Browsing by Author "Carter, John D."

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    The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
    (ELSEVIER, 2011) Carter, John D.; Cienfuegos, Rodrigo
    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. (C) 2010 Elsevier Masson SAS. All rights reserved.