2021-04-19T09:27:14Z
http://oa.upm.es/cgi/oai2
oai:oa.upm.es:6174
2016-04-20T15:29:08Z
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Mean Flow Effects in Model Equations for Faraday Waves
Rüdiger, Sten
Vega de Prada, José Manuel
Mathematics
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.
E.T.S.I. Aeronáuticos (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
2004
info:eu-repo/semantics/bookPart
Book Section
Mean Flow Effects in Model Equations for Faraday Waves | En: Dynamics and Bifurcation of Patterns in Dissipative Systems | pag. 174-193 | World Scientific Publishing | 2004
PeerReviewed
application/pdf
eng
http://ebooks.worldscinet.com/ISBN/9789812567840/9789812567840_0010.html
info:eu-repo/semantics/openAccess
http://oa.upm.es/6174/