Method for Measuring the Dispersion of Capillary Wave Slopes on the Sea Surface

V. V. Sterlyadkin✉, K. V. Kulikovsky, M. V. Likhacheva

MIREA - Russian Technological University, Moscow, Russian Federation

✉ e-mail: sterlyadkin@mail.ru

Abstract

Purpose. The purpose of this study is to substantiate and practically apply a new method for fast (0.01 s) recording of capillary wave parameters under natural conditions.

Methods and Results. The method is based on recording an image of a thin laser beam incidence on the sea surface. The radiation scattered in the water is refracted at the rough interface and is recorded by a video camera located at the side. The beam image deviations are proportional to the surface slopes at the point of radiation exit. The largest slopes, exceeding 30°, are characteristic of capillary waves; this makes the method particularly effective for recording them. It has become possible to record waves with an amplitude of 30 µm from a distance of 5–8 m. When intense capillary ripples occur below the point of beam incidence on the surface, a light “skirt” is formed, the width of which grows with increasing slope. The distribution of the scattered-light intensity in the cross-section of the light “skirt” makes it possible to calculate the slope distributions for each frame or the probability function for a given time interval. The developed method for the operational determination of the distribution of capillary wave slopes is applied to study the capillary structure of various areas of sea waves, namely the crests and troughs. It is established that the dispersion of capillary slopes in the troughs is significantly lower than that on the crests, which is consistent with previously reported data.

Conclusions. A new method for remote measurement of capillary wave slopes on the sea surface is proposed; it permits measurements to be carried out over surface areas of 10 × 10 cm in 0.01 s. The given example shows that at a significant wave height (1.1 ± 0.1) m and a wind speed of (7.4 ± 0.5) m/s, the average dispersion of the capillary component was 0.0256 on the crests and 0.008 in the troughs. The advantage of the method is that it makes it possible to carry out measurements in a wide range of weather conditions, both during the night and the day.

Keywords

capillary waves, in situ measurements, slope distribution, slope dispersion, laser wave recorder

Acknowledgements

The study was carried out with the financial support of the Russian Science Foundation, grant No. 23-17-00189 “Investigation of the relationship between the surface wind and the dynamics of wind wave development on the sea surface and the processes of microwave radiation transfer at the sea surface–atmosphere boundary”, https://rscf.ru/project/23-17-00189/.

About the authors

Viktor V. Sterlyadkin, Professor at the Department of Physics and Technical Mechanics, MIREA - Russian Technological University (78 Prospekt Vernadskogo, Moscow, 119454, Russian Federation), DSc. (Phys.-Math.), ORCID ID: 0000-0002-1832-8608, Web of Science ResearcherID: D‑7125-2017, Scopus Author ID: 6505940691, SPIN-code: 8368-0889, sterlyadkin@mail.ru

Konstantin V. Kulikovsky, Associate Professor at the Department of Physics and Technical Mechanics, MIREA - Russian Technological University (78 Prospekt Vernadskogo, Moscow, 119454, Russian Federation), CSc. (Tech.), ORCID ID: 0000-0001-9296-6424, Scopus Author ID: 57223241696, Web of Science ResearcherID: D-7125-2017, SPIN-code: 8368-0889, constantinkk@mail.ru

Maria V. Likhacheva, Senior Lecturer at the Department of Physics and Technical Mechanics, MIREA - Russian Technological University (78 Prospekt Vernadskogo, Moscow, 119454, Russian Federation), ORCID ID: 0009-0007-6021-080X, Scopus Author ID: 23005642200, Web of Science ResearcherID: OBN-9238-2025, SPIN-code: 4548-9098, likhacheva.m@gmail.com

Original russian text

Original Russian Text © V. V. Sterlyadkin, K. V. Kulikovsky, M. V. Likhacheva, 2026, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 42, Iss. 2, pp. 198–215 (2026)

For citation

Sterlyadkin, V.V., Kulikovsky, K.V. and Likhacheva, M.V., 2026. Method for Measuring the Dispersion of Capillary Wave Slopes on the Sea Surface. Physical Oceanography, 33(2), pp. 246-262.

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