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

Abstract

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 (1999) [J. Comput. Phys., v.155, 96]. Its validation is checked against the linear theory. In a nonlinear regime, qualitative comparison is made with an earlier vortex-sheet simulation of two dimensional Faraday waves by Wright et al. (2000) [J. Fluid Mech., v.400, 1]. 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 et al. (1998) [J. Fluid Mech., v.369, 273], is successfully simulated with the present phase-field method.

17 pages, 7 figures

References in corpus (5)

• Amplitude equations and pattern selection in Faraday waves
• Numerical simulation of Faraday waves
• Phase-field model for the Rayleigh--Taylor instability of immiscible fluids
• Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops
• Spatio temporal characterization of interfacial Faraday waves: A new absorption technique

Cited by in corpus (2)

• On the nature of the magnetic Rayleigh-Taylor instability in Astrophysical Plasma: The case of uniform magnetic field strength
• Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally