Морской гидрофизический журнал. 2021; 37: 333-349
Модельные и экспериментальные оценки интенсивности вертикального перемешивания в верхнем однородном
https://doi.org/10.22449/0233-7584-2021-3-333-349Аннотация
Цель. На основе усовершенствованной многомасштабной модели проведен качественный и количественный анализ экспериментальных данных об интенсивности турбулентности, а также их сопоставление с теоретическими и полуэмпирическими соотношениями для описания вклада различных источников турбулентности.
Методы и результаты. Проведен сравнительный анализ экспериментальных данных и модельных расчетов характеристик турбулентности вблизи поверхности моря. Рассмотрены методы теоретического оценивания генерации турбулентности в приповерхностном слое моря различными физическими процессами. Результаты расчетов по известным моделям турбулентного обмена сравнивались с экспериментальными данными, собранными на протяжении нескольких лет сотрудниками отдела турбулентности МГИ РАН при помощи специализированной аппаратуры. По результатам анализа определены возможности применения рассмотренных моделей для расчета интенсивности турбулентности в разных гидрометеорологических условиях. При слабом ветре ни одна из моделей не давала результатов, соответствующих данным измерений. При умеренных ветрах результаты моделирования демонстрируют вполне удовлетворительное согласие с экспериментальными данными, при сильных ветрах наилучшие результаты дает многомасштабная модель. Эта модель была доработана для оценки вклада двух других механизмов генерации – стоксова дрейфа и циркуляций Ленгмюра.
Выводы. Для объективной оценки интенсивности турбулентного обмена необходимо учитывать три основных механизма генерации турбулентности: сдвиг скорости течения, волнение и обрушение волн. Каждый из этих механизмов может доминировать в разном диапазоне глубин в зависимости от гидрометеорологической ситуации. Согласно расчетам по усовершенствованной модели, учет стоксова дрейфа добавляет от 2 до 17 % к суммарной диссипации в верхнем 30-метровом слое, а вклад ленгмюровских циркуляций, рассчитываемый по зависимости скорости вертикального переноса кинетической энергии от числа Ленгмюра, может достигать 15 % при малых числах Ленгмюра.
Список литературы
1. Монин А. С., Озмидов Р. В. Океанская турбулентность. Л. : Гидрометеоиздат, 1981. 320 с.
2. A global perspective on Langmuir turbulence in the ocean surface boundary layer / S. E. Belcher [еt al.] // Geophysical Research Letters. 2012. Vol. 39, iss. 18. L18605. https://doi.org/10.1029/2012GL052932
3. Федоров К. Н., Гинзбург А. И. Приповерхностный слой океана. Л. : Гидрометеоиздат, 1988. 303 с.
4. Доброклонский С. В. Турбулентная вязкость в поверхностном слое моря и волнение // Доклады АН СССР. 1947. Т. 58, № 7. С. 1345–1348.
5. Бенилов А. Ю. О генерации турбулентности в океане поверхностными волнами // Известия АН СССР. Физика атмосферы и океана. 1973. Т. 9, № 3. С. 293–303.
6. Benilov A. Y., Ly L. N. Modelling of surface waves breaking effects in the ocean upper layer // Mathematical and Computer Modelling. 2002. Vol. 35, iss. 1–2. Р. 191–213. doi:10.1016/S0895-7177(01)00159-5
7. Csanady G. T. The free surface turbulent shear layer // Journal of Physical Oceanography. 1984. Vol. 14, iss. 2. P. 402–411. https://doi.org/10.1175/1520-0485(1984)014<0402:TFSTSL>2.0.CO;2
8. Craig P. D., Banner M. L. Modelling of wave-enhanced turbulence in the ocean surface layer // Journal of Physical Oceanography. 1994. Vol. 24, iss. 12. P. 2546–2559. doi:10.1175/15200485(1994)024<2546:MWETIT>2.0.CO;2
9. On the vertical structure of wind-driven sea currents / V. Kudryavtsev [et al.] // Journal of Physical Oceanography. 2008. Vol. 38, iss. 10. P. 2121–2144. https://doi.org/10.1175/2008JPO3883.1
10. Чухарев А. М. Модель турбулентности со многими временны́ ми масштабами для приповерхностного слоя моря // Известия РАН. Физика атмосферы и океана. 2013. Т. 49, № 4. С. 477–488. doi:10.7868/S0002351513040020
11. Craik A. D. D., Leibovich S. A rational model for Langmuir circulation // Journal of Fluid Mechanics. 1976. Vol. 73, part 3. P. 401–426.
