A discussion on Neumann-Kelvin model for progressive water waves

Philippe Destuynder (1) , Caroline Fabre (2)

1 CNAM - Conservatoire National des Arts et Métiers [CNAM]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This paper focus on the role of the capillary in the modelling and the analysis of progressive waves at the surface of the sea. It is proved that the classical Neumann-Kelvin model is fully instable and should be modified in order to be mechanically reliable. It is shown that the easiest way to take the capillary into account is to use a formulation where the normal displacement of the free surface appears as a main unknown variable.

Mots clés: water waves; unstabilities; wave equations; spectral theory; non-linear models

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Destuynder, Caroline Fabre. A discussion on Neumann-Kelvin model for progressive water waves. 2009. ⟨hal-00429737⟩