Морской гидрофизический журнал. 2020; 36: 740-756
Каким образом океанические вихри могут быть столь долгоживущими
https://doi.org/10.22449/0233-7584-2020-6-740-756Аннотация
Цель. Теоретически обосновать удивительную долгоживучесть (до 5 лет) индивидуальных вихрей в Мировом океане на фоне сильных флуктуаций океанических течений и вопреки дисперсионным свойствам волн Россби – цель данной работы.
Методы и результаты. Эволюция бароклинных вихрей рассматривается в гибридной двухслойной модели океана над топографическим склоном на бета-плоскости. В верхнем слое с сильными аномалиями потенциальной завихренности течения считаются сбалансированными; в нижнем слое при слабых аномалиях потенциальной завихренности течения описываются в традиционном квазигеострофическом приближении. Аналитическое описание дано для медленно изменяющихся почти круглых вихрей в зональном течении с вертикальным сдвигом скорости, характерным для океана в субтропиках. Теория показывает, как бароклинный вихрь сопровождается подветренными волнами Россби. Дрейф вихря поперек среднего течения определяется преимущественно бароклинно-дипольной структурой представленного решения, при этом потеря энергии вихрем, связанная с генерированием волн Россби, может быть компенсирована запасом энергии в средних течениях.
Выводы. Построенная модель дает разумные оценки дрейфа и переноса энергии для типичных океанских вихрей с сильными аномалиями потенциальной завихренности. Прямая подпитка энергии долгоживущих вихрей бароклинными средними течениями независимо от их устойчивости имеет большое значение для лучшего понимания физических механизмов, объясняющих значительную продолжительность жизни геофизических вихрей и особенности их перемещения.
Список литературы
1. Large-scale multi-buoy experiment in the Tropical Atlantic / L. M. Brekhovskikh [et al.] // Deep Sea Research and Oceanographic Abstracts. 1971. Vol. 18, iss. 12. P. 1189–1206. https://doi.org/10.1016/0011-7471(71)90026-X
2. Koshlyakov M. N., Monin A. S. Synoptic Eddies in the Ocean // Annual Review of Earth and Planetary Sciences. 1978. Vol. 6. P. 495–523. https://doi.org/10.1146/annurev.ea.06.050178.002431
3. Eddies in Marine Science / Ed. A. R. Robinson. Berlin-Heidelberg-New York-Tokyo : Springer-Verlag, 1983. 609 p. https://doi.org/10.1002/zamm.19850650123
4. Кошляков М. Н., Белокопытов В. Н. Синоптические вихри открытого океана: обзор экспериментальных исследований // Морской гидрофизический журнал. 2020. Т. 36, № 6. С. 613–627. doi:10.22449/0233-7584-2020-6-613-627
5. McWilliams J. C. The Nature and Consequences of Oceanic Eddies // Ocean Modeling in an Eddying Regime / Eds. M. W. Hecht, H. Hasumi. Washington, DC : American Geophysical Union, 2008. Vol. 177. P. 5–15. doi:10.1029/177GM03.11
6. Global heat and salt transports by eddy movement / C. Dong [et al.] // Nature Communications. 2014. Vol. 5. 3294. https://doi.org/10.1038/ncomms4294
7. Chen G., Han G., Yang X. On the intrinsic shape of oceanic eddies derived from satellite altimetry // Remote Sensing of Environment. 2019. Vol. 228. P. 75–89. https://doi.org/10.1016/j.rse.2019.04.011
8. McWilliams J. C. Submesoscale, coherent vortices in the ocean // Reviews of Geophysics. 1985. Vol. 23, iss. 2. P. 165–182. doi:10.1029/RG023i002p00165
9. Flierl G. R. Isolated Eddy Models in Geophysics // Annual Review of Fluid Mechanics. 1987. Vol. 19. P. 493–530. https://doi.org/10.1146/annurev.fl.19.010187.002425
10. Коротаев Г. К. Теоретическое моделирование синоптической изменчивости океана. Киев : Наукова думка, 1988. 157 с.
