Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region

Three turbulence closure schemes, designed for stratified shallow water flows, are presented. They are based upon k-epsilon theory and use respectively two, one or zero transport equations for turbulent variables. The models are first tested on the evolution of a wind-driven turbulent layer in a stratified fluid. The results are at least qualitatively in agreement with observational and experimental data. A discussion is given about the existence of self-similar solutions. The models are compared next with the observational data of the Rhine outflow area. The periodic variation in the density structure, forced by wind and tides and which is clearly visible in the data, is predicted by the model. A physical interpretation of the model results is given in the absence of wind forcing. The effects of estuarine circulation, tidal straining and mixing on the development or breakdown of stratification are well represented by the model calculations.