Articles | Volume 24, issue 4
https://doi.org/10.5194/npg-24-581-2017
© 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-24-581-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| Highlight paper
| 
09 Oct 2017
Research article | Highlight paper |
| 09 Oct 2017
Balanced source terms for wave generation within the Hasselmann equation
Vladimir Zakharov
Department of Mathematics, University of Arizona, Tucson, AZ 85721,
USA
Lebedev Physical Institute RAS, Leninsky 53, Moscow 119991,
Russia
Novosibirsk State University, Novosibirsk, 630090, Russia
Waves and Solitons LLC, 1719 W. Marlette Ave., Phoenix, AZ 85015,
USA
Donald Resio
Taylor Engineering Research Institute, University of North
Florida, Jacksonville, FL, USA
Andrei Pushkarev
CORRESPONDING AUTHOR
Department of Mathematics, University of Arizona, Tucson, AZ 85721,
USA
Lebedev Physical Institute RAS, Leninsky 53, Moscow 119991,
Russia
Novosibirsk State University, Novosibirsk, 630090, Russia
Waves and Solitons LLC, 1719 W. Marlette Ave., Phoenix, AZ 85015,
USA
Viewed
Total article views: 6,758 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Dec 2016)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 4,899 | 1,481 | 378 | 6,758 | 343 | 442 |
- HTML: 4,899
- PDF: 1,481
- XML: 378
- Total: 6,758
- BibTeX: 343
- EndNote: 442
Total article views: 6,240 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 09 Oct 2017)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 4,673 | 1,225 | 342 | 6,240 | 329 | 407 |
- HTML: 4,673
- PDF: 1,225
- XML: 342
- Total: 6,240
- BibTeX: 329
- EndNote: 407
Total article views: 518 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Dec 2016)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 226 | 256 | 36 | 518 | 14 | 35 |
- HTML: 226
- PDF: 256
- XML: 36
- Total: 518
- BibTeX: 14
- EndNote: 35
Viewed (geographical distribution)
Total article views: 6,758 (including HTML, PDF, and XML)
Thereof 6,121 with geography defined
and 637 with unknown origin.
Total article views: 6,240 (including HTML, PDF, and XML)
Thereof 5,629 with geography defined
and 611 with unknown origin.
Total article views: 518 (including HTML, PDF, and XML)
Thereof 492 with geography defined
and 26 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
29 citations as recorded by crossref.
- Evolution of wind-induced wave groups in water of finite depth M. Maleewong & R. Grimshaw
- Blowup driven by critical balance in a differential kinetic model of gravity wave turbulence D. Schubring et al.
- SELF-SIMILAR AND LASER-LIKE REGIMES IN NUMERICAL MODELING OF HASSELMANN KINETIC EQUATION FOR OCEAN WAVES A. Pushkarev & V. Zakharov
- Нелинейное усиление океанских волн в проливах A. Pushkarev & V. Zakharov
- Landsat-8 Observations of Foam Coverage under Fetch-Limited Wave Development V. Dulov et al.
- Generation of Wave Groups by Shear Layer Instability R. Grimshaw
- Long-term wave height forecasting using VMD-informer L. Shen et al.
- Quantifying air–water turbulence with moment field equations C. Conroy et al.
- Comparison of Different Models for Wave Generation of The Hasselmann Equation A. Pushkarev
- Nonlinear amplification of ocean waves in straits A. Pushkarev & V. Zakharov
- Quasi-linear approximation for description of turbulent boundary layer and wind wave growth Y. Troitskaya et al.
- Evolution of water wave groups with wind action M. Maleewong & R. Grimshaw
- Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation M. Maleewong & R. Grimshaw
- Evolution of Water Wave Groups in the Forced Benney–Roskes System M. Maleewong & R. Grimshaw
- Wind-Driven Sea Spectra Resilience as a Statistical Attractor A. Pushkarev et al.
- Analytic theory of a wind-driven sea V. Zakharov
- Two-dimensional modulation instability of wind waves R. Grimshaw
- On ST6 Source Terms Model Assessment and Alternative A. Pushkarev et al.
- Invariantnost' evolyutsii spektrov vetrovykh voln v okeane kak statisticheskiy attraktor A. Pushkarev et al.
- Weak‐Turbulent Theory of Wind‐Driven Sea V. Zakharov et al.
