15/03/2018 – A. Cheskonov – Dispersive and hydrostatic models of breaking waves on shallow water
Séminaire exceptionnel – 15 mars 2018 – 11h salle 250
Dispersive and hydrostatic models of breaking waves on shallow water
Alexander Cheskonov – Novosibirsk State Univ.
The main goal of the talk is to present a method for constructing mathematical models of breaking waves. The proposed approach is based on a two-layer modelling, where the upper turbulent layer is considered within the framework of shear shallow water flows while the lower layer is potential and can be described by the Serre-Green-Naghdi or Saint-Venant type models. The interaction between the layers is taken into account through a natural mixing process. The obtained models correctly describe the vorticity generation and turbulent bores. Moreover, the dispersive model allows us to describe the transition from an undular bore to a breaking bore. We also derive a two-layer model for the interaction between a bubbly shear layer and long internal waves over topography. The corresponding numerical results on the formation of large amplitude internal waves, including periodic and damped oscillating solutions, are presented. This work was done in collaboration with S.L. Gavrilyuk and V.Yu. Liapidevskii.