11. Korotaev G. K. Radiating Vortices in Geophysical Fuid Dynamics // Surveys in Geophysics. 1997. Vol. 18, iss. 6. P. 567–618. doi:10.1023/A:1006583017505
12. Nezlin M. V., Sutyrin G. G. Problems of simulation of large, long-lived vortices in the atmospheres of the giant planets (jupiter, saturn, neptune) // Surveys in Geophysics. 1994. Vol. 15, iss. 1. P. 63–99. doi:10.1007/BF00665687
13. Carton X. Hydrodynamical modeling of oceanic vortices // Surveys in Geophysics. 2001. Vol. 22, iss. 3. P. 179–263. doi:10.1023/A:1013779219578
14. Sokolovskiy M. A., Verron J. Dynamics of Vortex Structures in a Stratified Rotating Fluid // Atmospheric and Oceanographic Science Library. Vol. 47. Cham : Springer, 2014. 382 p. doi:10.1007/978-3-319-00789-2
15. Stern M. E. Minimal properties of planetary eddies // Journal of Marine Research. 1975. Vol. 33, iss. 1. P. 1–13.
16. Ларичев В. Д., Резник Г. М. О двумерных уединенных волнах Россби // Доклады Академии наук СССР. 1976. Т. 231, № 5. C. 1077–1079. URL: http://www.mathnet.ru/links/ab484331932b9f8f6f361e722e3cb8e3/dan40813.pdf (дата обращения: 15.10.2020).
17. Meleshko V. V., van Heijst G. J. F. On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid // Journal of Fluid Mechanics. 1994. Vol. 272. P. 157–182. https://doi.org/10.1017/S0022112094004428
18. The theory of the beta-plane baroclinic topographic modons / Z. Kizner [et al.] // Geophysical and Astrophysical Fluid Dynamics. 2003. Vol. 97, iss. 3. P. 175–211. doi:10.1080/0309192031000108706
19. Михайлова Э. Н., Шапиро Н. Б. Двумерная модель эволюции синоптических возмущений в океане // Известия Академии наук СССР. Физика атмосферы и океана. 1980. Т. 16, № 8. С 823–833.
20. Петвиашвили В. И. Красное пятно Юпитера и дрейфовый солитон в плазме // Письма в Журнал экспериментальной и теоретической физики. 1980. Т. 32, вып. 11. С. 632–635. URL: http://www.jetpletters.ac.ru/cgi-bin/articles/download.cgi/478/article_7558.pdf (дата обращения: 30.10.2020).
21. Сутырин Г. Г. К теории уединенных антициклонов во вращающейся жидкости // Доклады Академии наук СССР. 1985. Т. 280, № 5. C. 1101–1105.
22. Sutyrin G. G., Yushina I. G. Numerical Modelling of the Formation, Evolution, Interaction and Decay of Isolated Vortices // Mesoscale/Synoptic Coherent structures in Geophysical Turbulence / Eds. J. C. J. Nihoul, B. M. Jamart. Elsevier Oceanographic Series, 1989. Vol. 50. P. 721–736. doi:10.1016/S0422-9894(08)70217-4
23. Chelton D. B., Schlax M. G., Samelson R. M. Global observations of nonlinear mesoscale eddies // Progress in Oceanography. 2011. Vol. 91, iss. 2. P. 167–216. doi:10.1016/j.pocean.2011.01.002
24. Sutyrin G. G. Super long-lived ocean eddies // Сборник трудов Международного симпозиума «Мезомасштабные и субмезомасштабные процессы в гидросфере и атмосфере» (МСП-2018). Москва : ИО РАН, 2018. С. 46–47. doi:10.29006/978-5-9901449-4-1-2018-11
25. Коротаев Г. К. Структура, динамика и энергетика синоптической изменчивости океана. Севастополь, 1980. 64 с. (Препринт / МГИ).
