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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">hydrophysics</journal-id><journal-title-group><journal-title xml:lang="ru">Фундаментальная и прикладная гидрофизика</journal-title><trans-title-group xml:lang="en"><trans-title>Fundamental and Applied Hydrophysics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2073-6673</issn><issn pub-type="epub">2782-5221</issn><publisher><publisher-name>St. Petersburg Research Center of the Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.59887/fpg/5g5t-4mzd-94ab</article-id><article-id custom-type="elpub" pub-id-type="custom">hydrophysics-676</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФУНДАМЕНТАЛЬНЫЕ ВОПРОСЫ ГИДРОФИЗИКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FUNDAMENTAL ISSUES OF HYDROPHYSICS</subject></subj-group></article-categories><title-group><article-title>Оценка времени жизни «барашка» обрушивающейся волны</article-title><trans-title-group xml:lang="en"><trans-title>Estimation of the “whitecap” lifetime of breaking wave</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кориненко</surname><given-names>А. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Korinenko</surname><given-names>A. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>299011, Капитанская ул., 2, г. Севастополь</p></bio><bio xml:lang="en"><p>299011, Kapitanskaya Str., 2, Sevastopol</p></bio><email xlink:type="simple">korinenko.alex@mhi-ras.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Малиновский</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Malinovsky</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>299011, Капитанская ул., 2, г. Севастополь</p></bio><bio xml:lang="en"><p>299011, Kapitanskaya Str., 2, Sevastopol</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дулов</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Dulov</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>299011, Капитанская ул., 2, г. Севастополь</p></bio><bio xml:lang="en"><p>299011, Kapitanskaya Str., 2, Sevastopol</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кудрявцев</surname><given-names>В. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Kudryavtsev</surname><given-names>V. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>299011, Капитанская ул., 2, г. Севастополь; 195196, Малоохтинский пр., д. 98, г. Санкт-Петербург</p></bio><bio xml:lang="en"><p>299011, Kapitanskaya Str., 2, Sevastopol; 195196, Malookhtinsky Pr., 98, St. Petersburg</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Морской гидрофизический институт, РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Marine Hydrophysical Institute, Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Морской гидрофизический институт, РАН; Российский государственный гидрометеорологический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Marine Hydrophysical Institute, Russian Academy of Sciences; Russian State Hydrometeorological University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>01</day><month>04</month><year>2022</year></pub-date><volume>15</volume><issue>1</issue><fpage>61</fpage><lpage>72</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Кориненко А.Е., Малиновский В.В., Дулов В.А., Кудрявцев В.Н., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Кориненко А.Е., Малиновский В.В., Дулов В.А., Кудрявцев В.Н.</copyright-holder><copyright-holder xml:lang="en">Korinenko A.E., Malinovsky V.V., Dulov V.A., Kudryavtsev V.N.