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Theory of small aspect ratio waves in deep water
Kraenkel A., Leon J., Manna M.A.
Physica D: Nonlinear Phenomena 211 (2005) 377-390 - http://hal.in2p3.fr/in2p3-00149077
Science non linéaire/Formation de Structures et Solitons
Science non linéaire/Systèmes Solubles et Intégrables
Theory of small aspect ratio waves in deep water
A. Kraenkel, J. Leon1, M. A. Manna1
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
CNRS : UMR5207 – IN2P3 – Université Montpellier II - Sciences et techniques
Bât 13- 1er Et. - CC 070 Place Eugène Bataillon 34095 MONTPELLIER CEDEX 5
In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution.

Articles dans des revues avec comité de lecture
Physica D: Nonlinear Phenomena
Publisher Elsevier
ISSN 0167-2789 

LaTex file, 16 pages, 4 figures
Water waves – Asymptotic methods – Nonlinear dynamics
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