- Breather Turbulence: Exact Spectral and Stochastic Solutions of the Nonlinear Schrödinger Equation A. Osborne
- Numerical Considerations for Quantifying Air–Water Turbulence with Moment Field Equations C. Conroy et al.
- Enhanced ocean wave modeling by including effect of breaking under both deep- and shallow-water conditions Y. Xu & X. Yu
- On different approaches to statistical description of ocean waves A. Pushkarev
- A staged calibration strategy for SWAN whitecapping term coefficients to improve significant wave height and mean wave period H. Zhang et al.
- Inconsistent Spectral Evolution in Operational Wave Models due to Inaccurate Specification of Nonlinear Interactions D. Ardag & D. Resio
- Laser-like wave amplification in straits A. Pushkarev
- Highly nonlinear wind waves in Currituck Sound: dense breather turbulence in random ocean waves A. Osborne et al.
- Evolution of water wave packets by wind in shallow water M. Maleewong & R. Grimshaw
29 citations as recorded by crossref.
- Evolution of wind-induced wave groups in water of finite depth M. Maleewong & R. Grimshaw
- Blowup driven by critical balance in a differential kinetic model of gravity wave turbulence D. Schubring et al.
- SELF-SIMILAR AND LASER-LIKE REGIMES IN NUMERICAL MODELING OF HASSELMANN KINETIC EQUATION FOR OCEAN WAVES A. Pushkarev & V. Zakharov
- Нелинейное усиление океанских волн в проливах A. Pushkarev & V. Zakharov
- Landsat-8 Observations of Foam Coverage under Fetch-Limited Wave Development V. Dulov et al.
- Generation of Wave Groups by Shear Layer Instability R. Grimshaw
- Long-term wave height forecasting using VMD-informer L. Shen et al.
- Quantifying air–water turbulence with moment field equations C. Conroy et al.
- Comparison of Different Models for Wave Generation of The Hasselmann Equation A. Pushkarev
- Nonlinear amplification of ocean waves in straits A. Pushkarev & V. Zakharov
- Quasi-linear approximation for description of turbulent boundary layer and wind wave growth Y. Troitskaya et al.
- Evolution of water wave groups with wind action M. Maleewong & R. Grimshaw
- Amplification of Wave Groups in the Forced Nonlinear Schrödinger Equation M. Maleewong & R. Grimshaw
- Evolution of Water Wave Groups in the Forced Benney–Roskes System M. Maleewong & R. Grimshaw
- Wind-Driven Sea Spectra Resilience as a Statistical Attractor A. Pushkarev et al.
- Analytic theory of a wind-driven sea V. Zakharov
- Two-dimensional modulation instability of wind waves R. Grimshaw
- On ST6 Source Terms Model Assessment and Alternative A. Pushkarev et al.
- Invariantnost' evolyutsii spektrov vetrovykh voln v okeane kak statisticheskiy attraktor A. Pushkarev et al.
- Weak‐Turbulent Theory of Wind‐Driven Sea V. Zakharov et al.
- Breather Turbulence: Exact Spectral and Stochastic Solutions of the Nonlinear Schrödinger Equation A. Osborne
- Numerical Considerations for Quantifying Air–Water Turbulence with Moment Field Equations C. Conroy et al.
- Enhanced ocean wave modeling by including effect of breaking under both deep- and shallow-water conditions Y. Xu & X. Yu
- On different approaches to statistical description of ocean waves A. Pushkarev
- A staged calibration strategy for SWAN whitecapping term coefficients to improve significant wave height and mean wave period H. Zhang et al.
- Inconsistent Spectral Evolution in Operational Wave Models due to Inaccurate Specification of Nonlinear Interactions D. Ardag & D. Resio
- Laser-like wave amplification in straits A. Pushkarev
- Highly nonlinear wind waves in Currituck Sound: dense breather turbulence in random ocean waves A. Osborne et al.
- Evolution of water wave packets by wind in shallow water M. Maleewong & R. Grimshaw
Saved (final revised paper)
Latest update: 24 May 2026
Short summary
The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models. Currently, they operate in the
black box with the tuning knobsmodes, since there is no consensus on universal wind input and wave-breaking dissipation source terms, and require re-tuning for different boundary and external conditions. We offer a physically justified framework able to reproduce theoretical properties of the HE and experimental field data without re-tuning of the model.
The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models....