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://hydrophysics.spbrc.ru/jour/article/view/676">https://hydrophysics.spbrc.ru/jour/article/view/676</self-uri><abstract><p>Представлены результаты исследования времени жизни обрушений ветровых волн (барашков) и пространственного распределения моментов зарождения обрушений по профилю длинной поверхностной волны, полученные в ходе специализированных экспериментов с океанографической платформы в Черном море. Регистрация барашков осуществлялась по видеозаписям морской поверхности. Одновременно с видеозаписями измерялись характеристики поверхностного волнения, а также регистрировалась метеорологическая информация. Показано, что распределение времени жизни барашка хорошо описывается экспоненциальным законом. Установлено, что отношение времени жизни индивидуального барашка к периоду обрушивающейся волны равно 0,3, а распределения этого отношения подобны для различных ветровых и волновых условий. Показано, что зарождение барашков происходит преимущественно в районе гребня длинной волны со смещением на ее передний склон в среднем на 9,6° фазы длинной волны. Возникнув на переднем фронте, барашек за время жизни смещается на задний фронт длинной волны, так что разность фаз между зарождением обрушения и максимумом доли поверхности, занятой барашками, составляет 21,6°.</p></abstract><trans-abstract xml:lang="en"><p>The paper presents the results of a study of the lifetime of wind-wave breaking (“whitecaps”) and the spatial distribution of the moments of wave-breaking initiation along the profile of a long surface wave. The results obtained during the specialized experiments from an oceanographic platform in the Black Sea are given. The registration of the whitecaps was carried out based on the video recordings of the sea surface. The surface waves’ characteristics were measured and the meteorological information was recorded simultaneously with the video recordings. It is shown that the distribution of the whitecaps’ lifetime is well described by an exponential law. It was found that the ratio of the lifetime of an individual whitecap to the period of the breaking wave is 0.3. The distributions of the above-mentioned ratio are similar for different wind and wave conditions. It is indicated that the generation of whitecaps occurs mainly in the region of the crest of a long wave with a shift to its front slope on average by 9.6 of the phase of the long wave. The whitecap having arisen at the leading edge shifts to the trailing edge of the long wave during its lifetime, so that the phase difference between the breaking initiation and the maximum of the surface fraction covered by the whitecaps equals 21.6.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>обрушения ветровых волн</kwd><kwd>время жизни барашка</kwd><kwd>натурные исследования</kwd><kwd>начальный момент обрушения ветровой волны</kwd><kwd>модуляция обрушений коротких волн длинными волнами</kwd></kwd-group><kwd-group xml:lang="en"><kwd>wind wave breaking</kwd><kwd>whitecap lifetime</kwd><kwd>field studies</kwd><kwd>initial moment of wind wave breaking</kwd><kwd>modulation of short wave breaking by long waves</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена по проекту Российского научного фонда № 21-17-00236, https://rscf.ru/project/21-17-00236/ с использованием архивных данных, полученных в рамках государственных заданий 0555-2021-0004 и 0763-2020-0005</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Zappa C.J., McGillis W.R., Raymond P.A., Edson J.B., Hintsa E.J., Zemmelink H.J., Dacey J.W.H., Ho D.T. Environmental turbulent mixing controls on air-water gas exchange in marine and aquatic systems // Journal of Geophysical Research Letters. 2007. Vol. 34, No 10. doi: 10.1029/2006GL028790</mixed-citation><mixed-citation xml:lang="en">Zappa C.J., McGillis W.R., Raymond P.A., Edson J.B., Hintsa E.J., Zemmelink H.J., Dacey J.W.H., Ho D.T. Environmental turbulent mixing controls on air-water gas exchange in marine and aquatic systems. Journal of Geophysical Research Letters. 2007, 34, 10. doi: 10.1029/2006GL028790</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Thorpe S.A. Energy loss by breaking waves // Journal of Physical Oceanography. 1993. Vol. 23, No 11. P. 2498–2502. doi: 10.1175/1520-0485(1993)023&lt;2498:ELBBW&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Thorpe S.A. Energy loss by breaking waves. Journal of Physical Oceanography. 1993, 23, 11, 2498–2502. doi: 10.1175/1520-0485(1993)023&lt;2498:ELBBW&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Kudryavtsev V.N., Shrira V., Dulov V.A., Malinovsky V.V. On the vertical structure of wind-driven sea currents // Journal of Physical Oceanography. 