с 01.01.1972 по 01.01.2024
Севастополь, Россия
УДК 551.466.3 Волнение (ветровые волны) и зыбь
УДК 551.466.326 Статическое распределение волнения
УДК 55 Геология. Геологические и геофизические науки
УДК 550.34 Сейсмология
УДК 550.383 Главное магнитное поле Земли
ГРНТИ 37.01 Общие вопросы геофизики
ГРНТИ 37.15 Геомагнетизм и высокие слои атмосферы
ГРНТИ 37.25 Океанология
ГРНТИ 37.31 Физика Земли
ГРНТИ 38.01 Общие вопросы геологии
ГРНТИ 36.00 ГЕОДЕЗИЯ. КАРТОГРАФИЯ
ГРНТИ 37.00 ГЕОФИЗИКА
ГРНТИ 38.00 ГЕОЛОГИЯ
ГРНТИ 39.00 ГЕОГРАФИЯ
ГРНТИ 52.00 ГОРНОЕ ДЕЛО
ОКСО 05.00.00 Науки о Земле
ББК 26 Науки о Земле
ТБК 63 Науки о Земле. Экология
BISAC SCI SCIENCE
The verification of statistical models of sea surface elevations based on the decomposition of the wave profile into degrees of a small parameter (wave steepness) and in terms of multidimensional integrals of wave spectra was carried out. For verification, wave measurement data were used to calculate the skewness and excess kurtosis of surface elevations, as well as the distribution of crests and troughs. Two factors are identified that limit the use of estimates of skewness Aη and excess kurtosis Eη obtained from existing models. First, the model estimates Aη and Eη are always non-negative, although the measurement data show that the lower limit of the ranges in which the skewness and excess kurtosis change is in the region of negative values. Secondly, almost all existing models are one-parameter models, using wave steepness and wave age as predictors; whereas the measured data indicate that there is no clear relationship. The values of Aη and Eη vary greatly for fixed values of the predictors. Existing statistical models can only describe average changes Aη and Eη. This limits the scope of their application. The analysis of the probability density functions of the troughs FT h and crests FCr showed that the function calculated for Aη < 0 in the region above the distribution mode exceeds the values corresponding to the Rayleigh distribution, and the relationship FT h ≈ FCr holds. The second order nonlinear model is inconsistent with this result. Negative skewness values are observed much less frequently than positive ones, so the functions FT h and FCr calculated for the whole ensemble of situations are consistent with the second-order nonlinear model.
sea surface, statistical models, skewness, excess kurtosis, crest distributions, trough distributions
1. Annenkov, S. Y., and V. I. Shrira (2013), Large-time evolution of statistical moments of wind-wave fields, Journal of Fluid Mechanics, 726, 517–546, https://doi.org/10.1017/jfm.2013.243. EDN: https://elibrary.ru/RJIEDX
2. Annenkov, S. Y., and V. I. Shrira (2014), Evaluation of Skewness and Kurtosis of Wind Waves Parameterized by JONSWAP Spectra, Journal of Physical Oceanography, 44(6), 1582–1594, https://doi.org/10.1175/JPO-D-13-0218.1. EDN: https://elibrary.ru/SPJJXZ
3. Badulin, S. I., V. G. Grigorieva, P. A. Shabanov, et al. (2021), Sea state bias in altimetry measurements within the theory of similarity for wind-driven seas, Advances in Space Research, 68(2), 978–988, https://doi.org/10.1016/j.asr.2019.11.040. EDN: https://elibrary.ru/XICQZH
4. Benjamin, T. B., and J. E. Feir (1967), The disintegration of wave trains on deep water. Part 1. Theory, Journal of Fluid Mechanics, 27(3), 417–430, https://doi.org/10.1017/s002211206700045x.
5. Boccotti, P. (2000), Wave Mechanics for Ocean Engineering. Vol. 64, Elsevier Oceanography Series.
6. Cheng, Y., Q. Xu, L. Gao, et al. (2019), Sea State Bias Variability in Satellite Altimetry Data, Remote Sensing, 11(10), 1176, https://doi.org/10.3390/rs11101176.
