Published June 1, 2021
| Version v1
Publication
A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows
Description
In geophysics, the shallow water model is a good approximation of the incompressible
Navier-Stokes system with free surface and it is widely used for its mathematical structure and its computational
efficiency. However, applications of this model are restricted by two approximations under
which it was derived, namely the hydrostatic pressure and the vertical averaging. Each approximation
has been addressed separately in the literature: the first one was overcome by taking into account the
hydrodynamic pressure (e.g. the non-hydrostatic or the Green-Naghdi models); the second one by
proposing a multilayer version of the shallow water model.
In the present paper, a hierarchy of new models is derived with a layerwise approach incorporating
non-hydrostatic effects to approximate the Euler equations. To assess these models, we use a rigorous
derivation process based on a Galerkin-type approximation along the vertical axis of the velocity field and
the pressure, it is also proven that all of them satisfy an energy equality. In addition, we analyse the linear
dispersion relation of these models and prove that the latter relations converge to the dispersion relation
for the Euler equations when the number of layers goes to infinity.
Abstract
Ministerio de Economía y Competitividad MTM2015-70490-C2-2-RAdditional details
Identifiers
- URL
- https://idus.us.es/handle//11441/111263
- URN
- urn:oai:idus.us.es:11441/111263