2008. Vol. 38, No 10. P. 2121–2144. doi: 10.1175/2008JPO3883.1</mixed-citation><mixed-citation xml:lang="en">Kudryavtsev V.N., Shrira V., Dulov V.A., Malinovsky V.V. On the vertical structure of wind-driven sea currents. Journal of Physical Oceanography. 2008, 38, 10, 2121–2144. doi: 10.1175/2008JPO3883.1</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Troitskaya Y., Kandaurov A., Ermakova O., Kozlov D., Sergeev D., Zilitinkevich S. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds // Scientific Reports. 2017. Vol. 7. 1614. doi: 10.1038/s41598-017-01673-9</mixed-citation><mixed-citation xml:lang="en">Troitskaya Y., Kandaurov A., Ermakova O., Kozlov D., Sergeev D., Zilitinkevich S. Bag-breakup fragmentation as the dominant mechanism of sea-spray production in high winds. Scientific Reports. 2017, 7, 1614. doi: 10.1038/s41598-017-01673-9</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Kudryavtsev V., Chapron B. On growth rate of wind waves: impact of short-scale breaking modulations // Journal of Physical Oceanography. 2016. Vol. 46, No 1. P. 349–360. doi: 10.1175/JPO-D-14-0216.1</mixed-citation><mixed-citation xml:lang="en">Kudryavtsev V., Chapron B. On growth rate of wind waves: impact of short-scale breaking modulations. Journal of Physical Oceanography. 2016, 46, 1, 349–360. doi: 10.1175/JPO-D-14-0216.1</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Troitskaya Y., Sergeev D., Kandaurov A., Vdovin M., Zilitinkevich S. The effect of foam on waves and the aerodynamic roughness of the water surface at high winds // Journal of Physical Oceanography. 2019. Vol. 49. doi: 10.1175/JPO-D-18-0168.1</mixed-citation><mixed-citation xml:lang="en">Troitskaya Y., Sergeev D., Kandaurov A., Vdovin M., Zilitinkevich S. The effect of foam on waves and the aerodynamic roughness of the water surface at high winds. Journal of Physical Oceanography. 2019, 49. doi: 10.1175/JPO-D-18-0168.1</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Thorpe S.A., Belloul M.B., Hall A.J. Internal waves and whitecaps // Nature. 1987. Vol. 330. P. 740–742. doi: 10.1038/330740a0</mixed-citation><mixed-citation xml:lang="en">Thorpe S.A., Belloul M.B., Hall A.J. Internal waves and whitecaps. Nature. 1987, 330, 740–742. doi: 10.1038/330740a0</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Dulov V.A., Kudryavtsev V.N., Sherbak O.G., Grodsky S.A. Observations of wind wave breaking in the gulf stream frontal zone // The Global Atmosphere and Ocean System. 1998. Vol. 6, No 3. P. 209–242.</mixed-citation><mixed-citation xml:lang="en">Dulov V.A., Kudryavtsev V.N., Sherbak O.G., Grodsky S.A. Observations of wind wave breaking in the gulf stream frontal zone. The Global Atmosphere and Ocean System. 1998, 6, 3, 209–242.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Kubryakov A.A., Kudryavtsev V.N., Stanichny S.V. Application of Landsat imagery for the investigation of wave breaking // Remote Sensing of Environment. 2021. Vol. 253. 112144. doi: 10.1016/j.rse.2020.112144</mixed-citation><mixed-citation xml:lang="en">Kubryakov A.A., Kudryavtsev V.N., Stanichny S.V. Application of Landsat imagery for the investigation of wave breaking. Remote Sensing of Environment. 2021, 253, 112144. doi: 10.1016/j.rse.2020.112144</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Бондур В.Г., Шарков Е.А. Статистические характеристики пенных образований на взволнованной морской поверхности // Океанология. 1982. Т. 22, № 3. С. 372–378.</mixed-citation><mixed-citation xml:lang="en">Bondur V.G., Sharkov Е.А. Statistical characteristics of foam formations on a disturbed sea-surface. Okeanologiya. 1982, 22, 3, 372–378 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Monahan E.C., Woolf D.K. Comments on «Variations of whitecap coverage with wind stress and water temperature» // Journal of Physical Oceanography. 1989. Vol. 19, No 5. P. 706–709. doi: 10.1175/1520-0485(1989)019&lt;0706:COOWCW&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Monahan E.C., Woolf D.K. Comments on “Variations of whitecap coverage with wind stress and water temperature”. Journal of Physical Oceanography. 