7. Donelan, M. A., J. Hamilton, W. H. Hui, and R. W. Stewart (1985), Directional spectra of wind-generated ocean waves, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 315(1534), 509–562, https://doi.org/10.1098/rsta.1985.0054.
8. Forristall, G. Z. (2000), Wave Crest Distributions: Observations and Second-Order Theory, Journal of Physical Oceanography, 30(8), 1931–1943, https://doi.org/10.1175/1520-0485(2000)030<1931:WCDOAS>2.0.CO;2.
9. Gao, Z., Z. Sun, and S. Liang (2020), Probability density function for wave elevation based on Gaussian mixture models, Ocean Engineering, 213, 107,815, https://doi.org/10.1016/j.oceaneng.2020.107815. EDN: https://elibrary.ru/ETUQAK
10. Grigorieva, V. G., S. K. Gulev, and V. D. Sharmar (2020), Validating Ocean Wind Wave Global Hindcast with Visual Observations from VOS, Oceanology, 60(1), 9–19, https://doi.org/10.1134/S0001437020010130. EDN: https://elibrary.ru/BIPGVV
11. Guedes Soares, C., Z. Cherneva, and E. M. Antão (2004), Steepness and asymmetry of the largest waves in storm sea states, Ocean Engineering, 31(8–9), 1147–1167, https://doi.org/10.1016/J.OCEANENG.2003.10.014.
12. Huang, N. E., and S. R. Long (1980), An experimental study of the surface elevation probability distribution and statistics of wind-generated waves, Journal of Fluid Mechanics, 101(1), 179–200, https://doi.org/10.1017/s0022112080001590.
13. Huang, N. E., S. R. Long, C. C. Tung, et al. (1983), A non-Gaussian statistical model for surface elevation of nonlinear random wave fields, Journal of Geophysical Research: Oceans, 88(C12), 7597–7606, https://doi.org/10.1029/JC088iC12p07597.
14. Janssen, P. A. E. M. (2003), Nonlinear Four-Wave Interactions and Freak Waves, Journal of Physical Oceanography, 33(4), 863–884, https://doi.org/10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2.
15. Janssen, P. A. E. M., and J.-R. Bidlot (2009), On the extension of the freak wave warning system and its verification, European Centre for Medium-Range Weather Forecasts, https://doi.org/10.21957/uf1sybog.
16. Jha, A. K., and S. R. Winterstein (2000), Nonlinear Random Ocean Waves: Prediction and Comparison with Data, in ETCE/OMAE Joint Conference Energy for the New Millennium, New Orleans, LA, ASME.
17. Kinsman, B. (1965), Wind waves; their generation and propagation on the ocean surface, Prentice Hall Inc, Englewood Cliffs, N.J.
18. Longuet-Higgins, M. S. (1952), On the statistical distributions of sea waves, Journal of Marine Research, XI(3), 245–261.
19. Longuet-Higgins, M. S. (1957), The statistical analysis of a random, moving surface, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 249(966), 321–387, https://doi.org/10.1098/rsta.1957.0002.
20. Longuet-Higgins, M. S. (1963), The effect of non-linearities on statistical distributions in the theory of sea waves, Journal of Fluid Mechanics, 17(03), 459, https://doi.org/10.1017/S0022112063001452.
21. Luxmoore, J. F., S. Ilic, and N. Mori (2019), On kurtosis and extreme waves in crossing directional seas: a laboratory experiment, Journal of Fluid Mechanics, 876, 792–817, https://doi.org/10.1017/jfm.2019.575. EDN: https://elibrary.ru/RINICP
22. Mikhailichenko, S. Y., A. V. Garmashov, and V. V. Fomin (2016), Verification of the SWAN wind waves model by observations on the stationary oceanographic platform of the Black Sea Hydrophysical Polygon of RAS, Ecological Safety of Coastal and Shelf Zones of Sea, (2), 52–57 (in Russian), EDN: https://elibrary.ru/WKTQOX.
23. Mori, N., and P. A. E. M. Janssen (2006), On Kurtosis and Occurrence Probability of Freak Waves, Journal of Physical Oceanography, 36(7), 1471–1483, https://doi.org/10.1175/jpo2922.1. EDN: https://elibrary.ru/LSBCWP
24. Naess, A. (1985), On the distribution of crest to trough wave heights, Ocean Engineering, 12(3), 221–234, https://doi.org/10.1016/0029-8018(85)90014-9.
