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Numerical simulation of supersquare patterns in Faraday waves

Published online by Cambridge University Press:  08 May 2015

L. Kahouadji ,
N. Périnet ,
L. S. Tuckerman ,
S. Shin ,
J. Chergui  and
D. Juric
L. Kahouadji
Affiliation:
PMMH (UMR 7636 CNRS - ESPCI - UPMC Paris 6 - UPD Paris 7 - PSL), 10 rue Vauquelin, 75005 Paris, France Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
N. Périnet
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
L. S. Tuckerman*
Affiliation:
PMMH (UMR 7636 CNRS - ESPCI - UPMC Paris 6 - UPD Paris 7 - PSL), 10 rue Vauquelin, 75005 Paris, France
S. Shin
Affiliation:
Department of Mechanical and System Design Engineering, Hongik University, Seoul 121-791, Republic of Korea
J. Chergui
Affiliation:
LIMSI-CNRS, Bât 508, rue John von Neumann - 91405 Orsay, France
D. Juric
Affiliation:
LIMSI-CNRS, Bât 508, rue John von Neumann - 91405 Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

We report the first simulations of the Faraday instability using the full three-dimensional Navier–Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid front-tracking/level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in square and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of Douady & Fauve (Europhys. Lett., vol. 6, 1988, pp. 221–226) and Douady (J. Fluid Mech., vol. 221, 1990, pp. 383–409) is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared with the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the centre.

JFM classification

Waves/Free-surface Flows: Faraday waves Nonlinear Dynamical Systems: Pattern formation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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Kahouadji et al. supplementary movie

Evolution of interface height (left) and vertical velocity (right) over one oscillation period in a square container.

Download Kahouadji et al. supplementary movie(Video)
Video 12.7 MB

Kahouadji et al. supplementary movie

Evolution of interface height (left) and vertical velocity (right) over one oscillation period in a cylindrical container.

Download Kahouadji et al. supplementary movie(Video)
Video 13.6 MB