12. Structure and variability of Langmuir circulation during the Surface Waves Processes Program / A. J. Plueddemann [et al.] // Journal of Geophysical Research: Oceans. 1996. Vol. 101, iss. C2. P. 3525–3543. https://doi.org/10.1029/95JC03282
13. Tsai W., Hung L. Three-dimensional modeling of small-scale processes in the upper boundary layer bounded by a dynamic ocean surface // Journal of Geophysical Research: Oceans. 2007. Vol. 112, iss. C2. C02019. doi:10.1029/2006JC003686
14. Kukulka T., Plueddemann A. J., Sullivan P. P. Nonlocal transport due to Langmuir circulation in a coastal ocean // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C12. C12007. doi:10.1029/2012JC008340
15. Langmuir Circulation: An agent for vertical restratification? / K. Li [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1945–1958. doi:10.1175/JPO-D-11-0225.1
16. Roles of breaking waves and Langmuir circulation in the surface boundary layer of a coastal ocean / S. Li [et al.] // Journal of Geophysical Research: Oceans. 2013. Vol. 118, iss. 10. P. 5173–5187. doi:10.1002/jgrc.20387
17. The wavy Ekman layer: Langmuir circulations, breaking waves, and Reynolds stress / J. C. McWilliams [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1793– 1816. doi:10.1175/JPO-D-12-07.1
18. Langmuir Turbulence in Swell / J. C. McWilliams [et al.] // Journal of Physical Oceanography. 2014. Vol. 44, iss. 3. P. 870–890. doi:10.1175/JPO-D-13-0122.1
19. Transient Evolution of Langmuir Turbulence in Ocean Boundary Layers Driven by Hurricane Winds and Waves / P. P. Sullivan [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1959–1980. doi:10.1175/JPO-D-12-025.1
20. Characterization and modulation of Langmuir circulation in Chesapeake Bay / M. E. Scully [et al.] // Journal of Physical Oceanography. 2015. Vol. 45, iss. 10. P. 2621–2639. doi:10.1175/JPO-D-14-0239.1
21. Katsaros K. B., Ataktürk S. S. Dependence of wave-breaking statistics on wind stress and wave development // Breaking Waves / M. L. Banner, R. H. J. Grimshaw (Eds.. Berlin : Springer, 1992. P. 119–132. https://doi.org/10.1007/978-3-642-84847-6_9
22. Melville W. K., Veron F., White C. J. The velocity field under breaking waves: Coherent structures and turbulence // Journal of Fluid Mechanics. 2002. Vol. 454. P. 203–233. doi:10.1017/S0022112001007078
23. 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. https://doi.org/10.1017/S0022112085002221
24. Romero L., Melville W. K., Kleiss J. M. Spectral Energy Dissipation due to Surface Wave Breaking // Journal of Physical Oceanography. 2012. Vol. 42, iss. 9. P. 1421–1444. https://doi.org/10.1175/JPO-D-11-072.1
25. Romero L. Distribution of surface wave breaking fronts // Geophysical Research Letters. 2019. Vol. 46, iss. 17–18. P. 10463–10474. https://doi.org/10.1029/2019GL083408
26. Чухарев А. М., Зубов А. Г., Павленко О. И. Экспериментальная оценка скорости диссипации турбулентной энергии в подповерхностном слое моря в штормовых условиях // Морской гидрофизический журнал. 2018. Т. 34, № 4. С. 329–342. doi:10.22449/0233-75842018-4-329-342
27. 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
28. Wave-induced mixing in the upper ocean: Distribution and application to a global ocean circulation model / F. Qiao [et al.] // Geophysical Research Letters. 2004. Vol. 31, iss. 11. L11303. doi:10.1029/2004GL019824
29. Babanin A. V. On a wave-induced turbulence and a wave-mixed upper ocean layer // Geophysical Research Letters. 2006. Vol. 33, iss. 20. L20605. doi:10.1029/2006GL027308
30. Babanin A. V., Onorato M., Qiao F. Surface waves and wave-coupled effects in lower atmosphere and upper ocean // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C11. C00J01. doi:10.1029/2012JC007932
31. Turbulent mixing due to surface waves indicated by remote sensing of suspended particulate matter and its implementation into coupled modeling of waves, turbulence, and circulation / A. Pleskachevsky [et al.] // Journal of Physical Oceanography. 2011. Vol. 41, iss. 4. P. 708– 724. https://doi.org/10.1175/2010JPO4328.1
