Standing wave description of nearly conservative, parametrically excited waves in extended systems

Mancebo, Francisco J. and Vega de Prada, José Manuel (2004). Standing wave description of nearly conservative, parametrically excited waves in extended systems. "Physica D: Nonlinear Phenomena", v. 197 (n. 3-4); pp. 346-363. ISSN 0167-2789. https://doi.org/10.1016/j.physd.2004.07.006.

Description

Title: Standing wave description of nearly conservative, parametrically excited waves in extended systems
Author/s:
  • Mancebo, Francisco J.
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Physica D: Nonlinear Phenomena
Date: October 2004
ISSN: 0167-2789
Volume: 197
Subjects:
Freetext Keywords: Nearly conservative systems; Amplitude equations; Parametrically driven waves; Standing Faraday waves; Mean flow
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We consider the standing wavetrains that appear near threshold in a nearly conservative, parametrically excited, extended system that is invariant under space translations and reflection. Sufficiently close to threshold, the relevant equation is a Ginzburg-Landau equation whose cubic coefficient is extremely sensitive to wavenumber shifts, which can only be understood in the context of a more general quintic equation that also includes two cubic terms involving the spatial derivative. This latter equation is derived from the standard system of amplitude equations for counterpropagating waves, whose validity is well established today. The coefficients of the amplitude equation for standing waves are obtained for 1D Faraday waves in a deep container, to correct several gaps in former analyses in the literature. This application requires to also consider the effect of the viscous mean flow produced by the surface waves, which couples the dynamics of the surface waves themselves with the free surface deformation induced by the mean flow.

More information

Item ID: 6061
DC Identifier: http://oa.upm.es/6061/
OAI Identifier: oai:oa.upm.es:6061
DOI: 10.1016/j.physd.2004.07.006
Official URL: http://adsabs.harvard.edu/abs/2004PhyD..197..346M
Deposited by: Memoria de Investigacion 2
Deposited on: 17 Feb 2011 11:34
Last Modified: 20 Apr 2016 14:42
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