and estuaries. © 2008 Elsevier Ltd. All rights reserved.