Abstract
Since the discovery of crispations on a vibrating fluid layer, numerous types of patterns formed on fluid surfaces have been revealed. Here we report the observation of polygonal patterns of Faraday waves in vibrating water containers with parabolic and other concave bottoms. These patterns manifest themselves as simple geometric figures of symmetries ranging from elliptical up to heptagonal, with wavelengths much larger than the capillary length. Hence, they are intrinsically different from the previously studied patterns in vibrating drops or puddles and represent a particular variety of nonlinear shallow-water gravity waves or tidal waves in concave basins. Of specific interest is their resemblance to the collective excitations recently discovered in a driven Bose–Einstein condensate, not only sharing identical square-root scaling dispersion and pattern dynamics but also possessing similar nonlinear features like hard-spring nonlinearity. Based on the close correspondence, we propose an analogue of the patterning dynamics for classical and quantum fluid systems subject to confinement and argue that the analogy is mathematically valid even in the nonlinear regime.
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Data availability
The videos of selected experiments and simulations are provided with the supplementary materials.
Code availability
The OpenFOAM case files and the code for simulations of the unified model are available at https://github.com/lxynju/Polygon.
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Acknowledgements
We acknowledge S. Guo for her help with the experiments. This work was supported by the National Science Foundation of China under Grant No. 12174191. We are grateful to the High Performance Computing Center of Nanjing University for carrying out the simulations on its blade cluster system.
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X.W. supervised the research. X.W. and X.L. conceived the experiments. X.L. performed the experiments and simulations. X.W. and X.L. analysed the data and wrote the paper.
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Supplementary Discussion, Figs. 1–10 and Table 1.
Supplementary Video 1
Experimental observation of polygonal patterns in a relatively small paraboloidal container of diameter 20 cm.
Supplementary Video 2
Experimental observation of polygonal patterns in a large Chinese steel pan of diameter 50 cm.
Supplementary Video 3
Direct numerical simulation based on Navier–Stokes equations for real water exactly as same as the experiment in Supplementary Video 1 and for ideal fluid of no dissipation.
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Liu, X., Wang, X. Polygonal patterns of Faraday water waves analogous to collective excitations in Bose–Einstein condensates. Nat. Phys. 20, 287–293 (2024). https://doi.org/10.1038/s41567-023-02294-y
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DOI: https://doi.org/10.1038/s41567-023-02294-y
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