26. Flierl G. R. Rossby Wave Radiation from a Strongly Nonlinear Warm Eddy // Journal of Physical Oceanography. 1984. Vol. 14, iss. 1. P. 47–58. https://doi.org/10.1175/1520-0485(1984)014<0047:RWRFAS>2.0.CO;2
27. McDonald N. R. The decay of cyclonic eddies by Rossby wave radiation // Journal of Fluid Mechanics. 1998. Vol. 361. P. 237–252. doi:10.1017/S0022112098008696
28. Nycander J. Drift Velocity of Radiating Quasigeostrophic Vortices // Journal of Physical Oceanography. 2001. Vol. 31, iss. 8. P. 2178–2185. https://doi.org/10.1175/1520-0485(2001)031<2178:DVORQV>2.0.CO;2
29. Сутырин Г. Г. О влиянии бета-эффекта на эволюцию локализованного вихря // Доклады Академии наук СССР. 1987. Т. 296, № 5. С. 1076–1080. URL: http://www.mathnet.ru/links/bb945265df7fd03879fae801ee00058a/dan48090.pdf (дата обращения: 30.10.2020).
30. Kravtsov S., Reznik G. Numerical solutions of the singular vortex problem // Physics of Fluids. 2019. Vol. 31, iss. 6. 066602. https://doi.org/10.1063/1.5099896
31. Gill A. E., Green J. S. A., Simmons A. J. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies // Deep Sea Research and Oceanographic abstracts. 1974. Vol. 21, iss. 7. P. 499–528. https://doi.org/10.1016/0011-7471(74)90010-2
32. Vallis G. K. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge : Cambridge University Press, 2006. 745 p.
33. Ferrari R., Wunsch C. Ocean Circulation Kinetic Energy: Reservoirs, Sources, and Sinks // Annual Review of Fluid Mechanics. 2009. Vol. 41. P. 253–282. https://doi.org/10.1146/annurev.fluid.40.111406.102139
34. Venaille A., Vallis G., Smith S. Baroclinic Turbulence in the Ocean: Analysis with Primitive Equation and Quasigeostrophic Simulations // Journal of Physical Oceanography. 2011. Vol. 41, iss. 9. P. 1605–1623. doi: 10.1175/JPO-D-10-05021.1
35. Radko T., Peixoto de Carvalho D., Flanagan J. Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model // Journal of Physical Oceanography. 2014. Vol. 44, iss. 7. P. 1919–1940. https://doi.org/10.1175/JPO-D-13-0248.1
36. Vandermeirsh F., Morel Y., Sutyrin G. Resistance of a Coherent Vortex to a Vertical Shear // Journal of Physical Oceanography. 2002. Vol. 32, iss. 11. P. 3089–3100. https://doi.org/10.1175/1520-0485(2002)032<3089:ROACVT>2.0.CO;2
37. Sutyrin G. G., Radko T. Why the most long-lived eddies are found in the subtropical ocean westward flows // Ocean Modelling. 2020. (in press).
38. Richardson L. F. Weather Prediction by Numerical Process. Cambridge : The University Press, 1922. 258 p. URL: https://archive.org/details/weatherpredictio00richrich (date of access: 30.10.2020).
39. Монин А. С. Прогноз погоды как задача физики. М. : Наука, 1969. 184 с.
40. Kamenkovich V. M., Koshlyakoy M. N., Monin A. S. Synoptic Eddies in the Ocean. Series: Environmental Fluid Mechanics 5 / Ed. A. S. Monin. Netherlands, Dordrecht : Springer, 1986. 443 p.
41. Sutyrin G. G., Grimshaw R. Frictional effects on the deep-flow feedback on the β-drift of a baroclinic vortex over sloping topography // Deep Sea Research Part I: Oceanographic Research Papers. 2005. Vol. 52, iss. 1. P. 2156–2167. doi:10.1016/j.dsr.2005.06.017
42. Сутырин Г. Г. Синоптические движения конечной амплитуды // Доклады Академии наук СССР.1986. Т. 290, № 5. C. 1084–1088. URL: http://www.mathnet.ru/links/5662892d8fad089be8eb8a118be68902/dan47702.pdf (дата обращения: 15.10.2020).
