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Onset patterns in a simple model of localized parametric forcing.
MedLine Citation:
PMID:  24229255     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
We investigate pattern selection at onset in a parametrically and inhomogeneously forced partial differential equation obtained by generalizing Mathieu's equation to include spatial interactions. No separation of scales is assumed. The proposed model is directly relevant to the case of parametrically forced surface waves, such as cross-waves, excited by the horizontal vibration of a fluid, where the forcing is localized to a finite region near the endwall or wavemaker. The availability of analytical solutions in the limit of piecewise constant forcing allows us investigate in detail the dependence of selected eigenfunctions on spatial detuning, forcing width, damping, boundary conditions, and container size. A wide range of onset patterns are located and described, many of which are rotated, modulated, or both, and deviate far from simple crosswise oriented standing waves. The linear selection mechanisms governing this multiplicity of potential onset patterns are discussed.
Authors:
J Porter; I Tinao; A Laverón-Simavilla; J Rodríguez
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Publication Detail:
Type:  Journal Article     Date:  2013-10-21
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  88     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2013 Oct 
Date Detail:
Created Date:  2013-11-15     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  042913     Citation Subset:  IM    
Affiliation:
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain.
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