A discussion on Neumann–Kelvin's model for progressive water waves

Abstract

This article focuses on the role of the capillarity in the modelling and the analysis of progressive waves at the surface of the sea. It is proved that the classical Neumann–Kelvin's model is fully unstable and should be modified in order to be mechanically reliable.

Keywords:

• water waves
• instabilities
• wave equations
• spectral theory
• nonlinear models

AMS Subject Classifications::

• Primary: 74F10
• 35L85
• 35R35
• Secondary: 76B15
• 35L70
• 35Q35

Acknowledgements

The authors thank Th. Gazzola and X.B. Chen from Bureau Veritas for their judicious remarks and valuable comments during this work.