43. Sutyrin G. G. Agradient velocity, vortical motion and gravity waves in a rotating shallowwater model // Quarterly Journal of the Royal Meteorological Society. 2004. Vol. 130, iss. 601. P. 1977–1989. https://doi.org/10.1256/qj.03.54
44. Phillips N. A. Energy Transformations and Meridional Circulations associated with simple Baroclinic Waves in a two level, Quasi-geostrophic Model // Tellus. 1954. Vol. 6, iss. 3. P. 273–286. https://doi.org/10.1111/j.2153-3490.1954.tb01123.x
45. Scales, Growth Rates, and Spectral Fuxes of Baroclinic Instability in the Ocean / R. Tulloch [et al.] // Journal of Physical Oceanography. 2011. Vol. 41, iss. 6. P. 1057–1076. https://doi.org/10.1175/2011JPO4404.1
46. Thompson A. F., Young W. R. Scaling Baroclinic Eddy Fluxes: Vortices and Energy Balance // Journal of Physical Oceanography. 2006. Vol. 36, iss. 4. P. 720–738. https://doi.org/10.1175/JPO2874.1
47. Reznik G. M., Sutyrin G. G. Baroclinic topographic modons // Journal of Fluid Mechanics. 2001. Vol. 437. P. 121–142. doi: 10.1017/S0022112001004062
48. Sutyrin G. G., Flierl G. R. Intense Vortex Motion on the Beta Plane: Development of the Beta Gyres // Journal of Atmospheric Sciences. 1994. Vol. 51, iss. 5. P. 773–790. https://doi.org/10.1175/1520-0469(1994)051<0773:IVMOTB>2.0.CO;2
49. SIDDIES Corridor: A Major East-West Pathway of Long-Lived Surface and Subsurface Eddies Crossing the Subtropical South Indian Ocean / A. F. Dilmahamod [et al.] // Journal of Geophysical Research: Oceans. 2018. Vol. 123, iss. 8. P. 5406–5425. https://doi.org/10.1029/2018JC013828
50. Sutyrin G. G. How baroclinic vortices intensify resulting from erosion of their cores and/or changing environment // Ocean Modelling. 2020. Vol. 156. 101711. https://doi.org/10.1016/j.ocemod.2020.101711
51. Pegliasco C., Chaigneau A., Morrow R. Main eddy vertical structures observed in the four major Eastern Boundary Upwelling Systems // Journal of Geophysical Research: Oceans. 2015. Vol. 120, iss. 9. P. 6008–6033. https://doi.org/10.1002/2015JC010950
52. Burgess B. H., Dritschel D. G., Scott R. K. Vortex scaling ranges in two-dimensional turbulence // Physics of Fluids. 2017. Vol. 29, iss. 11. 111104. https://doi.org/10.1063/1.4993144
53. Сутырин Г. Г. Азимутальные волны и симметризация интенсивного вихря // Доклады Академии наук СССР. 1989. Т. 304, № 5. С. 1086–1091. URL: http://www.mathnet.ru/links/8a31183a00e5c592d7d0ebfc624dda46/dan48505.pdf (дата обращения: 30.10.2020).
