Practical use of variational principles for modeling water waves
Abstract
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 the 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 travelling wave solutions are constructed when possible.
Domains
Fluid mechanics [physics.class-ph] Fluids mechanics [physics.class-ph] Analysis of PDEs [math.AP] Ocean, Atmosphere Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI] Fluid Dynamics [physics.flu-dyn] Atmospheric and Oceanic Physics [physics.ao-ph] Classical Physics [physics.class-ph]Origin | Files produced by the author(s) |
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