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Soliton gas dynamics and rogue wave enhancement in a natural coastal environment

Rodrigo Cienfuegos1,2,3,*, Patricio A. Catalán4, Raúl P. Flores4, Maricarmen Guerra2,5, Felipe Lucero3, José Galaz1,2, Sander Wahls6, Paola Díaz1, Rodolfo Gómez1 et al.

César Esparza1,2

  • *Contact author: rcienfue@uc.cl
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Phys. Rev. Research 7, 043129 – Published 3 November, 2025

DOI: https://doi.org/10.1103/9zhq-j1sj

Abstract

We document a field experiment in which a path to strongly interacting soliton gas dynamics is observed within an intermittently open/closed estuary. We show that the shallow estuary mouth acts as a low-pass filter for incoming ocean waves, damping energy within the swell frequency band (0.04–1 Hz) and allowing surf-zone generated infragravity waves (frequency band 0.004–0.04 Hz) to enter the semienclosed shallow lagoon formed near the estuary mouth. These long waves penetrate under highly nonlinear conditions with Ursell numbers consistent with multisoliton fission regimes. The k–ω spectrum of the incident wave trains is consistent with solitonic kinematics, demonstrating that solitons are released by the fission of incoming infragravity waves at the lagoon entrance. Continuous injection of solitonic wave trains and intense wave-wave interactions enhanced by the shallow and gradually varying bathymetry within the estuary lagoon lead to a quasistationary soliton gas regime with a substantially increased probability of rogue wave occurrence compared with linear wave theory. The Korteweg-de Vries nonlinear Fourier transform reveals that nearly half of the measured signal energy is explained by solitonic modes, confirming the key role that solitons have in enhancing rogue wave emergence in natural coastal settings.

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References (76)

  1. J. E. Allen, The early history of solitons (solitary waves), Phys. Scr. 57, 436 (1998).
  2. N. J. Zabusky and M. D. Kruskal, Interaction of “solitons” in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett. 15, 240 (1965).
  3. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford University Press, Oxford, UK, 1995).
  4. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Discrete solitons in optics, Phys. Rep. 463, 1 (2008).
  5. S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, and S. A. Derevyanko, Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives, Optica 4, 307 (2017).
  6. P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Microresonator-based solitons for massively parallel coherent optical communications, Nature (London) 546, 274 (2017).
  7. V. D. Djordjevic and L. G. Redekopp, The fission and disintegration of internal solitary waves moving over two-dimensional topography, J. Phys. Oceanogr. 8, 1016 (1978).
  8. A. R. Osborne, Nonlinear ocean waves and the inverse scattering transform, Scattering, edited by R. Pike and P. Sabatier (Academic Press, London, 2010), Vol. 97.
  9. A. Chabchoub, N. Hoffmann, and N. P. Akhmediev, Rogue wave observation in a water wave tank, Phys. Rev. Lett. 106, 204502 (2011).
  10. M. J. Ablowitz and D. E. Baldwin, Nonlinear shallow ocean-wave soliton interactions on flat beaches, Phys. Rev. E 86, 036305 (2012).
  11. M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Rogue waves and their generating mechanisms in different physical contexts, Phys. Rep. 528, 47 (2013).
  12. A. Costa, A. R. Osborne, D. T. Resio, S. Alessio, E. Chrivì, E. Saggese, K. Bellomo, and C. E. Long, Soliton turbulence in shallow water ocean surface waves, Phys. Rev. Lett. 113, 108501 (2014).
  13. A. Slunyaev, Persistence of hydrodynamic envelope solitons: Detection and rogue wave occurrence, Phys. Fluids 33, 036606 (2021).
  14. I. Teutsch, M. Brühl, R. Weisse, and S. Wahls, Contribution of solitons to enhanced rogue wave occurrence in shallow depths: a case study in the southern North Sea, Nat. Hazards Earth Syst. Sci. 23, 2053 (2023).
  15. N. J. Zabusky and C. J. Galvin, Shallow-water waves, the Korteweg-deVries equation and solitons, J. Fluid Mech. 47, 811 (1971).
  16. H. Yeh, W. Li, and Y. Kodama, Mach reflection and KP solitons in shallow water, Eur. Phys. J.: Spec. Top. 185, 97 (2010).
  17. I. Redor, E. Barthélemy, H. Michallet, M. Onorato, and N. Mordant, Experimental evidence of a hydrodynamic soliton gas, Phys. Rev. Lett. 122, 214502 (2019).
  18. V. E. Zakharov, Kinetic equation for solitons, Sov. Phys. JETP 33, 538 (1971).
  19. G. A. El and A. M. Kamchatnov, Kinetic equation for a dense soliton gas, Phys. Rev. Lett. 95, 204101 (2005).
  20. P. Suret, S. Randoux, A. Gelash, D. Agafontsev, B. Doyon, and G. El, Soliton gas: Theory, numerics, and experiments, Phys. Rev. E 109, 061001 (2024).
  21. A. E. Gennady, Soliton gas in integrable dispersive hydrodynamics, J. Stat. Mech.: Theory Exp. (2021) 114001.
  22. F. Mitschke, G. Steinmeyer, and A. Schwache, Generation of one-dimensional optical turbulence, Physica D 96, 251 (1996).
  23. P. Walczak, S. Randoux, and P. Suret, Optical rogue waves in integrable turbulence, Phys. Rev. Lett. 114, 143903 (2015).
  24. P. Suret, R. E. Koussaifi, A. Tikan, C. Evain, S. Randoux, C. Szwaj, and S. Bielawski, Single-shot observation of optical rogue waves in integrable turbulence using time microscopy, Nat. Commun. 7, 13136 (2016).
  25. P. Suret, A. Tikan, F. Bonnefoy, F. Copie, G. Ducrozet, A. Gelash, G. Prabhudesai, G. Michel, A. Cazaubiel, E. Falcon, G. El, and S. Randoux, Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves, Phys. Rev. Lett. 125, 264101 (2020).
  26. T. Leduque, E. Barthélemy, H. Michallet, J. Sommeria, and N. Mordant, Space–time statistics of 2D soliton gas in shallow water studied by stereoscopic surface mapping, Exp. Fluids 65, 84 (2024).
  27. G. Marcucci, D. Pierangeli, A. J. Agranat, R.-K. Lee, E. DelRe, and C. Conti, Topological control of extreme waves, Nat. Commun. 10, 5090 (2019).
  28. S. Randoux, P. Walczak, M. Onorato, and P. Suret, Intermittency in integrable turbulence, Phys. Rev. Lett. 113, 113902 (2014).
  29. S. Randoux, P. Walczak, M. Onorato, and P. Suret, Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency, Physica D 333, 323 (2016).
  30. D. S. Agafontsev, S. Randoux, and P. Suret, Extreme rogue wave generation from narrowband partially coherent waves, Phys. Rev. E 103, 032209 (2021).
  31. T. Congy, G. El, G. Roberti, A. Tovbis, S. Randoux, and P. Suret, Statistics of extreme events in integrable turbulence, Phys. Rev. Lett. 132, 207201 (2024).
  32. V. E. Zakharov, Turbulence in integrable systems, Stud. Appl. Math. 122, 219 (2009).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9zhq-j1sj for contextual oceanographic, hydrographic and estuarine conditions during the reported field campaign.
  34. D. Khojasteh, S. Rao, S. McSweeney, R. Ibaceta, R. J. Nicholls, J. French, W. Glamore, J. L. Largier, J. Adams, M. G. Hughes, M. Barry, H. E. Power, J. Du, T. A. Tucker, R. Cienfuegos, P. A. Catalan, and D. Hanslow, Intermittent estuaries deserve global attention as vulnerable and vital ecosystems, Commun. Earth Environ. 6, 443 (2025).
  35. R. Cienfuegos, P. A. Catalán, F. Lucero, P. Díaz, R. Flores, M. Guerra, F. Venegas, A. Ossandón, and L. Araya, Continuous interannual monitoring of artificial and natural breachings of an intermittently open/closed estuary in central Chile, in Proceedings of the Coastal Dynamics 2025 Conference, Aveiro, Portugal (Springer Nature, London, 2025).
  36. R. Cienfuegos, P. A. Catalan, R. Flores, M. Guerra, J. Galaz, E. Magaña, and F. Lucero, Dataset for “Soliton gas dynamics and rogue wave enhancement in a natural coastal environment” [Data set], Zenodo (2025), doi:10.5281/zenodo.17192781.
  37. P. Bonneton, D. Lannes, K. Martins, and H. Michallet, A nonlinear weakly dispersive method for recovering the elevation of irrotational surface waves from pressure measurements, Coastal Eng. 138, 1 (2018).
  38. A. Grinsted, J. C. Moore, and S. Jevrejeva, Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes Geophys. 11, 561 (2004).
  39. https://grinsted.github.io/wavelet-coherence/.
  40. S. Winder, Analog and Digital Filter Design, 2nd ed. (Elsevier, 2002).
  41. T. H. C. Herbers, S. Elgar, and R. T. Guza, Infragravity-frequency (0.005–0.05 Hz) motions on the shelf. Part I: Forced waves, J. Phys. Oceanogr. 24, 917 (1994).
  42. T. H. C. Herbers, S. Elgar, R. T. Guza, and W. C. O'Reilly, Infragravity-frequency (0.005–0.05 Hz) motions on the shelf. Part II: Free waves, J. Phys. Oceanogr. 25, 1063 (1995).
  43. A. Sheremet, R. T. Guza, S. Elgar, and T. H. C. Herbers, Observations of nearshore infragravity waves: Seaward and shoreward propagating components, J. Geophys. Res.: Oceans 107, 10-1 (2002).
  44. X. Bertin et al., Infragravity waves: From driving mechanisms to impacts, Earth-Sci. Rev. 177, 774 (2018).
  45. M. J. Tucker and E. G. Pitt, Waves in Ocean Engineering (Elsevier, 2001), Vol. 5.
  46. J. Gemmrich and L. Cicon, Generation mechanism and prediction of an observed extreme rogue wave, Sci. Rep. 12, 1718 (2022).
  47. K. T. Holland, R. A. Holman, T. C. Lippmann, J. Stanley, and N. Plant, Practical use of video imagery in nearshore oceanographic field studies, IEEE J. Oceanic Eng. 22, 81 (1997).
  48. G. Bradski, The OpenCV library, Dr. Dobb’s J. Software Tools 3 (2000).
  49. https://www.planet.com.
  50. E. Magaña, F. S. Costabal, and W. Brevis, Image velocimetry using direct displacement field estimation with neural networks for fluids, arXiv:2501.18641.
  51. I. Redor, H. Michallet, N. Mordant, and E. Barthélemy, Experimental study of integrable turbulence in shallow water, Phys. Rev. Fluids 6, 124801 (2021).
  52. S. Trillo, G. Deng, G. Biondini, M. Klein, G. F. Clauss, A. Chabchoub, and M. Onorato, Experimental observation and theoretical description of multisoliton fission in shallow water, Phys. Rev. Lett. 117, 144102 (2016).
  53. R. Cienfuegos, E. Barthélemy, and P. Bonneton, Wave-breaking model for Boussinesq-type equations including roller effects in the mass conservation equation, J. Waterw. Port Coastal Ocean Eng. 136, 10 (2010).
  54. R. Cienfuegos, Surfing waves from the ocean to the river with the Serre-Green-Naghdi equations, J. Hydraul. Eng. 149, 04023032 (2023).
  55. E. Mignot and R. Cienfuegos, On the application of a Boussinesq model to river flows including shocks, Coastal Eng. 56, 23 (2009).
  56. J. D. Carter, D. Henderson, and P. Panayotaros, The spatial Whitham equation, J. Fluid Mech. 996, A42 (2024).
  57. M. Brühl, P. J. Prins, S. Ujvary, I. Barranco, S. Wahls, and P. L.-F. Liu, Comparative analysis of bore propagation over long distances using conventional linear and KdV-based nonlinear Fourier transform, Wave Motion 111, 102905 (2022).
  58. Y.-C. Lee, M. Brühl, and S. Wahls, When do JONSWAP spectra lead to soliton gases in deep water conditions? in International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2023), Vol. 86878, p. V005T06A101.
  59. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for solving the Korteweg-deVries equation, Phys. Rev. Lett. 19, 1095 (1967).
  60. S. Wahls, S. Chimmalgi, and P. J. Prins, FNFT: A software library for computing nonlinear Fourier transforms, J. Open Source Software 3, 597 (2018).
  61. P. J. Prins and S. Wahls, Reliable computation of the eigenvalues of the discrete KdV spectrum, Appl. Math. Comput. 433, 127361 (2022).
  62. P. de Koster, M. Brühl, and S. Wahls, Water-depth identification from free-surface data using the KdV-based nonlinear Fourier transform, in International Conference on Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers, 2022), Vol. 85901, p. V05BT06A056.
  63. S. L. McSweeney, J. C. Stout, and D. M. Kennedy, Variability in infragravity wave processes during estuary artificial entrance openings, Earth Surf. Processes Landforms 45, 3414 (2020).
  64. P. Müller, C. Garrett, and A. Osborne, Rogue waves, Oceanography 18, 66 (2005).
  65. K. Dysthe, H. E. Krogstad, and P. Müller, Oceanic rogue waves, Annu. Rev. Fluid Mech. 40, 287 (2008).
  66. D. Dutykh and E. Pelinovsky, Numerical simulation of a solitonic gas in KdVand KdV–BBM equations, Phys. Lett. A 378, 3102 (2014).
  67. E. Pelinovsky and A. Sergeeva, Numerical modeling of the KdV random wave field, Eur. J. Mech. B Fluids 25, 425 (2006).
  68. G. Symonds, D. A. Huntley, and A. J. Bowen, Two-dimensional surf beat: Long wave generation by a time-varying breakpoint, J. Geophys. Res.: Oceans 87, 492 (1982).
  69. T. Moura and T. Baldock, Remote sensing of the correlation between breakpoint oscillations and infragravity waves in the surf and swash zone, J. Geophys. Res.: Oceans 122, 3106 (2017).
  70. M. E. Williams and M. T. Stacey, Tidally discontinuous ocean forcing in bar‐built estuaries: The interaction of tides, infragravity motions, and frictional control, J. Geophys. Res.: Oceans 121, 571 (2016).
  71. X.-M. Li, A new insight from space into swell propagation and crossing in the global oceans, Geophys. Res. Lett. 43, 5202 (2016).
  72. J. D. Carter and R. Cienfuegos, The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations, Eur. J. Mech. B Fluids 30, 259 (2011).
  73. D. Mitsotakis, D. Dutykh, and J. Carter, On the nonlinear dynamics of the traveling-wave solutions of the Serre system, Wave Motion 70, 166 (2017).
  74. S. Tkachenko, S. Gavrilyuk, and K.-M. Shyue, Hyperbolicity of the modulation equations for the Serre–Green–Naghdi model, Water Waves 2, 299 (2020).
  75. Y. Goda, Random Seas and Design of Maritime Structures (World Scientific Publishing Company, Singapore, 2010), Vol. 33.
  76. V. E. Zakharov, Weak turbulence in media with a decay spectrum, J. Appl. Mech. Tech. Phys. 6, 22 (1965).

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Phys. Rev. Research 7, 043129– Published 3 November, 2025
  • Received 30 November 2023
  • Accepted 23 September 2025
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