Non-hydrostatic layer-averaged Euler system with layerwise linear horizontal velocity
Résumé
A new hierarchy of non-hydrostatic layer-averaged models for the non-stationary Euler equations is presented in this work, with improved dispersion relations. They are a generalisation of the layeraveraged models introduced in [9], named LDNH models, where the vertical profile of the horizontal velocity is layerwise constant. This assumption implies that solutions of LDNH can be seen as a first order Galerkin approximation of Euler equations. This work focuses on particular weak solutions where the horizontal velocity is layerwise linear on z and possibly discontinuous across layer interfaces. Several closure relations of the layer-averaged system with non-hydrostatic pressure are presented. The resulting models are named LIN-NH p models, with p = 0, 1, 2. Parameter p indicates the degree of the vertical velocity profile considered in the approximation of the vertical momentum equation. All the introduced models satisfy a dissipative energy balance. Finally, an analysis and a comparison of the dispersive properties of each model are carried out. We show that Models LIN-NH 1 and LIN-NH 2 provide a better dispersion relation, group velocity and shoaling than LDNH models.
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