Probability of the Appearance of Abnormal Waves in the Coastal Zone of the Black Sea at the Southern Coast of Crimea

A. S. Zapevalov*, A. V. Garmashov

Marine Hydrophysical Institute of RAS, Sevastopol, Russia

* e-mail: sevzepter@mail.ru

Abstract

The paper analyzes the probability of appearance of abnormal waves in the coastal zone of the Black Sea. The analysis is based on the data of wave measurements carried out on a stationary oceanographic platform of the Marine Hydrophysical Institute of RAS. Two indices were used to identify abnormal waves. The first index AI is the ratio of the maximum and significant wave heights, the second index CI is the ratio of the maximum crest height and significant wave height. The values of the AI index are mainly in the range from 1.25 to 2.75, the values of the CI index are in the range from 0.7 to 1.5. It is shown that both indices are statistically independent of the steepness and the skewness, a high correlation is observed only with the excess kurtosis λ4. The correlation coefficients between AI and λ4 and between CI and λ4 are 0.57 and 0.49, respectively. The probability of appearance of abnormal waves calculated on the basis of the AI index is higher than that calculated on the basis of the CI index. This is explained by the fact that there are three forms of abnormal waves, which are identified as follows: positive form, whose crest is more than 50 % higher than its trough with respect to the mean sea level, negative form, whose troughs are more than 50 % greater than their crests and a sign-variable form (intermediate). The CI index does not allow distinguishing abnormal waves of a negative form and not always distinguishes abnormal waves of a sign-variable form. The correlation coefficient between indices AI and CI is 0.64.

Keywords

abnormal wave, abnormality index, steepness, skewness, excess kurtosis, Black Sea

Acknowledgments

The work was carried out under state assignment of FSBSI FRC MHI no. FNNN-2021-0003, no. FNNN-2022-0003.

For citation

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 the Sea, (3), pp. 6–15. doi:10.22449/2413-5577-2022-3-6-15

DOI

10.22449/2413-5577-2022-3-6-15

References

  1. Divinsky, B.V., Levin, B.V., Lopatukhin, L.I., Pelinovsky, E.N. and Slyunyaev, A.V., 2004. A Freak Wave in the Black Sea: Observations and Simulation. Doklady Earth Sciences, 395(3), pp. 438–443.
  2. 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
  3. Janssen, P.A.E.M., 2003. Nonlinear Four-Wave Interactions and Freak Waves. Journal of Physical Oceanography, 33(4), pp. 863–884. https://doi.org/10.1175/1520-0485(2003)33863:NFIAFW2.0.CO;2
  4. Ruban, V.P., 2013. Rogue Waves at Low Benjamin-Feir Indices: Numerical Study of the Role of Nonlinearity. JETP Letters, 97(12), pp. 686–689. https://doi.org/10.1134/S0021364013120096
  5. Pelinovsky, E.N. and Shurgalina, E.G., 2016. Formation of Freak Waves in a Soliton Gas Described by the Modified Korteweg–de Vries Equation. Doklady Physics, 61(9), 423–426. doi:10.1134/S1028335816090032
  6. Forristall, G.Z., 2005. Understanding Rogue Waves: Are New Physics Really Necessary? In: University of Hawaii, 2005. Proceedings of the 14th ‘Aha Huliko’a Winter Workshop 2005 on Rogue Waves January 25–28, Honolulu, USA. Honolulu: University of Hawaii. Available at: http://www.soest.hawaii.edu/PubServices/2005pdfs/foreword.pdf [Accessed: 8 August 2022].
  7. Hjelmervik, K. and Trulsen, K., 2009. Freak Wave Statistics on Collinear Currents. Journal of Fluid Mechanics, 637, pp. 267–284. doi:10.1017/S0022112009990607
  8. Semedo, A., Sušelj, K., Rutgersson, A. and Sterl, A., 2011. A Global View on the Wind Sea and Swell Climate and Variability from ERA-40. Journal of Climate, 24(5), pp. 1461–1479. doi:10.1175/2010JCLI3718.1
  9. 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
  10. Guedes Soares, C., Cherneva, Z. and Antão, E.M., 2003. Characteristics of Abnormal Waves in North Storm Sea States. Applied Ocean Research, 25(6), pp. 337–344. doi:10.1016/j.apor.2004.02.005
  11. Glejin, J., Kumar, V.S., Nair, T.M.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. Available at: http://nopr.niscpr.res.in/handle/123456789/34450 [Accessed: 8 August 2022].
  12. Cattrell, A.D., Srokosz, M., Moat, B.I. and Marsh, R., 2018. Can Rogue Waves Be Predicted Using Characteristic Wave Parameters? Journal of Geophysical Research: Oceans, 123(8), pp. 5624–5636. doi:10.1029/2018JC013958
  13. 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
  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. 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
  16. Solov'ev, Y.P. and Ivanov, V.A., 2007. Preliminary Results of Measurements of Atmospheric Turbulence over the Sea. Physical Oceanography, 17(3), pp. 154–172. https://doi.org/10.1007/s11110-007-0013-9
  17. 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
  18. 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, 27715. doi:10.1038/srep27715
  19. 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
  20. Mori, N. and Janssen, P.A.E.M., 2006. On Kurtosis and Occurrence Probability of Freak Waves. Journal of Physical Oceanography, 36(7), pp. 1471–1483. doi:10.1175/JPO2922.1
  21. 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. https://doi.org/10.24057/2071-9388-2012-5-1-84-111
  22. 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

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