25. Pelinovsky, E. N., and E. G. Shurgalina (2016), Formation of freak waves in a soliton gas described by the modified Korteweg-de Vries equation, Doklady Physics, 61(9), 423–426, https://doi.org/10.1134/S1028335816090032. EDN: https://elibrary.ru/XFIOCR
26. Phillips, O. M. (1960), On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions, Journal of Fluid Mechanics, 9(2), 193–217, https://doi.org/10.1017/S0022112060001043.
27. Stansell, P. (2004), Distributions of freak wave heights measured in the North Sea, Applied Ocean Research, 26(1–2), 35–48, https://doi.org/10.1016/j.apor.2004.01.004.
28. Stokes, G. G. (1849), On the Theory of Oscillatory Waves, in Mathematical and Physical Papers vol.1, pp. 197–229, Cambridge University Press, https://doi.org/10.1017/CBO9780511702242.013.
29. Stopa, J. E., F. Ardhuin, A. Babanin, and S. Zieger (2016), Comparison and validation of physical wave parameterizations in spectral wave models, Ocean Modelling, 103, 2–17, https://doi.org/10.1016/j.ocemod.2015.09.003. EDN: https://elibrary.ru/YDENAU
30. Tayfun, M. A., and M. A. Alkhalidi (2016), Distribution of Surface Elevations in Nonlinear Seas, in Offshore Technology Conference Asia. March 22-25, 2016, OTC, Kuala Lumpur, Malaysia, https://doi.org/10.4043/26436-ms.
31. Toffoli, A., J. Monbaliu, M. Onorato, et al. (2007), Second-Order Theory and Setup in Surface Gravity Waves: A Comparison with Experimental Data, Journal of Physical Oceanography, 37(11), 2726–2739, https://doi.org/10.1175/2007JPO3634.1. EDN: https://elibrary.ru/XWUYPL
32. Toffoli, A., E. Bitner-Gregersen, M. Onorato, and A. V. Babanin (2008), Wave crest and trough distributions in a broadbanded directional wave field, Ocean Engineering, 35(17–18), 1784–1792, https://doi.org/10.1016/j.oceaneng.2008.08.010. EDN: https://elibrary.ru/MDTMWB
33. Young, I. R., and M. A. Donelan (2018), On the determination of global ocean wind and wave climate from satellite observations, Remote Sensing of Environment, 215, 228–241, https://doi.org/10.1016/j.rse.2018.06.006.
34. Zakharov, V. E. (1967), The instability of waves in nonlinear dispersive media, Soviet Physics JETP, 24(4), 740–744.
35. Zapevalov, A. S. (2024), Statistical distributions of crests and trough of sea surface waves, Ecological Safety of Coastal and Shelf Zones of Sea, (3), 49–58 (in Russian), EDN: https://elibrary.ru/CYOWEE.
36. Zapevalov, A. S., and A. V. Garmashov (2021), Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea, Physical Oceanography, 28(4), https://doi.org/10.22449/1573-160X-2021-4-414-425. EDN: https://elibrary.ru/BPYYSU
37. Zapevalov, A. S., and A. V. Garmashov (2022), The Appearance of Negative Values of the Skewness of Sea-Surface Waves, Izvestiya, Atmospheric and Oceanic Physics, 58(3), 263–269, https://doi.org/10.1134/s0001433822030136. EDN: https://elibrary.ru/CQGNUW
38. Zapevalov, A. S., and A. V. Garmashov (2024), Ratio between trough and crest of surface waves in the coastal zone of the Black Sea, Physical Oceanography, 31(1), 71–78. EDN: https://elibrary.ru/KEQHHH
39. Zavadsky, A., D. Liberzon, and L. Shemer (2013), Statistical Analysis of the Spatial Evolution of the Stationary Wind Wave Field, Journal of Physical Oceanography, 43(1), 65–79, https://doi.org/10.1175/jpo-d-12-0103.1. EDN: https://elibrary.ru/RJAUDF