54. Sutyrin G. G. On the vortex intensification due to stretching out of weak satellites // Physics of Fluids. 2019. Vol. 31, iss. 7. 075103. https://doi.org/10.1063/1.5098068
55. Sutyrin G. G., Radko T. On the peripheral intensification of two-dimensional vortices in smaller-scale randomly forcing flow // Physics of Fluids. 2019. Vol. 31, iss. 10. 101701. https://doi.org/10.1063/1.5118752
56. Benilov E. S. Stability of vortices in a two-layer ocean with uniform potential vorticity in the lower layer // Journal of Fluid Mechanics. 2004. Vol. 502. P. 207–232. doi:10.1017/S0022112003007547
57. Sutyrin G. Generation of deep eddies by a turning baroclinic jet // Deep Sea Research Part I: Oceanographic Research Papers. 2015. Vol. 101. P. 1–6. doi:10.1016/j.dsr.2015.02.011
58. Sutyrin G. G., Radko T. Stabilization of Isolated Vortices in a Rotating Stratified Fluid // Fluids. 2016. Vol. 1, iss 3. 26. doi:10.3390/fluids1030026
59. Sutyrin G. Why compensated cold-core rings look stable // Geophysical Research Letters. 2015. Vol. 42, iss. 13. P. 5395–5402. doi:10.1002/2015GL064378
60. Sutyrin G. G. On sharp vorticity gradients in elongating baroclinic eddies and their stabilization with a solid-body rotation // Geophysical Research Letters. Vol. 43, iss. 11. P. 5802–5811. doi:10.1002/2016GL069019.
61. Legras B., Dritschel D. Vortex stripping and the generation of high vorticity gradients in twodimensional flows // Applied Scientific Research. 1993. Vol. 51. P. 445–455. doi.org/10.1007/BF01082574
62. Mariotti A., Legras B., Dritschel D. G. Vortex stripping and the erosion of coherent structures in two-dimensional flows // Physics of Fluids. 1994. Vol. 6, iss. 12. 3954. https://doi.org/10.1063/1.868385
63. Legras B., Dritschel D. D., Caillol P. The erosion of a distributed two-dimensional vortex in a background straining flow // Journal of Fluid Mechanics. 2001. Vol. 441. P. 369–398. https://doi.org/10.1017/S002211200100502X
64. Sutyrin G., Carton X. Vortex interaction with a zonal Rossby wave in a quasi-geostrophic model // Dynamics of Atmospheres and Oceans. 2006. Vol. 41, iss. 2. P. 85–102. doi:10.1016/j.dynatmoce.2005.10.004
65. Sutyrin G. G. Maintenance of quick fluid rotation in the cores of long-lived Arctic eddies // Journal of Marine Systems. 1992. Vol. 3, iss. 6. P. 489–496 doi:10.1016/0924-7963(92)90019-5
Morskoy Gidrofizicheskiy Zhurnal. 2020; 36: 740-756
How Oceanic Vortices can be Super Long-Lived
https://doi.org/10.22449/0233-7584-2020-6-740-756Abstract
Purpose. The article is aimed at substantiating theoretically amazing longevity (up to 5 years) of the individual vortices in the World Ocean against the background of strong fluctuations of the ocean currents and regardless of the Rossby wave dispersion features.
Methods and Results. Evolution of the baroclinic vortices is considered in a hybrid two-layer ocean model over a topographic slope on the beta-plane. In the upper layer with strong potential vorticity anomalies, the currents are assumed to be balanced; in the lower layer at week potential vorticity anomalies, the currents are described in the traditional quasi-geostrophic approximation. Slow evolving almost circular vortices embedded in a vertically sheared current typical of the subtropical part of the ocean are described analytically. The theory shows how a baroclinic vortex is followed by the lee Rossby waves. The vortex drift across the mean current is conditioned mainly by the baroclinic-dipole structure of the represented solution; at that the vortex energy loss related to the Rossby wave radiation can be compensated by the energy stored in the mean currents.
Conclusions. The constructed model provides reasonable estimates of the energy drift and transfer typical of the ocean vortices with strong anomalies of potential vorticity. Direct support of long-lived vortices by the energy of the baroclinic mean flows irrespective of their stability, is of great importance for better understanding the physical mechanisms relating to significant longetivity of the geophysical vortices and the features of their movement.
