Practical use of variational principles for modeling water waves

Didier Clamond, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving a variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact traveling wave solutions are constructed when possible.

Original languageBritish English
Pages (from-to)25-36
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Issue number1
StatePublished - 1 Jan 2012


  • Approximations
  • Hamiltonian
  • Lagrangian
  • Relaxation
  • Variational principle
  • Water waves


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