Pontificia Universidad Católica de Chile Pontificia Universidad Católica de Chile
Carter J.D. and Cienfuegos R. (2011)

The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations. http://dx.doi.org/10.1016/j.euromechflu.2010.12.002

Revista : European Journal of Mechanics B-Fluids
Volumen : 30
Número : 3
Páginas : 259-268
Tipo de publicación : ISI Ir a publicación


The Serre equations are a pair of strongly nonlinear, weakly dispersive, Boussinesq-type partial differential equations. They model the evolution of the surface elevation and the depth-averaged horizontal velocity of an inviscid, irrotational, incompressible, shallow fluid. They admit a three-parameter family of cnoidal wave solutions with improved kinematics when compared to KdV theory. We examine their linear stability and establish that waves with sufficiently small amplitude/steepness are stable while waves with sufficiently large amplitude/steepness are unstable.