32. Турбулентность, индуцируемая штормовыми волнами на глубокой воде / С. Ю. Кузнецов [и др.] // Морской гидрофизический журнал. 2015. № 5. С. 23–34. doi:10.22449/02337584-2015-5-23-34
33. Wu L., Rutgersson A., Sahlée E. Upper-ocean mixing due to surface gravity waves // Journal of Geophysical Research: Oceans. 2015. Vol. 120, iss. 12. P. 8210–8228. doi:10.1002/2015JC011329
34. Kitaigorodskii S. A., Lumley J. L. Wave-turbulence interactions in the upper ocean. Part I: The energy balance of the interacting fields of surface wind waves and wind-induced three-dimensional turbulence // Journal of Physical Oceanography. 1983. Vol. 13, iss. 11. P. 1977–1987. https://doi.org/10.1175/1520-0485(1983)013<1977:WTIITU>2.0.CO;2
35. A three-dimensional surface wave–ocean circulation coupled model and its initial testing / F. Qiao [et al.] // Ocean Dynamics. 2010. Vol. 60, iss. 5. P. 1339–1355. doi:10.1007/s10236-010-0326-y
36. Large W. G., McWilliams J. C., Doney S. C. Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization // Reviews of Geophysics. 1994. Vol. 32, iss. 4. Р. 363–403. https://doi.org/10.1029/94RG01872
37. Mellor G. L., Yamada T. Development of a turbulence closure model for geophysical fluid problems // Reviews of Geophysics. 1982. Vol. 2, iss. 4. P. 851–875. https://doi.org/10.1029/RG020i004p00851
38. McWilliams J. C., Sullivan P. P. Vertical mixing by Langmuir circulations // Spill Science & Technology Bulletin. 2000. Vol. 6, iss. 3–4. P. 225–237. http://dx.doi.org/10.1016/S13532561(01)00041-X
39. Li M., Garrett C., Skyllingstad E. A regime diagram for classifying turbulent large eddies in the upper ocean // Deep Sea Research Part I: Oceanographic Research Papers. 2005. Vol. 52, iss. 2. P. 259–278. doi:10.1016/j.dsr.2004.09.004
40. Harcourt R. R., D’Asaro E. A. Large-eddy simulation of Langmuir turbulence in pure wind seas // Journal of Physical Oceanography. 2008. Vol. 38, iss. 7. P.1542–1562. doi:10.1175/2007JPO3842.1
41. The form and orientation of Langmuir cells for misaligned winds and waves / L. P. Van Roekel [et al.] // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C5. C05001. doi:10.1029/2011JC007516
42. Ardhuin F., Jenkins A. D. On the interaction of surface waves and upper ocean turbulence // Journal of Physical Oceanography. 2006. Vol. 36, iss. 3. P. 551–557. https://doi.org/10.1175/JPO2862.1
43. Kantha L. H., Clayson C. A. On the effect of surface gravity waves on mixing in the oceanic mixed layer // Ocean Modelling. Vol. 6, iss. 2. P. 101–124. https://doi.org/10.1016/S14635003(02)00062-8
44. Измерительный комплекс «Сигма-1» для исследования мелкомасштабных характеристик гидрофизических полей в верхнем слое моря / А. С. Самодуров [и др.] // Морской гидрофизический журнал. 2005. № 5. С. 60–71.
45. Evolution of air-sea interaction parameters during the temperature front passage: The measurements on an oceanographic platform / I. A. Repina [et al.] // Atmospheric Research. 2009. Vol. 94, iss. 1. P. 74–80. http://dx.doi.org/10.1016/j.atmosres.2008.11.007
46. Чухарев А. М., Репина И. А. Взаимодействие пограничных слоев моря и атмосферы на малых и средних масштабах в прибрежной зоне // Морской гидрофизический журнал. 2012. № 2. С. 60–78.
Morskoy Gidrofizicheskiy Zhurnal. 2021; 37: 333-349
Model and Experimental Estimates of Vertical Mixing Intensity in the Sea Upper Homogeneous Layer
https://doi.org/10.22449/0233-7584-2021-3-333-349Abstract
Purpose. The study is aimed at qualitative and quantitative analysis (based on the updated previously proposed multiscale model) of the experimental data on turbulence intensity and their comparison with theoretical and semi-empirical relationships for the purpose of describing the contributions of various turbulence sources.
