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Subharmonic capillary–gravity waves in large containers subject to horizontal vibrations

Published online by Cambridge University Press:  17 December 2013

José M. Perez-Gracia ,
Jeff Porter ,
Fernando Varas  and
José M. Vega
José M. Perez-Gracia
Affiliation:
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
Jeff Porter
Affiliation:
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
Fernando Varas
Affiliation:
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
José M. Vega*
Affiliation:
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
*
†Email address for correspondence: josemanuel.vega@upm.es
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Abstract

This paper deals with nearly inviscid, capillary–gravity, modulated waves parametrically excited by monochromatic horizontal vibrations in liquid containers whose width and depth are both large compared with the wavelength of the excited waves. A general linear amplitude equation is derived with appropriate boundary conditions that provides the threshold acceleration and associated spatiotemporal patterns, which compare very well with experimental measurements and visualizations. The primary instability is associated with a pair of complex Floquet multipliers that are close to (but strictly different from) −1, meaning that the instability is not strictly (2:1) subharmonic. The resulting (quasi-periodic) waves are generally oblique, not perpendicular to the vibrating endwalls. The extension of the theory to other confined systems such as vibrating containers of arbitrary shape and vibrating drops is also considered.

JFM classification

Waves/Free-surface Flows: Capillary waves Instability: Parametric instability Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 739 , 25 January 2014 , pp. 196 - 228
Copyright
©2013 Cambridge University Press 

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