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. Negative Skewness of Sea Surface Elevation and Freak Waves. Physical Oceanography, 31(1), pp. 71-78.

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