Shallow water equations for large bathymetry variations

Abstract

In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing suitable constraints. Thus, the derivation procedure does not explicitly involve any small parameter.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2011shallowwater,
  author = {Dutykh, D. and Clamond, D.},
  title = {Shallow water equations for large bathymetry variations},
  journal = {J. Phys. A: Math. Theor.},
  year = {2011},
  volume = {44},
  pages = {332001},
  doi = {10.1088/1751-8113/44/33/332001},
  abstract = {In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing suitable constraints. Thus, the derivation procedure does not explicitly involve any small parameter.},
  keywords = {variational principle, Saint-Venant equations, large bathymetry variations, shallow water ansatz, gravity waves, Shallow water, shallow water equations, small parameter, nonlinear shallow water equations, long waves, seabed variations}
}