Methods and Results. A comparative analysis of experimental data and model calculations of turbulence characteristics near the sea surface was performed. The methods of theoretical assessing generation of turbulence in the near-surface sea layer by various physical processes are considered. The results of calculations by the well-known models of turbulent exchange were compared with the experimental data collected by the scientists of the Turbulence Department of MHI, RAS, using the specialized equipment. The analysis results made it possible to determine the possibility of applying the considered models for calculating turbulence intensity under different hydrometeorological conditions. At light winds, none of the models yielded the results which matched the measurement data. At moderate winds, the simulation results showed quite satisfactory agreement with the experiment data; and for strong winds, the multiscale model results were the best. This model was modified to assess the contributions of two other mechanisms of turbulence generation: the Stokes drift and the Langmuir circulations.
Conclusions. Objective assessment of the turbulent exchange intensity requires taking into account of three main mechanisms of turbulence generation, namely flow velocity shear, wave motions and wave breaking. Depending on the hydrometeorological situation, each of these mechanisms can dominate in a certain depth range. The calculations performed using the updated model showed that the Stokes drift added 2–17 % to the total dissipation in the upper 30-meter layer, whereas the contribution of the Langmuir circulations calculated through dependence of the vertical velocity of kinetic energy transfer upon the Langmuir number, can reach 15 % for small Langmuir numbers.
References
1. Monin A. S., Ozmidov R. V. Okeanskaya turbulentnost'. L. : Gidrometeoizdat, 1981. 320 s.
2. A global perspective on Langmuir turbulence in the ocean surface boundary layer / S. E. Belcher [et al.] // Geophysical Research Letters. 2012. Vol. 39, iss. 18. L18605. https://doi.org/10.1029/2012GL052932
3. Fedorov K. N., Ginzburg A. I. Pripoverkhnostnyi sloi okeana. L. : Gidrometeoizdat, 1988. 303 s.
4. Dobroklonskii S. V. Turbulentnaya vyazkost' v poverkhnostnom sloe morya i volnenie // Doklady AN SSSR. 1947. T. 58, № 7. S. 1345–1348.
5. Benilov A. Yu. O generatsii turbulentnosti v okeane poverkhnostnymi volnami // Izvestiya AN SSSR. Fizika atmosfery i okeana. 1973. T. 9, № 3. S. 293–303.
6. Benilov A. Y., Ly L. N. Modelling of surface waves breaking effects in the ocean upper layer // Mathematical and Computer Modelling. 2002. Vol. 35, iss. 1–2. R. 191–213. doi:10.1016/S0895-7177(01)00159-5
7. Csanady G. T. The free surface turbulent shear layer // Journal of Physical Oceanography. 1984. Vol. 14, iss. 2. P. 402–411. https://doi.org/10.1175/1520-0485(1984)014<0402:TFSTSL>2.0.CO;2
8. Craig P. D., Banner M. L. Modelling of wave-enhanced turbulence in the ocean surface layer // Journal of Physical Oceanography. 1994. Vol. 24, iss. 12. P. 2546–2559. doi:10.1175/15200485(1994)024<2546:MWETIT>2.0.CO;2
9. On the vertical structure of wind-driven sea currents / V. Kudryavtsev [et al.] // Journal of Physical Oceanography. 2008. Vol. 38, iss. 10. P. 2121–2144. https://doi.org/10.1175/2008JPO3883.1
10. Chukharev A. M. Model' turbulentnosti so mnogimi vremenný mi masshtabami dlya pripoverkhnostnogo sloya morya // Izvestiya RAN. Fizika atmosfery i okeana. 2013. T. 49, № 4. S. 477–488. doi:10.7868/S0002351513040020
11. Craik A. D. D., Leibovich S. A rational model for Langmuir circulation // Journal of Fluid Mechanics. 1976. Vol. 73, part 3. P. 401–426.
