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ACMS Abstracts: Fall 2016

Nicolas Seguin (Universite Nantes)

Non-hydrostatic extension of classical shallow-water models

When modeling incompressible flows with a free surface, many situations are compatible with the so-called shallow-water assumption: the length of the domain is much larger than the average depth. Starting from the Navier-Stokes equations or the Euler equations for water flows with free surface, average processing or asymptotic analysis may lead to the Saint-Venant equations, which is a classical hyperbolic system of conservation laws. The goal of this talk is to go one step further, accounting for vertical effects. This leads to dispersive equations, such as the well-known Green–Naghdi model. Despite the change of nature of the equations, we will see that many properties are shared by the Saint-Venant equations and the Green–Naghdi equations.