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Predicting mixing processes, especially transverse mixing, downstream of river confluences is necessary for assessing and modelling the fate of pollutants transported in river networks, but it is still challenging. Typically, there is a lack of transverse mixing solutions implemented in 1‐D hydrodynamical models widely used in river engineering applications. To investigate the mixing processes developing downstream of a medium‐sized river confluence, three high‐resolution in‐situ surveys are conducted at the Rhône‐Saône confluence in France, based on geolocated specific conductivity and hydro‐acoustic measurements. Contrasting mixing situations are observed depending on hydrological conditions. In some cases, the two flows mix slowly due to turbulent shear at their vertical interface. This can be modeled by an analytical solution of the advection‐diffusion equation. In other cases, the waters from one of the two tributaries move under the waters of the other tributary. The induced local circulation enhances transverse mixing but not vertical mixing and the flow remains stratified vertically, which may be missed when surface or satellite images are analyzed qualitatively. Stratification may be predicted by comparing the time scales for shear and density‐driven adjustment. Shear‐dominated transverse mixing of depth‐average concentrations can be predicted analytically and implemented in 1‐D hydrodynamical models. However, the initiation of apparently rapid transverse mixing due to density‐driven circulation remains to be better understood and quantified.