12. Structure and variability of Langmuir circulation during the Surface Waves Processes Program / A. J. Plueddemann [et al.] // Journal of Geophysical Research: Oceans. 1996. Vol. 101, iss. C2. P. 3525–3543. https://doi.org/10.1029/95JC03282
13. Tsai W., Hung L. Three-dimensional modeling of small-scale processes in the upper boundary layer bounded by a dynamic ocean surface // Journal of Geophysical Research: Oceans. 2007. Vol. 112, iss. C2. C02019. doi:10.1029/2006JC003686
14. Kukulka T., Plueddemann A. J., Sullivan P. P. Nonlocal transport due to Langmuir circulation in a coastal ocean // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C12. C12007. doi:10.1029/2012JC008340
15. Langmuir Circulation: An agent for vertical restratification? / K. Li [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1945–1958. doi:10.1175/JPO-D-11-0225.1
16. Roles of breaking waves and Langmuir circulation in the surface boundary layer of a coastal ocean / S. Li [et al.] // Journal of Geophysical Research: Oceans. 2013. Vol. 118, iss. 10. P. 5173–5187. doi:10.1002/jgrc.20387
17. The wavy Ekman layer: Langmuir circulations, breaking waves, and Reynolds stress / J. C. McWilliams [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1793– 1816. doi:10.1175/JPO-D-12-07.1
18. Langmuir Turbulence in Swell / J. C. McWilliams [et al.] // Journal of Physical Oceanography. 2014. Vol. 44, iss. 3. P. 870–890. doi:10.1175/JPO-D-13-0122.1
19. Transient Evolution of Langmuir Turbulence in Ocean Boundary Layers Driven by Hurricane Winds and Waves / P. P. Sullivan [et al.] // Journal of Physical Oceanography. 2012. Vol. 42, iss. 11. P. 1959–1980. doi:10.1175/JPO-D-12-025.1
20. Characterization and modulation of Langmuir circulation in Chesapeake Bay / M. E. Scully [et al.] // Journal of Physical Oceanography. 2015. Vol. 45, iss. 10. P. 2621–2639. doi:10.1175/JPO-D-14-0239.1
21. Katsaros K. B., Ataktürk S. S. Dependence of wave-breaking statistics on wind stress and wave development // Breaking Waves / M. L. Banner, R. H. J. Grimshaw (Eds.. Berlin : Springer, 1992. P. 119–132. https://doi.org/10.1007/978-3-642-84847-6_9
22. Melville W. K., Veron F., White C. J. The velocity field under breaking waves: Coherent structures and turbulence // Journal of Fluid Mechanics. 2002. Vol. 454. P. 203–233. doi:10.1017/S0022112001007078
23. 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. https://doi.org/10.1017/S0022112085002221
24. Romero L., Melville W. K., Kleiss J. M. Spectral Energy Dissipation due to Surface Wave Breaking // Journal of Physical Oceanography. 2012. Vol. 42, iss. 9. P. 1421–1444. https://doi.org/10.1175/JPO-D-11-072.1
25. Romero L. Distribution of surface wave breaking fronts // Geophysical Research Letters. 2019. Vol. 46, iss. 17–18. P. 10463–10474. https://doi.org/10.1029/2019GL083408
26. Chukharev A. M., Zubov A. G., Pavlenko O. I. Eksperimental'naya otsenka skorosti dissipatsii turbulentnoi energii v podpoverkhnostnom sloe morya v shtormovykh usloviyakh // Morskoi gidrofizicheskii zhurnal. 2018. T. 34, № 4. S. 329–342. doi:10.22449/0233-75842018-4-329-342
27. Korinenko A. E., Malinovskii V. V., Kudryavtsev V. N. Eksperimental'nye issledovaniya statisticheskikh kharakteristik obrushenii vetrovykh voln // Morskoi gidrofizicheskii zhurnal. 2018. T. 34, № 6. C. 534–547. doi:10.22449/0233-7584-2018-6-534-547
28. Wave-induced mixing in the upper ocean: Distribution and application to a global ocean circulation model / F. Qiao [et al.] // Geophysical Research Letters. 2004. Vol. 31, iss. 11. L11303. doi:10.1029/2004GL019824
29. Babanin A. V. On a wave-induced turbulence and a wave-mixed upper ocean layer // Geophysical Research Letters. 2006. Vol. 33, iss. 20. L20605. doi:10.1029/2006GL027308
