FLUVIAL TO TORRENTIAL PHASE TRANSITION IN OPEN CANALS

Network flows and specifically water flow in open canals can be modeled by systems of balance laws defined on graphs. The shallow water or Saint-Venant system of balance laws is one of the most used model and present two phases: fluvial or sub-critical and torrential or super-critical. Phase transitions may occur within the same canal but transitions related to networks are less investigated. In this paper we provide a complete characterization of possible phase transitions for a case study of a simple scenario with two canals and one junction. However, our analysis allows the study of more complicate networks. Moreover, we provide some numerical simulations to show the theory at work.