1989, 19, 5, 706–709. doi: 10.1175/1520–0485(1989)019&lt;0706:COOWCW&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Шарков Е.А. Обрушающиеся морские волны: структура, геометрия, электродинамика. M.: Научный мир, 2009. 304 c.</mixed-citation><mixed-citation xml:lang="en">Sharkov Е.А. Breaking ocean waves: geometry, structure and remote sensing. Berlin; Heidelberg; N.У., Springer/PRAXIS, 2007. 278 р.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Phillips O.M. Radar returns from the sea surface — Bragg scattering and breaking waves // Journal of Physical Oceanography. 1988. Vol. 18, No 8. P. 1065–1074. doi: 10.1175/1520-0485(1988)018&lt;1065:RRFTSS&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Phillips O.M. Radar returns from the sea surface-Bragg scattering and breaking waves. Journal of Physical Oceanography. 1988, 18, 8, 1065–1074. doi: 10.1175/1520–0485(1988)018&lt;1065:RRFTSS&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Kudryavtsev V.N., Hauser D., Caudal G., Chapron B. A semiempirical model of the normalized radar cross-section of the sea surface 1. Background model // Journal of Geophysical Research. 2003.Vol. 108, No C3. doi: 10.1029/2001JC001003</mixed-citation><mixed-citation xml:lang="en">Kudryavtsev V.N., Hauser D., Caudal G., Chapron B. A semiempirical model of the normalized radar cross-section of the sea surface 1. Background model. Journal of Geophysical Research. 2003, 108, C3. doi: 10.1029/2001JC001003</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Шарков Е.А. Экспериментальные исследования времени жизни дисперсной фазы обрушивающейся гравитационной волны // Известия АН. ФАО. 1994. T. 30, № 6. C. 844–847.</mixed-citation><mixed-citation xml:lang="en">Sharkov E.A. Experimental studies of the lifetime of the dispersed phase of a breaking gravitational wave. Izvestiya AN USSR Fizika Atmosfery i Okeana. 1994, 30, 6, 844–847 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Callaghan A.H., Deane G.B., Stokes M.D., Ward B. Observed variation in the decay time of oceanic whitecap foam // Journal of Geophysical Research. 2012. Vol. 117, No C9. doi: 10.1029/2012JC008147</mixed-citation><mixed-citation xml:lang="en">Callaghan A.H., Deane G.B., Stokes M.D., Ward B. Observed variation in the decay time of oceanic whitecap foam. Journal of Geophysical Research. 2012, 117, C9. doi: 10.1029/2012JC008147</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Ding L., Farmer D.M. Observation of breaking surface wave statistics // Journal of Physical Oceanography. 1994. Vol. 24, No 6. P. 1368–1387. doi: 10.1175/1520-0485(1994)024&lt;1368:OOBSWS&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Ding L., Farmer D.M. Observation of breaking surface wave statistics. Journal of Physical Oceanography. 1994, 24, 6, 1368–1387. doi: 10.1175/1520-0485(1994)024&lt;1368:OOBSWS&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Bortkovskii R.S., Novak V.A. Statistical dependences of sea state characteristics on water temperature and wind-wave age // Journal of Marine Systems. 1993. Vol. 4, No 2–3. P. 161–169. doi: 10.1016/0924-7963(93)90006-8</mixed-citation><mixed-citation xml:lang="en">Bortkovskii R.S., Novak V.A. Statistical dependences of sea state characteristics on water temperature and wind-wave age. Journal of Marine Systems. 1993, 4, 2–3, 161–169. doi: 10.1016/0924-7963(93)90006-8</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Phillips O.M., Posner F.L., Hansen J.P. High range resolution radar measurements of the speed distribution of breaking events in wind-generated ocean waves: Surface impulse and wave energy dissipation rates // Journal of Physical Oceanography. 2001. Vol. 31, No 2. P. 450–460. doi: 10.1175/1520-0485(2001)031&lt;0450:HRRRMO&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Phillips O.M., Posner F.L., Hansen J.P. High range resolution radar measurements of the speed distribution of breaking events in wind-generated ocean waves: Surface impulse and wave energy dissipation rates. Journal of Physical Oceanography. 