30. Babanin A. V., Onorato M., Qiao F. Surface waves and wave-coupled effects in lower atmosphere and upper ocean // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C11. C00J01. doi:10.1029/2012JC007932
31. Turbulent mixing due to surface waves indicated by remote sensing of suspended particulate matter and its implementation into coupled modeling of waves, turbulence, and circulation / A. Pleskachevsky [et al.] // Journal of Physical Oceanography. 2011. Vol. 41, iss. 4. P. 708– 724. https://doi.org/10.1175/2010JPO4328.1
32. Turbulentnost', indutsiruemaya shtormovymi volnami na glubokoi vode / S. Yu. Kuznetsov [i dr.] // Morskoi gidrofizicheskii zhurnal. 2015. № 5. S. 23–34. doi:10.22449/02337584-2015-5-23-34
33. Wu L., Rutgersson A., Sahlée E. Upper-ocean mixing due to surface gravity waves // Journal of Geophysical Research: Oceans. 2015. Vol. 120, iss. 12. P. 8210–8228. doi:10.1002/2015JC011329
34. Kitaigorodskii S. A., Lumley J. L. Wave-turbulence interactions in the upper ocean. Part I: The energy balance of the interacting fields of surface wind waves and wind-induced three-dimensional turbulence // Journal of Physical Oceanography. 1983. Vol. 13, iss. 11. P. 1977–1987. https://doi.org/10.1175/1520-0485(1983)013<1977:WTIITU>2.0.CO;2
35. A three-dimensional surface wave–ocean circulation coupled model and its initial testing / F. Qiao [et al.] // Ocean Dynamics. 2010. Vol. 60, iss. 5. P. 1339–1355. doi:10.1007/s10236-010-0326-y
36. Large W. G., McWilliams J. C., Doney S. C. Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization // Reviews of Geophysics. 1994. Vol. 32, iss. 4. R. 363–403. https://doi.org/10.1029/94RG01872
37. Mellor G. L., Yamada T. Development of a turbulence closure model for geophysical fluid problems // Reviews of Geophysics. 1982. Vol. 2, iss. 4. P. 851–875. https://doi.org/10.1029/RG020i004p00851
38. McWilliams J. C., Sullivan P. P. Vertical mixing by Langmuir circulations // Spill Science & Technology Bulletin. 2000. Vol. 6, iss. 3–4. P. 225–237. http://dx.doi.org/10.1016/S13532561(01)00041-X
39. Li M., Garrett C., Skyllingstad E. A regime diagram for classifying turbulent large eddies in the upper ocean // Deep Sea Research Part I: Oceanographic Research Papers. 2005. Vol. 52, iss. 2. P. 259–278. doi:10.1016/j.dsr.2004.09.004
40. Harcourt R. R., D’Asaro E. A. Large-eddy simulation of Langmuir turbulence in pure wind seas // Journal of Physical Oceanography. 2008. Vol. 38, iss. 7. P.1542–1562. doi:10.1175/2007JPO3842.1
41. The form and orientation of Langmuir cells for misaligned winds and waves / L. P. Van Roekel [et al.] // Journal of Geophysical Research: Oceans. 2012. Vol. 117, iss. C5. C05001. doi:10.1029/2011JC007516
42. Ardhuin F., Jenkins A. D. On the interaction of surface waves and upper ocean turbulence // Journal of Physical Oceanography. 2006. Vol. 36, iss. 3. P. 551–557. https://doi.org/10.1175/JPO2862.1
43. Kantha L. H., Clayson C. A. On the effect of surface gravity waves on mixing in the oceanic mixed layer // Ocean Modelling. Vol. 6, iss. 2. P. 101–124. https://doi.org/10.1016/S14635003(02)00062-8
44. Izmeritel'nyi kompleks «Sigma-1» dlya issledovaniya melkomasshtabnykh kharakteristik gidrofizicheskikh polei v verkhnem sloe morya / A. S. Samodurov [i dr.] // Morskoi gidrofizicheskii zhurnal. 2005. № 5. S. 60–71.
45. Evolution of air-sea interaction parameters during the temperature front passage: The measurements on an oceanographic platform / I. A. Repina [et al.] // Atmospheric Research. 2009. Vol. 94, iss. 1. P. 74–80. http://dx.doi.org/10.1016/j.atmosres.2008.11.007
46. Chukharev A. M., Repina I. A. Vzaimodeistvie pogranichnykh sloev morya i atmosfery na malykh i srednikh masshtabakh v pribrezhnoi zone // Morskoi gidrofizicheskii zhurnal. 2012. № 2. S. 60–78.
