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Numerical simulation of two-dimensional Faraday waves with phase-field modelling

Published online by Cambridge University Press:  23 September 2011

Kentaro Takagi  and
Takeshi Matsumoto
Kentaro Takagi*
Affiliation:
Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kitashirakawa Oiwaketyo Sakyoku, Kyoto 606-8502, Japan
Takeshi Matsumoto
Affiliation:
Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kitashirakawa Oiwaketyo Sakyoku, Kyoto 606-8502, Japan
*
†Email address for correspondence: [email protected]
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Abstract

A fully nonlinear numerical simulation of two-dimensional Faraday waves between two incompressible and immiscible fluids is performed by adopting the phase-field method with the Cahn–Hilliard equation due to Jacqmin (J. Comput. Phys., vol. 155, 1999, pp. 96–127). Its validation is checked against the linear theory. In the nonlinear regime, qualitative comparison is made with an earlier vortex-sheet simulation of two-dimensional Faraday waves by Wright, Yon & Pozrikidis (J. Fluid Mech., vol. 400, 2000, pp. 1–32). The vorticity outside the interface region is studied in this comparison. The period tripling state, which is observed in the quasi-two-dimensional experiment by Jiang, Perlin & Schultz (J. Fluid Mech., vol. 369, 1998, pp. 273–299), is successfully simulated with the present phase-field method.

JFM classification

Waves/Free-surface Flows: Faraday waves Multiphase and Particle-laden Flows: Multiphase flow Instability: Parametric instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 409 - 425
Copyright
Copyright © Cambridge University Press 2011

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