References
1. Large-scale multi-buoy experiment in the Tropical Atlantic / L. M. Brekhovskikh [et al.] // Deep Sea Research and Oceanographic Abstracts. 1971. Vol. 18, iss. 12. P. 1189–1206. https://doi.org/10.1016/0011-7471(71)90026-X
2. Koshlyakov M. N., Monin A. S. Synoptic Eddies in the Ocean // Annual Review of Earth and Planetary Sciences. 1978. Vol. 6. P. 495–523. https://doi.org/10.1146/annurev.ea.06.050178.002431
3. Eddies in Marine Science / Ed. A. R. Robinson. Berlin-Heidelberg-New York-Tokyo : Springer-Verlag, 1983. 609 p. https://doi.org/10.1002/zamm.19850650123
4. Koshlyakov M. N., Belokopytov V. N. Sinopticheskie vikhri otkrytogo okeana: obzor eksperimental'nykh issledovanii // Morskoi gidrofizicheskii zhurnal. 2020. T. 36, № 6. S. 613–627. doi:10.22449/0233-7584-2020-6-613-627
5. McWilliams J. C. The Nature and Consequences of Oceanic Eddies // Ocean Modeling in an Eddying Regime / Eds. M. W. Hecht, H. Hasumi. Washington, DC : American Geophysical Union, 2008. Vol. 177. P. 5–15. doi:10.1029/177GM03.11
6. Global heat and salt transports by eddy movement / C. Dong [et al.] // Nature Communications. 2014. Vol. 5. 3294. https://doi.org/10.1038/ncomms4294
7. Chen G., Han G., Yang X. On the intrinsic shape of oceanic eddies derived from satellite altimetry // Remote Sensing of Environment. 2019. Vol. 228. P. 75–89. https://doi.org/10.1016/j.rse.2019.04.011
8. McWilliams J. C. Submesoscale, coherent vortices in the ocean // Reviews of Geophysics. 1985. Vol. 23, iss. 2. P. 165–182. doi:10.1029/RG023i002p00165
9. Flierl G. R. Isolated Eddy Models in Geophysics // Annual Review of Fluid Mechanics. 1987. Vol. 19. P. 493–530. https://doi.org/10.1146/annurev.fl.19.010187.002425
10. Korotaev G. K. Teoreticheskoe modelirovanie sinopticheskoi izmenchivosti okeana. Kiev : Naukova dumka, 1988. 157 s.
11. Korotaev G. K. Radiating Vortices in Geophysical Fuid Dynamics // Surveys in Geophysics. 1997. Vol. 18, iss. 6. P. 567–618. doi:10.1023/A:1006583017505
12. Nezlin M. V., Sutyrin G. G. Problems of simulation of large, long-lived vortices in the atmospheres of the giant planets (jupiter, saturn, neptune) // Surveys in Geophysics. 1994. Vol. 15, iss. 1. P. 63–99. doi:10.1007/BF00665687
13. Carton X. Hydrodynamical modeling of oceanic vortices // Surveys in Geophysics. 2001. Vol. 22, iss. 3. P. 179–263. doi:10.1023/A:1013779219578
14. Sokolovskiy M. A., Verron J. Dynamics of Vortex Structures in a Stratified Rotating Fluid // Atmospheric and Oceanographic Science Library. Vol. 47. Cham : Springer, 2014. 382 p. doi:10.1007/978-3-319-00789-2
15. Stern M. E. Minimal properties of planetary eddies // Journal of Marine Research. 1975. Vol. 33, iss. 1. P. 1–13.
16. Larichev V. D., Reznik G. M. O dvumernykh uedinennykh volnakh Rossbi // Doklady Akademii nauk SSSR. 1976. T. 231, № 5. C. 1077–1079. URL: http://www.mathnet.ru/links/ab484331932b9f8f6f361e722e3cb8e3/dan40813.pdf (data obrashcheniya: 15.10.2020).
17. Meleshko V. V., van Heijst G. J. F. On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid // Journal of Fluid Mechanics. 1994. Vol. 272. P. 157–182. https://doi.org/10.1017/S0022112094004428
18. The theory of the beta-plane baroclinic topographic modons / Z. Kizner [et al.] // Geophysical and Astrophysical Fluid Dynamics. 2003. Vol. 97, iss. 3. P. 175–211. doi:10.1080/0309192031000108706
19. Mikhailova E. N., Shapiro N. B. Dvumernaya model' evolyutsii sinopticheskikh vozmushchenii v okeane // Izvestiya Akademii nauk SSSR. Fizika atmosfery i okeana. 1980. T. 16, № 8. S 823–833.
