HAL: hal-00716088, version 1

arXiv: 1207.2246

DOI: 10.1063/1.4768530

Detailed view

Export this paper BibTeX - EndNote - TEI - RefWorks -

Physics of Fluids, 24 (2012) 127102(2012)

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity

Roland Thomas (  Corresponding author ) 1, Christian Kharif 1, Miguel Manna 2

(2012-12-28)

A nonlinear Schrödinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. At third order we have shown the importance of the coupling between the mean flow induced by the modulation and the vorticity. Furthermore, it is shown that these plane wave solutions may be linearly stable to modulational instability for an opposite shear current independently of the dimensionless parameter kh, where k and h are the carrier wavenumber and depth respectively.

1:	Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE)
	CNRS : UMR6594 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Ecole Centrale de Marseille
2:	Laboratoire Charles Coulomb (L2C)
	CNRS : UMR5221 – Université Montpellier II - Sciences et techniques

Subject

:

Physics/Mechanics/Mechanics of the fluids Engineering Sciences/Mechanics/Fluids mechanics

Keyword(s): Gravity waves – vorticity – finite depth – nonlinear Schrödinger equation

hal-00716088, version 1

http://hal.archives-ouvertes.fr/hal-00716088

oai:hal.archives-ouvertes.fr:hal-00716088

From: Roland Thomas <>

Submitted on: Tuesday, 10 July 2012 09:04:07

Updated on: Friday, 29 March 2013 11:50:55