Non hydrostatic shallow water equations
Tomas Morales
Université de Séville
Date(s) : 24/06/2025 iCal
14h30 - 16h30
Non hydrostatic shallow water equations
Shallow water equations (SWE) have been successfully applied to many real life situations for the simulation of geophysical flows: river floods, sediment transport, tsunami modeling, etc. The main drawback is the assumption of hydrostatic pressure and the fact that it does not take into account the effects associated with dispersive waves.
In recent years, an effort has been made in the derivation of relatively simple mathematical models for shallow water flows that include long nonlinear water waves. To improve the nonlinear dispersive properties of the model, information on the vertical structure of the flow should be included.
To do so, the approach used by Boussinesq-type models is to retain some high-order terms in the Taylor expansion of the velocity potential. High-order Boussinesq-type models offer better dispersive properties. The counterpart is that extremely complex systems with high-order derivatives arise.
Alternatively, the development of non-hydrostatic pressure models for coastal water waves has been the topic of many studies over the past 30 years. The idea is that, in order to incorporate dispersive effects in SWE-type models, one should retain some vertical information on the structure of the flows. This means that following the usual average process when obtaining SWE, one cannot assume the vertical velocity nor non-hydrostatic pressure negligible. Therefore, the pressure is split into a hydrostatic and a non-hydrostatic part. Using this strategy one obtains the one layer non-hydrostatic shallow water model whcih gives better results in certain applications. Nevertheless, in some situations a better dispersion relation is needed. In order to so, one has to enrich the vertical description of the fluid, which can be achieved by using a multilayer or moment approach.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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