Ratio between Trough and Crest of Surface Waves in the Coastal Zone of the Black Sea

A. S. Zapevalov✉, A. V. Garmashov

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: sevzepter@mail.ru

Abstract

Purpose. The work is aimed at analyzing variability of the ratio between trough and crest of the sea surface waves, as well as the relationship of this ratio with the skewness of sea surface elevations.

Methods and Results. The analysis is based on the wave measurements performed from the stationary oceanographic platform located near the Southern Coast of Crimea in the Black Sea. The depth at the place where the platform is installed is about 30 m. The analyzed data array totals 17,083 twenty-minute measurement sessions. The freak waves were identified by the abnormality index AI equal to the ratio between the maximum wave height per session and the significant wave height. The freak waves with index AI > 2 were observed in 562 measurement sessions. This corresponds to a probability of their occurrence equal to 3.3%. The AI values range from 1.16 to 2.79. The ratio between the trough Th of the highest wave and its crest Cr is in the range 0.37 < Th/Cr < 1.47, at that the average value is 0.79.

Conclusions. Statistical characteristics of the waves revealed in the presence of freak waves differ noticeably from those obtained at AI < 2. In the situations when AI < 2, the probability of an event when the trough Th of the highest wave exceeds its crest Cr is 10.9%. The event with Th/Cr > 1 does not occur if AI < 1.4. When there are waves satisfying condition AI > 2, the probability of an event Th/Cr > 1 is 19.4%. It is shown that condition Th/Cr > 1 is not necessary for arising of a negative skewness of sea surface elevations. The probability of skewness large deviations from a zero value both towards positive values and towards negative ones, is higher at AI > 2 than at AI < 2. The statistical relationship between the skewness and the Th/Cr ratio is observed only for freak waves.

Keywords

sea surface, freak wave, abnormality index, skewness, Black Sea

Acknowledgements

The study was carried out within the framework of state assignment on theme FNNN-2021-0004 “Fundamental studies of oceanological processes which determine state and evolution of marine environment influenced by natural and anthropogenic factors, based on observation and modeling methods”.

Original russian text

Original Russian Text © A. S. Zapevalov, A. V. Garmashov, 2024, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 40, Iss. 1, pp. 78–86 (2024)

For citation

Zapevalov, A.S. and Garmashov, A.V., 2024. Ratio between Trough and Crest of Surface Waves in the Coastal Zone of the Black Sea. Physical Oceanography, 31(1), pp. 71-78.

