Modeling water waves beyond perturbations

Abstract

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein–Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.

Keywords

Bibliographic record

BibTeX Citation

@incollection{Clamond_2016_modeling_water_waves,
  title = {Modeling water waves beyond perturbations},
  author = {Clamond, D. and Dutykh, D.},
  booktitle = {New Approaches to Nonlinear Waves},
  editor = {Tobisch, E.},
  publisher = {Springer},
  year = {2016},
  pages = {197--210},
  doi = {10.1007/978-3-319-20690-5_7},
  url = {https://hal.archives-ouvertes.fr/hal-01102120/},
  series = {Lecture Notes in Physics},
  volume = {908},
  isbn = {978-3-319-20689-9},
  keywords = {Velocity Field, Variational Principle, Water Wave, Lagrangian Density, Gordon Equation}
}