2001, 31, 2, 450–460. doi: 10.1175/1520-0485(2001)031&lt;0450:HRRRMO&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Миронов А.С., Дулов В.А. Статистические характеристики событий и диссипация энергии при обрушении ветровых волн // Сборник научных трудов. Вып. 16. НАН Украины, МГИ, Севастополь, 2008. С. 97–115.</mixed-citation><mixed-citation xml:lang="en">Mironov A.S., Dulov V.A. Statistical characteristics of events and energy dissipation during wavebreaking. Sbornik Nauchnykh Trudov. NAN Ukrainy, MGI, Sevastopol. 2008, 16, 97–115 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Thorpe S.A., Hall A.J. The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar // Continental Shelf Research. 1983. Vol. 1, No 4. P. 353–384. doi: 10.1016/0278-4343(83)90003-1</mixed-citation><mixed-citation xml:lang="en">Thorpe S.A., Hall A.J. The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar. Continental Shelf Research. 1983, 1, 4, 353–384. doi: 10.1016/0278-4343(83)90003-1</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Pivaev P.D., Kudryavtsev V.N., Korinenko A.E., Malinovsky V.V. Field observations of breaking of dominant surface waves // Remote Sensing. 2021. Vol. 13, No 16. 3321. doi: 10.3390/rs13163321</mixed-citation><mixed-citation xml:lang="en">Pivaev P.D., Kudryavtsev V.N., Korinenko A.E., Malinovsky V.V. Field observations of breaking of dominant surface waves. Remote Sensing. 2021, 13, 16, 3321. doi: 10.3390/rs13163321</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Dulov V.A., Kudryavtsev V.N., Bol’shakov A.N. A field study of whitecap coverage and its modulations by energy containing surface waves // Gas Transfer at the Water Surface. Geophys. Monogr. 127 / Ed. Donelan M.A., Drennan W.M., Saltzman E.S., Wanninkhof R. AGU: Washington DC. USA, 2002. P. 187–192. doi: 10.1029/GM127p0187</mixed-citation><mixed-citation xml:lang="en">Dulov V.A., Kudryavtsev V.N., Bol’shakov A.N. A field study of whitecap coverage and its modulations by energy containing surface waves. Gas Transfer at the Water Surface. Geophys. Monogr. 127 / Ed. Donelan M.A., Drennan W.M., Saltzman E.S., Wanninkhof R. AGU, Washington DC, USA, 2002, 187–192. doi: 10.1029/GM127p0187</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Yurovsky Y.Y., Kudryavtsev V.N., Chapron B. Simultaneous radar and video observations of the sea surface in field conditions // Proceedings of the Electromagnetics Research Symposium — Spring (PIERS). St. Petersburg, 2017. P. 2559– 2565. doi: 10.1109/PIERS.2017.8262183</mixed-citation><mixed-citation xml:lang="en">Yurovsky Y.Y., Kudryavtsev V.N., Chapron B. Simultaneous radar and video observations of the sea surface in field conditions. Proceedings of the Electromagnetics Research Symposium — Spring (PIERS). St. Petersburg, 2017, 2559–2565. doi: 10.1109/PIERS.2017.8262183</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Dulov V.A., Korinenko A.E., Kudryavtsev V.N., Malinovsky V.V. Modulation of wind-wave breaking by long surface waves // Remote Sensing. 2021. Vol. 13, No 14. 2825. doi: 10.3390/rs13142825</mixed-citation><mixed-citation xml:lang="en">Dulov V.A., Korinenko A.E., Kudryavtsev V.N., Malinovsky V.V. Modulation of wind-wave breaking by long surface waves. Remote Sensing. 2021, 13, 14, 2825. doi: 10.3390/rs13142825</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Longuet-Higgins M.S., Stewart R.W. Changes in the form of short gravity waves on long waves and tidal currents // Journal of Fluid Mechanics. 1960. Vol. 8. P. 565–583. doi: 10.1017/S0022112060000803</mixed-citation><mixed-citation xml:lang="en">Longuet-Higgins M.S., Stewart R.W. Changes in the form of short gravity waves on long waves and tidal currents. Journal of Fluid Mechanics. 1960, 8, 565–583. doi: 10.1017/S0022112060000803</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Phillips O.M. On the response of short ocean wave components at a fixed wave number to ocean current variations // Journal of Physical Oceanography. 