The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations

Autor:	Rodrigo Cienfuegos, John D. Carter
Rok vydání:	2011
Předmět:	Physics Partial differential equation Mathematics::Analysis of PDEs General Physics and Astronomy Cnoidal wave Conservative vector field Physics::Fluid Dynamics Nonlinear system Amplitude Classical mechanics Inviscid flow Korteweg–de Vries equation Mathematical Physics Linear stability
Zdroj:	European Journal of Mechanics - B/Fluids. 30:259-268
ISSN:	0997-7546
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::be859215bd00ed3b08849bbe016479dc https://doi.org/10.1016/j.euromechflu.2010.12.002 Zobrazit plný text záznamu Full Text from ScienceDirect