References

  1. Longuet-Higgins, M.S., 1963. The Effect of Non-Linearities on Statistical Distributions in the Theory of Sea Waves. Journal of Fluid Mechanics, 17(3), pp. 459-480. doi:10.1017/S0022112063001452
  2. Hou, Y., Song, G., Zhao, X., Song, J. and Zheng Q., 2006. Statistical Distribution of Nonlinear Random Water Wave Surface Elevation. Chinese Journal of Oceanology and Limnology, 24(1), pp. 1-5. doi:10.1007/BF02842767
  3. Tayfun, M.A. and Alkhalidi, M.A., 2016. Distribution of Surface Elevations in Nonlinear Seas. In: OTC, 2016. Offshore Technology Conference Asia: Proceedings. Kuala Lumpur, Malaysia. OTC-26436-MS. doi:10.4043/26436-MS
  4. Janssen, P.A.E.M., 2003. Nonlinear Four-Wave Interactions and Freak Waves. Journal of Physical Oceanography, 33(4), pp. 863-884. doi.org/10.1175/1520- 0485(2003)33%3C863:NFIAFW%3E2.0.CO;2
  5. Annenkov, S.Y. and Shrira, V.I., 2014. Evaluation of Skewness and Kurtosis of Wind Waves Parameterized by JONSWAP Spectra. Journal of Physical Oceanography, 44(6), pp. 1582-1594. doi:10.1175/JPO-D-13-0218.1
  6. Jha, A.K. and Winterstein, S.R., 2000. Nonlinear Random Ocean Waves: Prediction and Comparison with Data. In: ASME, 2000. Proceedings of the 19th International Offshore Mechanics and Arctic Engineering Symposium. New Orleans, USA. Paper No. 00-6125.
  7. Guedes Soares, C., Cherneva, Z. and Antão, E.M., 2004. Steepness and Asymmetry of the Largest Waves in Storm Sea States. Ocean Engineering, 31(8-9), pp. 1147-1167. doi:10.1016/j.oceaneng.2003.10.014
  8. Bilyay, E., Ozbahceci, B.O. and Yalciner, A.C., 2011. Extreme Waves at Filyos, Southern Black Sea. Natural Hazards and Earth System Sciences, 11(3), pp. 659-666. doi:10.5194/nhess-11-659- 2011
  9. Zapevalov, A.S. and Garmashov, A.V., 2021. Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea. Physical Oceanography, 28(4), pp. 414-425. doi:10.22449/1573- 160X-2021-4-414-425
  10. Zapevalov, A.S. and Garmashov, A.V., 2022. The Appearance of Negative Values of the Skewness of Sea-Surface Waves. Izvestiya, Atmospheric and Oceanic Physics, 58(3), pp. 263-269. doi:10.1134/s0001433822030136
  11. Kharif, C., Pelinovsky, E. and Slunyaev, A., 2009. Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics. Berlin; Heidelberg: Springer, 216 p. doi:10.1007/978-3-540-88419-4
  12. Glejin, J., Kumar, V.S., Nair, T.B., Singh, J. and Nherakkol, A., 2014. Freak Waves off Ratnagiri, West Coast of India. Indian Journal of Geo-Marine Sciences, 43(7), pp. 1339-1342.
  13. Didenkulova, I. and Anderson, C., 2010. Freak Waves of Different Types in the Coastal Zone of the Baltic Sea. Natural Hazards and Earth System Sciences, 10(9), pp. 2021-2029. doi:10.5194/nhess-10-2021-2010
  14. Toloknov, Yu.N. and Korovushkin, A.I., 2010. The System of Collecting Hydrometeorological Information. In: MHI, 2010. Monitoring Systems of Environment. Sevastopol: ECOSI- Gidrofizika. Iss. 13, pp. 50-53 (in Russian).
  15. Solov'ev, Yu.P. and Ivanov, V.A., 2007. Preliminary Results of Measurements of Atmospheric Turbulence over the Sea. Physical Oceanography, 17(3), pp. 154-172. doi:10.1007/s11110-007- 0013-9
  16. Efimov, V.V. and Komarovskaya, O.I., 2019. Disturbances in the Wind Speed Fields due to the Crimean Mountains. Physical Oceanography, 26(2), pp. 123-134. doi:10.22449/1573-160X- 2019-2-123-134
  17. Ivanov, V.A., Dulov, V.A., Kuznetsov, S.Yu., Dotsenko, S.F., Shokurov, M.V., Saprykina, Ya.V., Malinovsky, V.V. and Polnikov, V.G., 2012. Risk Assessment of Encountering Killer Waves in the Black Sea. Geography, Environment, Sustainability, 5(1), pp. 84-111. doi:10.24057/2071-9388-2012-5-1-84-111
  18. Tao, A.-F., Peng, J., Zheng, J.-H., Wang, Y. and Wu, Y.-Q., 2015. Discussions on the Occurrence Probabilities of Observed Freak Waves. Journal of Marine Science and Technology, 23(6), pp. 923-928. doi:10.6119/JMST-015-0610-10
  19. Zapevalov, A.S. and Garmashov, A.V., 2022. Probability of the Appearance of Abnormal Waves in the Coastal Zone of the Black Sea at the Southern Coast of Crimea. Ecological Safety of the Coastal and Shelf Zones of Sea, (3), pp. 6-15. doi:10.22449/2413-5577-2022-3-6-15
  20. Luxmoore, J.F., Ilic, S. and Mori, N., 2019. On Kurtosis and Extreme Waves in Crossing Directional Seas: A Laboratory Experiment. Journal of Fluid Mechanics, 876, pp. 792-817. doi:10.1017/jfm.2019.575
  21. Fedele, F., Brennan, J., Ponce De León, S., Dudley, J. and Dias, F., 2016. Real World Ocean Rogue Waves Explained without the Modulational Instability. Scientific Reports, 6(1), 27715. doi:10.1038/srep27715

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