Practical use of variational principles for modeling water waves

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Clamond, Didier¹  Dutykh, Denys² 

[1] Univ Nice Sophia Antipolis, Lab JA Dieudonne, F-06108 Nice 2, France

[2] Univ Savoie, LAMA, UMR CNRS 5127, F-73376 Le Bourget Du Lac, France

关键词: Water waves;    Variational principle;    Lagrangian;    Hamiltonian;    Relaxation;    Approximations;   

DOI  :  10.1016/j.physd.2011.09.015

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free