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