Mean Flow Effects in Model Equations for Faraday Waves

Rüdiger, Sten and Vega de Prada, José Manuel (2004). Mean Flow Effects in Model Equations for Faraday Waves. In: "Dynamics and Bifurcation of Patterns in Dissipative Systems". Series B, 12 . World Scientific Publishing, Londres, UK, pp. 174-193. ISBN 981-238-946-6.

Description

Title: Mean Flow Effects in Model Equations for Faraday Waves
Author/s:
  • Rüdiger, Sten
  • Vega de Prada, José Manuel
Item Type: Book Section
Title of Book: Dynamics and Bifurcation of Patterns in Dissipative Systems
Título de Revista/Publicación: Dynamics and Bifurcation of Patterns in Dissipative Systems
Date: 2004
ISBN: 981-238-946-6
Volume: 12
Subjects:
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 review model equations for parametric surface waves (Faraday waves) in the limit of small viscous dissipation. The equations account for two effects of viscosity, namely damping of the waves and slowly varying streaming and large scale flows (mean flow). Equations for the mean flow can be derived by a multiple scale analysis and are coupled to an order parameter equation describing the evolution of the surface waves. In addition, the equations incorporate a phenomenological damping term due to viscous dissipation. The nonlinear terms, which are undetermined by the derivation of the equation for the surface waves, are chosen so that the primary bifurcation is to a set of standing waves in the form of stripes. Results for the secondary instabilities of the primary waves are presented, including a weak amplification of both Eckhaus and Transverse Amplitude Modulation instabilities due to the mean flow, and a new longitudinal oscillatory instability which is absent without mean flow. Generation of mean flow due to dislocation defects in regular patterns is studied by numerical simulations.

More information

Item ID: 6174
DC Identifier: http://oa.upm.es/6174/
OAI Identifier: oai:oa.upm.es:6174
Official URL: http://ebooks.worldscinet.com/ISBN/9789812567840/9789812567840_0010.html
Deposited by: Memoria de Investigacion 2
Deposited on: 25 Feb 2011 13:24
Last Modified: 20 Apr 2016 15:29
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