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Geometrical focusing of surface waves
Phys. Rev. Fluids 3, 094803 – Published 5 September, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.094803
Abstract
In this paper we investigate experimentally the waves produced by a parabolically shaped wave maker partially immersed into a water-filled basin and oscillating in the vertical direction. The main motivation of our study is to follow the analogy between light waves that focus on caustics, creating zones of intense light concentration, and surface waves in liquids. Similarly to light focusing, the surface waves undergo spatial focusing leading to the growth of their amplitudes till they reach a cusp singularity. We detect three regimes. In the first one, which corresponds to small forcing amplitudes, the wave field agrees well with geometrical optics and with Pearcey diffraction theory near the caustics. In the second regime, weak nonlinearities are detected. However, waves still focus as predicted. In the third regime, at large forcing amplitude, a large-scale mean flow is generated. This flow is concentrated in two symmetric jets emerging from the wave maker front wall and producing two counter-rotating eddies because of the finite size of the basin. This large-scale flow modifies the shape of the wave fronts and leads to a displacement of the cusp towards the wave maker, modifying the analogy between light and surface waves.
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References (19)
- M. Perlin, W. Choi, and Z. Tian, Breaking waves in deep and intermediate waters, Annu. Rev. Fluid Mech. 45, 115 (2013).
- L. Deike, W. Kendall Melville, and S. Popinet, Air entrainment and bubble statistics in breaking waves, J. Fluid Mech. 801, 91 (2016).
- N. E. Pizzo, L. Deike, and W. Kendall Melville, Current generation by deep-water breaking waves, J. Fluid Mech. 803, 275 (2016).
- A. Babanin, Breaking and Dissipation of Surface Waves (Cambridge University Press, Cambridge, 2011).
- J. Touboul and C. C. Kharif, Effects of vorticity on the generation of rogue waves due to dispersive focusing, Nat. Hazard 84 (Suppl. 2), 585 (2016).
- C. Fochesato, S. Grilli, and F. Dias, Numerical modeling of extreme rogue waves generated by directional energy focusing, Wave motion 44, 395 (2007).
- M. S. Longuet-Higgins, Breaking waves—In deep or shallow waters, in 10th Symp. on Naval Hydrodynamics, edited by Ralph D. Cooper and Stanley W. Doroff (Office of Naval Research, Department of Navy, Arlington, VA, 1974), p. 597.
- R. J. Rapp and W. K. Melville, Laboratory experiments of deep-water breaking waves, Phil. Trans. R. Soc. Lond. A 331, 735 (1990).
- K. She, C. A. Greated, and W. J. Easson, Experimental study of three-dimensional breaking wave kinematics, Appl. Ocean Res. 19, 329 (1997).
- Y. Pomeau, Caustics of nonlinear waves and related questions, Europhys. Lett. 11, 713 (1990).
- I. Pearcey, The structure of an electromagnetic field in the neighborhood of a cusp of a caustic, Phylos. Mag. 37, 311 (1946).
- J. Tejerina-Risso and P. Le Gal, Around the cusp singularity and the breaking of waves, Leonardo 47, 80 (2014).
- G. Ruiz Chavarria, P. Le Gal, M. Le Bars, and Y. Pomeau, Focalisation d'ondes de surface et déferlement, in Actes du XXe Congrès Français de Mécanique, edited by P. Picart, D. Chapelle, and M. Dahan (Presses Universitaires de la Franche-Comté, Besançon, France, 2012), p. 775.
- G. B. Airy, On the intensity of light in the neighbourhoud of a caustic, Trans. Cambridge Philos. Soc. 6, 379 (1838).
- F. Moisy, M. Rabaud, and K. Salsac, A synthetic Schlieren method for the measurement of the topography of a liquid surface, Exp. Fluids 46, 1021 (2009).
- P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, Global measurement of water waves by Fourier transform profilometry, Exp. Fluids 46, 1037 (2009).
- P. Meunier and T. Leweke, Analysis and minimization of errors due to high gradients in particle image velocimetry, Exp. Fluids 35, 408 (2003).
- G. Stokes, On the theory of the oscillatory waves, Trans. Cambridge Philos. Soc. 8, 441 (1847).
- H. Punzmann, N. Francois, H. Xia, G. Falcovich, and M. Shats, Generation and reversal of surface flows by propagating waves, Nat. Phys. 10, 658 (2014).
