Séance Séminaire

Séminaire ACSIOM

On a new mathematical model for open channel and river hydraulics

The modelling of hydrology of catchment basins and rivers holds a central place in environmental sciences, particularly in connection with water availability, urban sewer systems, flood risks and in particular for tsunamis. Indeed, rivers are known to be the tsunami highways. Waves penetrate through rivers much faster inland than the coastal inundation reaches over the ground, and may lead flooding in low-lying areas located several km away from the coastline. Modelling these processes and predicting the motion of water is a difficult task for which substantial effort has been devoted. To this purpose, in this talk, we present the first section-averaged non-linear and weakly dispersive model for open channel and river flows. These equations are the second order shallow water approximation of the section-averaged (three-dimensional) incompressible and irrotational Euler system. This new asymptotic model generalises the well-known one-dimensional Serre-Green- Naghdi (SGN) equations for rectangular section on uneven bottom to arbitrary channel/river section.