dorsal/arxiv
View SchemaSecondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves
| Authors | Wenbin Zhang, Jorge Vinals |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9311005 |
| URL | https://arxiv.org/abs/patt-sol/9311005 |
| DOI | 10.1103/PhysRevLett.74.690 |
| Journal | Phys. Rev. Lett. 74, 690 (1995) |
Abstract
A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a periodic standing wave state above onset is studied against Eckhaus, zig-zag and transverse amplitude modulations (TAM) as a function of the control parameter $\varepsilon$ and the detuning. A mechanism leading to a finite threshold for the TAM instability is identified. Numerical solutions of the model are in agreement with the stability diagram, and also reveal the existence of a transition to spatiotemporal chaotic states at a finite $\varepsilon$. Power spectra of temporal fluctuations in the chaotic state are broadband, decaying as a power law of the frequency $\omega^{-z}$ with $z \approx 4.0$.
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"abstract": "A two dimensional model is introduced to study pattern formation, secondary\ninstabilities and the transition to spatiotemporal chaos (weak turbulence) in\nparametric surface waves. The stability of a periodic standing wave state above\nonset is studied against Eckhaus, zig-zag and transverse amplitude modulations\n(TAM) as a function of the control parameter $\\varepsilon$ and the detuning. A\nmechanism leading to a finite threshold for the TAM instability is identified.\nNumerical solutions of the model are in agreement with the stability diagram,\nand also reveal the existence of a transition to spatiotemporal chaotic states\nat a finite $\\varepsilon$. Power spectra of temporal fluctuations in the\nchaotic state are broadband, decaying as a power law of the frequency\n$\\omega^{-z}$ with $z \\approx 4.0$.",
"arxiv_id": "patt-sol/9311005",
"authors": [
"Wenbin Zhang",
"Jorge Vinals"
],
"categories": [
"patt-sol",
"chao-dyn",
"cond-mat",
"nlin.CD",
"nlin.PS"
],
"doi": "10.1103/PhysRevLett.74.690",
"journal_ref": "Phys. Rev. Lett. 74, 690 (1995)",
"title": "Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves",
"url": "https://arxiv.org/abs/patt-sol/9311005"
},
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