20. Petviashvili V. I. Krasnoe pyatno Yupitera i dreifovyi soliton v plazme // Pis'ma v Zhurnal eksperimental'noi i teoreticheskoi fiziki. 1980. T. 32, vyp. 11. S. 632–635. URL: http://www.jetpletters.ac.ru/cgi-bin/articles/download.cgi/478/article_7558.pdf (data obrashcheniya: 30.10.2020).
21. Sutyrin G. G. K teorii uedinennykh antitsiklonov vo vrashchayushcheisya zhidkosti // Doklady Akademii nauk SSSR. 1985. T. 280, № 5. C. 1101–1105.
22. Sutyrin G. G., Yushina I. G. Numerical Modelling of the Formation, Evolution, Interaction and Decay of Isolated Vortices // Mesoscale/Synoptic Coherent structures in Geophysical Turbulence / Eds. J. C. J. Nihoul, B. M. Jamart. Elsevier Oceanographic Series, 1989. Vol. 50. P. 721–736. doi:10.1016/S0422-9894(08)70217-4
23. Chelton D. B., Schlax M. G., Samelson R. M. Global observations of nonlinear mesoscale eddies // Progress in Oceanography. 2011. Vol. 91, iss. 2. P. 167–216. doi:10.1016/j.pocean.2011.01.002
24. Sutyrin G. G. Super long-lived ocean eddies // Sbornik trudov Mezhdunarodnogo simpoziuma «Mezomasshtabnye i submezomasshtabnye protsessy v gidrosfere i atmosfere» (MSP-2018). Moskva : IO RAN, 2018. S. 46–47. doi:10.29006/978-5-9901449-4-1-2018-11
25. Korotaev G. K. Struktura, dinamika i energetika sinopticheskoi izmenchivosti okeana. Sevastopol', 1980. 64 s. (Preprint / MGI).
26. Flierl G. R. Rossby Wave Radiation from a Strongly Nonlinear Warm Eddy // Journal of Physical Oceanography. 1984. Vol. 14, iss. 1. P. 47–58. https://doi.org/10.1175/1520-0485(1984)014<0047:RWRFAS>2.0.CO;2
27. McDonald N. R. The decay of cyclonic eddies by Rossby wave radiation // Journal of Fluid Mechanics. 1998. Vol. 361. P. 237–252. doi:10.1017/S0022112098008696
28. Nycander J. Drift Velocity of Radiating Quasigeostrophic Vortices // Journal of Physical Oceanography. 2001. Vol. 31, iss. 8. P. 2178–2185. https://doi.org/10.1175/1520-0485(2001)031<2178:DVORQV>2.0.CO;2
29. Sutyrin G. G. O vliyanii beta-effekta na evolyutsiyu lokalizovannogo vikhrya // Doklady Akademii nauk SSSR. 1987. T. 296, № 5. S. 1076–1080. URL: http://www.mathnet.ru/links/bb945265df7fd03879fae801ee00058a/dan48090.pdf (data obrashcheniya: 30.10.2020).
30. Kravtsov S., Reznik G. Numerical solutions of the singular vortex problem // Physics of Fluids. 2019. Vol. 31, iss. 6. 066602. https://doi.org/10.1063/1.5099896
31. Gill A. E., Green J. S. A., Simmons A. J. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies // Deep Sea Research and Oceanographic abstracts. 1974. Vol. 21, iss. 7. P. 499–528. https://doi.org/10.1016/0011-7471(74)90010-2
