Serre-type equations in deep water

D. Dutykh, D. Clamond, M. Chhay

Research output: Contribution to journalReview articlepeer-review

2 Scopus citations

Abstract

This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well. Namely, we derive the deep water analogue of the celebrated SERRE-GREEN-NAGHDI equations which have become the standard model in shallow water environments. The relation to existing models is discussed. Moreover, the multi-symplectic structure of these equations is reported as well. The results of this work can be used to develop various types of robust structure-preserving variational integrators in deep water. The methodology of constructing approximate models presented in this study can be naturally extrapolated to other physical flow regimes as well.

Original languageBritish English
Pages (from-to)23-40
Number of pages18
JournalMathematical Modelling of Natural Phenomena
Volume12
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Deep water approximation
  • Free surface impermeability
  • Serre-Green-Naghdi equations
  • Variational principle

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