Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea

A. S. Zapevalov✉, A. V. Garmashov

Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation

✉ e-mail: sevzepter@mail.ru

Abstract

Purpose. The aim of the study is to analyze variability of the statistical moments characterizing deviations of the sea surface elevation distributions from the Gaussian.

Methods and Results. Field studies of the sea waves’ characteristics were carried out from the stationary oceanographic platform located in the Black Sea near the Southern coast of Crimea. The data obtained both in summer and winter, were used. The statistical moments were calculated separately for wind waves and swell. The measurements were performed in a wide range of meteorological conditions and wave parameters (wind speed varied from 0 to 26 m/s, wave age – from 0 to 5.2 and steepness – from 0.005 to 0.095). For wind waves, the coefficients of skewness correlation with the waves’ steepness and age were equal to 0.46 and 0.38. The kurtosis correlation coefficients with these parameters were small (0.09 and 0.07), but with the confidence level 99.8% – significant. For swell, the correlation coefficients were 1.5 – 2.0 times lower.

Conclusions. The statistical moments of the sea surface elevations of the third and higher orders are the indicators of the wave field nonlinearity, which should be taken into account when solving a wide range of the applied and fundamental problems. The deviations of the surface elevation distributions from the Gaussian one are not described unambiguously by the steepness and wave age. At the fixed values of these parameters, a large scatter in the skewness and kurtosis of the surface elevations is observed. This imposes significant limitations on the possibility of applying the nonlinear wave models based on the wave profile expansion by small parameter (steepness) degrees, in engineering calculations.

Keywords

sea surface, wind waves, swells, skewness, kurtosis, stationary oceanographic platform, Black Sea

Acknowledgements

The investigation was carried out within the framework of the state task on theme No. 0555-2021-0004 “Fundamental studies of the oceanological processes which determine the state and evolution of the marine environment influenced by natural and anthropogenic factors, based on the observation and modeling methods”.

Original russian text

Original Russian Text © A. S. Zapevalov, A. V. Garmashov, 2021, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 37, Iss. 4, pp. 447-459 (2021)

For citation

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

DOI

10.22449/1573-160X-2021-4-414-425

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