Numerical simulation of Faraday waves oscillated by two-frequency forcing

Abstract

We perform a numerical simulation of Faraday waves forced with two-frequency oscillations using a level-set method with Lagrangian-particle corrections (particle level-set method). After validating the simulation with the linear stability analysis, we show that square, hexagonal and rhomboidal patterns are reproduced in agreement with the laboratory experiments [Arbell and Fineberg, Phys. Rev. Lett. 84, 654 (2000) and Phys. Rev. Lett. 85, 756 (2000)]. We also show that the particle level-set's high degree of conservation of volume is necessary in the simulations. The numerical results of the rhomboidal states are compared with weakly nonlinear analysis. Difficulty in simulating other patterns of the two-frequency forced Faraday waves is discussed.

20 pages, 12 figures

References in corpus (15)

• Superlattice Patterns in Surface Waves
• Pattern formation in 2-frequency forced parametric waves
• Persistent holes in a fluid
• Numerical simulation of Faraday waves
• Parametrically Excited Surface Waves: Two-Frequency Forcing, Normal Form Symmetries, and Pattern Selection
• Two-frequency forced Faraday waves: Weakly damped modes and pattern selection
• Pattern formation in weakly damped parametric surface waves driven by two frequency components
• Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops
• Multi-frequency control of Faraday wave patterns
• Spatio temporal characterization of interfacial Faraday waves: A new absorption technique
• Alternating hexagonal and striped patterns in Faraday surface waves
• Broken symmetries and pattern formation in two-frequency forced Faraday waves
• Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves
• Spatial period-multiplying instabilities of hexagonal Faraday waves
• Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcing