Articles | Volume 24, issue 2
https://doi.org/10.5194/npg-24-237-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-237-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
06 Jun 2017
Research article |
| 06 Jun 2017
Ocean swell within the kinetic equation for water waves
P. P. Shirshov Institute of Oceanology of the Russian Academy of
Sciences, Moscow, Russia
Laboratory of Nonlinear Wave Processes, Novosibirsk State University, Novosibirsk, Russia
Vladimir E. Zakharov
P. P. Shirshov Institute of Oceanology of the Russian Academy of
Sciences, Moscow, Russia
Laboratory of Nonlinear Wave Processes, Novosibirsk State University, Novosibirsk, Russia
Department of Mathematics, University of Arizona, Tucson, USA
P. N. Lebedev Physical Institute of the Russian Academy of Sciences,
Moscow, Russia
Waves and Solitons LLC, Phoenix, Arizona, USA
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Cited
21 citations as recorded by crossref.
- Numerical Study of Isotropic Ocean Swell V. Geogjaev et al. https://doi.org/10.1134/S1028334X19120110
- The Phillips spectrum and a model of wind-wave dissipation S. Badulin & V. Zakharov https://doi.org/10.1134/S0040577920030034
- Comparison of Different Models for Wave Generation of The Hasselmann Equation A. Pushkarev https://doi.org/10.1016/j.piutam.2018.03.013
- On Surface Waves Generated by Extra-Tropical Cyclones—Part II: Simulations V. Cheshm Siyahi et al. https://doi.org/10.3390/rs15092377
- 2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time V. Kudryavtsev et al. https://doi.org/10.1029/2020JC016915
- Numerical Simulation of the Sea Surface Rogue Waves within the Framework of the Potential Euler Equations A. Slunyaev & A. Kokorina https://doi.org/10.1134/S0001433820020127
- Weak‐Turbulent Theory of Wind‐Driven Sea V. Zakharov et al. https://doi.org/10.1029/2018EA000471
- Inconsistent Spectral Evolution in Operational Wave Models due to Inaccurate Specification of Nonlinear Interactions D. Ardag & D. Resio https://doi.org/10.1175/JPO-D-17-0162.1
- Numerical analysis of a self-similar turbulent flow in Bose–Einstein condensates B. Semisalov et al. https://doi.org/10.1016/j.cnsns.2021.105903
- A self-similar description of the wave fields generated by tropical cyclones M. Yurovskaya et al. https://doi.org/10.1016/j.ocemod.2023.102184
- Invariantnost' evolyutsii spektrov vetrovykh voln v okeane kak statisticheskiy attraktor A. Pushkarev et al. https://doi.org/10.31857/S0370274X24120162
- Phase‐Coherent Amplification of Ocean Swells Over Submarine Canyons H. Tamura et al. https://doi.org/10.1029/2019JC015301
- Numerical and analytical calculations of the parameters of power-law spectra for deep water gravity waves V. Geogjaev & V. Zakharov https://doi.org/10.1134/S0021364017150012
- Wind-Driven Sea Spectra Resilience as a Statistical Attractor A. Pushkarev et al. https://doi.org/10.1134/S0021364024603932
- Analytic theory of a wind-driven sea V. Zakharov https://doi.org/10.1016/j.piutam.2018.03.005
- Sizing the largest ocean waves using the SWOT mission F. Ardhuin et al. https://doi.org/10.1073/pnas.2513381122
- Deep Learning-Based Inversion Method for Ocean Swell Waveheights From HF Radar Z. Shan et al. https://doi.org/10.1109/TGRS.2025.3606628
- Revealing wave-wave resonant interactions in ocean wind waves D. Maestrini et al. https://doi.org/10.1038/s42005-026-02653-0
- Kats–Kontorovich anisotropic solution in simulations of ocean swell S. Badulin et al. https://doi.org/10.1016/j.physd.2025.134906
- Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations S. Annenkov & V. Shrira https://doi.org/10.1017/jfm.2018.185
- The Caspian Sea as a full-scale experimental facility supported by altimetry measurements of wind-driven waves S. Badulin et al. https://doi.org/10.1016/j.dynatmoce.2025.101554
21 citations as recorded by crossref.
- Numerical Study of Isotropic Ocean Swell V. Geogjaev et al. https://doi.org/10.1134/S1028334X19120110
- The Phillips spectrum and a model of wind-wave dissipation S. Badulin & V. Zakharov https://doi.org/10.1134/S0040577920030034
- Comparison of Different Models for Wave Generation of The Hasselmann Equation A. Pushkarev https://doi.org/10.1016/j.piutam.2018.03.013
- On Surface Waves Generated by Extra-Tropical Cyclones—Part II: Simulations V. Cheshm Siyahi et al. https://doi.org/10.3390/rs15092377
- 2D Parametric Model for Surface Wave Development Under Varying Wind Field in Space and Time V. Kudryavtsev et al. https://doi.org/10.1029/2020JC016915
- Numerical Simulation of the Sea Surface Rogue Waves within the Framework of the Potential Euler Equations A. Slunyaev & A. Kokorina https://doi.org/10.1134/S0001433820020127
- Weak‐Turbulent Theory of Wind‐Driven Sea V. Zakharov et al. https://doi.org/10.1029/2018EA000471
- Inconsistent Spectral Evolution in Operational Wave Models due to Inaccurate Specification of Nonlinear Interactions D. Ardag & D. Resio https://doi.org/10.1175/JPO-D-17-0162.1
- Numerical analysis of a self-similar turbulent flow in Bose–Einstein condensates B. Semisalov et al. https://doi.org/10.1016/j.cnsns.2021.105903
- A self-similar description of the wave fields generated by tropical cyclones M. Yurovskaya et al. https://doi.org/10.1016/j.ocemod.2023.102184
- Invariantnost' evolyutsii spektrov vetrovykh voln v okeane kak statisticheskiy attraktor A. Pushkarev et al. https://doi.org/10.31857/S0370274X24120162
- Phase‐Coherent Amplification of Ocean Swells Over Submarine Canyons H. Tamura et al. https://doi.org/10.1029/2019JC015301
- Numerical and analytical calculations of the parameters of power-law spectra for deep water gravity waves V. Geogjaev & V. Zakharov https://doi.org/10.1134/S0021364017150012
- Wind-Driven Sea Spectra Resilience as a Statistical Attractor A. Pushkarev et al. https://doi.org/10.1134/S0021364024603932
- Analytic theory of a wind-driven sea V. Zakharov https://doi.org/10.1016/j.piutam.2018.03.005
- Sizing the largest ocean waves using the SWOT mission F. Ardhuin et al. https://doi.org/10.1073/pnas.2513381122
- Deep Learning-Based Inversion Method for Ocean Swell Waveheights From HF Radar Z. Shan et al. https://doi.org/10.1109/TGRS.2025.3606628
- Revealing wave-wave resonant interactions in ocean wind waves D. Maestrini et al. https://doi.org/10.1038/s42005-026-02653-0
- Kats–Kontorovich anisotropic solution in simulations of ocean swell S. Badulin et al. https://doi.org/10.1016/j.physd.2025.134906
- Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations S. Annenkov & V. Shrira https://doi.org/10.1017/jfm.2018.185
- The Caspian Sea as a full-scale experimental facility supported by altimetry measurements of wind-driven waves S. Badulin et al. https://doi.org/10.1016/j.dynatmoce.2025.101554
Saved (final revised paper)
Latest update: 09 Jun 2026
Short summary
In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.
In our simulations of sea swell, we show that its evolution exhibits remarkable features of...
