%0 Journal Article
%T Nonlinear Dynamics of Short Travelling Capillary-gravity Waves
%+ Laboratoire de Physique Théorique et Astroparticules (LPTA)
%+ Laboratoire de Physique Mathématique et Théorique (PMT)
%A Borzi, H. C.
%A Kraenkel, R.A
%A Manna, Miguel
%A Pereira, A.
%Z 9 pages
%< avec comité de lecture
%Z 04-047
%@ 1539-3755
%J Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
%I American Physical Society
%V 71
%P 026307
%8 2005-02-12
%D 2005
%R 10.1103/PhysRevE.71.026307
%K capillary waves
%K gravity waves
%K flow instability
%Z PACS: 47.10.+g; 47.20.Ky; 47.35.+i; 04.25.-g
%Z Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]Journal articles
%X We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-waves dynamics, we show that this system posseses (1+1) travelling waves solutions for almost all the values of the Bond number B (the special case B=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis.
%G English
%L hal-00338939
%U https://hal.science/hal-00338939
%~ IN2P3
%~ LPTA
%~ CNRS
%~ UNIV-MONTP2
%~ UNIV-MONTPELLIER
%~ UM1-UM2