1984. Vol. 14, No 9. P. 1425–1433. doi: 10.1175/1520-0485(1984)014&lt;1425:OTROSO&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Phillips O.M. On the response of short ocean wave components at a fixed wave number to ocean current variations. Journal of Physical Oceanography. 1984, 14, 9, 1425–1433. doi: 10.1175/1520–0485(1984)014&lt;1425:OTROSO&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Fairall C.W., Bradley E.F., Hare J.E., Grachev A.A., Edson J.B. Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm // Journal of Climate. 2003. Vol. 16, No 4. P. 571–591. doi: 10.1175/1520-0442(2003)016&lt;0571:BPOASF&gt;2.0.CO;2</mixed-citation><mixed-citation xml:lang="en">Fairall C.W., Bradley E.F., Hare J.E., Grachev A.A., Edson J.B. Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. Journal of Climate. 2003, 16, 4, 571–591. doi: 10.1175/1520-0442(2003)016&lt;0571:BPOASF&gt;2.0.CO;2</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Кориненко А.Е., Малиновский В.В., Кудрявцев В.Н. Экспериментальные исследования статистических характеристик обрушений ветровых волн // Морской гидрофизический журнал. 2018. Т. 34, № 6. C. 534–547. doi: 10.22449/0233-7584-2018-6-534-547</mixed-citation><mixed-citation xml:lang="en">Korinenko A.E., Malinovsky V.V., Kudryavtsev V.N. Experimental research of statistical characteristics of wind wave breaking. Physical Oceanography. 2018, 25, 6, 489–500. doi: 10.22449/1573-160X-2018-6-489-500</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Кориненко А.Е., Малиновский В.В., Кудрявцев В.Н., Дулов В.А. Статистические характеристики обрушений и их связь с диссипацией энергии ветровых волн по данным натурных измерений // Морской гидрофизический журнал. 2020. Т. 36, № 5. С. 514–531. doi: 10.22449/0233-7584-2020-5-514-531</mixed-citation><mixed-citation xml:lang="en">Korinenko A.E., Malinovsky V.V., Kudryavtsev V.N., Dulov V.A. Statistical characteristics of wave breakings and their relation with the wind waves’ energy dissipation based on the field measurements. Physical Oceanography. 2020, 27, 5, 472–488. doi: 10.22449/1573-160X-2020-5-472-488</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Mironov A.S., Dulov V.A. Detection of wave breaking using sea surface video records // Measurement Science and Technology. 2008. Vol. 19. P. 015405. doi: 10.1088/0957-0233/19/1/015405</mixed-citation><mixed-citation xml:lang="en">Mironov A.S., Dulov V.A. Detection of wave breaking using sea surface video records. Measurement Science and Technology. 2008, 19, 015405. doi: 10.1088/0957-0233/19/1/015405</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Kleiss J.M., Melville W.K. Observations of wave breaking kinematics in fetch-limited seas // Journal of Physical Oceanography. 2010. Vol. 40, No 12. P. 2575–2604. doi: 10.1175/2010JPO4383.1</mixed-citation><mixed-citation xml:lang="en">Kleiss J.M., Melville W.K. Observations of wave breaking kinematics in fetch-limited seas. Journal of Physical Oceanography. 2010, 40, 12, 2575–2604. doi: 10.1175/2010JPO4383.1</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Kleiss J.M., Melville W.K. The analysis of sea surface imagery for whitecap kinematics // Journal of Atmospheric and Oceanic Technology. 2011. Vol. 28, No 2. P. 219–243. doi: 10.1175/2010JTECHO744.1</mixed-citation><mixed-citation xml:lang="en">Kleiss J.M., Melville W.K. The analysis of sea surface imagery for whitecap kinematics. Journal of Atmospheric and Oceanic Technology. 2011, 28, 2, 219–243. doi: 10.1175/2010JTECHO744.1</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Phillips O.M. Spectral and statistical properties of the equilibrium range in wind-generated gravity waves // Journal of Fluid Mechanics. 1985. Vol. 156. P. 505–531. doi: 10.1017/S0022112085002221</mixed-citation><mixed-citation xml:lang="en">Phillips O.M. Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. Journal of Fluid Mechanics. 1985, 156, 505–531. doi: 10.1017/S0022112085002221</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
