dorsal/arxiv
View SchemaAmplitude equations and pattern selection in Faraday waves
| Authors | Peilong Chen, Jorge Vinals |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9712003 |
| URL | https://arxiv.org/abs/patt-sol/9712003 |
| DOI | 10.1103/PhysRevE.60.559 |
| Journal | Phys. Rev. E 60, 559 (1999) |
Abstract
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma much less than 1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold,... patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.
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"abstract": "A nonlinear theory of pattern selection in parametric surface waves (Faraday\nwaves) is presented that is not restricted to small viscous dissipation. By\nusing a multiple scale asymptotic expansion near threshold, a standing wave\namplitude equation is derived from the governing equations. The amplitude\nequation is of gradient form, and the coefficients of the associated Lyapunov\nfunction are computed for regular patterns of various symmetries as a function\nof a viscous damping parameter gamma. For gamma approximately 1, the selected\nwave pattern comprises a single standing wave (stripe pattern). For gamma much\nless than 1, patterns of square symmetry are obtained in the capillary regime\n(large frequencies). At lower frequencies (the mixed gravity-capillary regime),\na sequence of six-fold (hexagonal), eight-fold,... patterns are predicted. For\neven lower frequencies (gravity waves) a stripe pattern is again selected. Our\npredictions of the stability regions of the various patterns are in\nquantitative agreement with recent experiments conducted in large aspect ratio\nsystems.",
"arxiv_id": "patt-sol/9712003",
"authors": [
"Peilong Chen",
"Jorge Vinals"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.60.559",
"journal_ref": "Phys. Rev. E 60, 559 (1999)",
"title": "Amplitude equations and pattern selection in Faraday waves",
"url": "https://arxiv.org/abs/patt-sol/9712003"
},
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