32. Vallis G. K. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge : Cambridge University Press, 2006. 745 p.
33. Ferrari R., Wunsch C. Ocean Circulation Kinetic Energy: Reservoirs, Sources, and Sinks // Annual Review of Fluid Mechanics. 2009. Vol. 41. P. 253–282. https://doi.org/10.1146/annurev.fluid.40.111406.102139
34. Venaille A., Vallis G., Smith S. Baroclinic Turbulence in the Ocean: Analysis with Primitive Equation and Quasigeostrophic Simulations // Journal of Physical Oceanography. 2011. Vol. 41, iss. 9. P. 1605–1623. doi: 10.1175/JPO-D-10-05021.1
35. Radko T., Peixoto de Carvalho D., Flanagan J. Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model // Journal of Physical Oceanography. 2014. Vol. 44, iss. 7. P. 1919–1940. https://doi.org/10.1175/JPO-D-13-0248.1
36. Vandermeirsh F., Morel Y., Sutyrin G. Resistance of a Coherent Vortex to a Vertical Shear // Journal of Physical Oceanography. 2002. Vol. 32, iss. 11. P. 3089–3100. https://doi.org/10.1175/1520-0485(2002)032<3089:ROACVT>2.0.CO;2
37. Sutyrin G. G., Radko T. Why the most long-lived eddies are found in the subtropical ocean westward flows // Ocean Modelling. 2020. (in press).
38. Richardson L. F. Weather Prediction by Numerical Process. Cambridge : The University Press, 1922. 258 p. URL: https://archive.org/details/weatherpredictio00richrich (date of access: 30.10.2020).
39. Monin A. S. Prognoz pogody kak zadacha fiziki. M. : Nauka, 1969. 184 s.
40. Kamenkovich V. M., Koshlyakoy M. N., Monin A. S. Synoptic Eddies in the Ocean. Series: Environmental Fluid Mechanics 5 / Ed. A. S. Monin. Netherlands, Dordrecht : Springer, 1986. 443 p.
41. Sutyrin G. G., Grimshaw R. Frictional effects on the deep-flow feedback on the β-drift of a baroclinic vortex over sloping topography // Deep Sea Research Part I: Oceanographic Research Papers. 2005. Vol. 52, iss. 1. P. 2156–2167. doi:10.1016/j.dsr.2005.06.017
42. Sutyrin G. G. Sinopticheskie dvizheniya konechnoi amplitudy // Doklady Akademii nauk SSSR.1986. T. 290, № 5. C. 1084–1088. URL: http://www.mathnet.ru/links/5662892d8fad089be8eb8a118be68902/dan47702.pdf (data obrashcheniya: 15.10.2020).
43. Sutyrin G. G. Agradient velocity, vortical motion and gravity waves in a rotating shallowwater model // Quarterly Journal of the Royal Meteorological Society. 2004. Vol. 130, iss. 601. P. 1977–1989. https://doi.org/10.1256/qj.03.54
44. Phillips N. A. Energy Transformations and Meridional Circulations associated with simple Baroclinic Waves in a two level, Quasi-geostrophic Model // Tellus. 1954. Vol. 6, iss. 3. P. 273–286. https://doi.org/10.1111/j.2153-3490.1954.tb01123.x
45. Scales, Growth Rates, and Spectral Fuxes of Baroclinic Instability in the Ocean / R. Tulloch [et al.] // Journal of Physical Oceanography. 2011. Vol. 41, iss. 6. P. 1057–1076. https://doi.org/10.1175/2011JPO4404.1
46. Thompson A. F., Young W. R. Scaling Baroclinic Eddy Fluxes: Vortices and Energy Balance // Journal of Physical Oceanography. 2006. Vol. 36, iss. 4. P. 720–738. https://doi.org/10.1175/JPO2874.1
47. Reznik G. M., Sutyrin G. G. Baroclinic topographic modons // Journal of Fluid Mechanics. 2001. Vol. 437. P. 121–142. doi: 10.1017/S0022112001004062
48. Sutyrin G. G., Flierl G. R. Intense Vortex Motion on the Beta Plane: Development of the Beta Gyres // Journal of Atmospheric Sciences. 1994. Vol. 51, iss. 5. P. 773–790. https://doi.org/10.1175/1520-0469(1994)051<0773:IVMOTB>2.0.CO;2
49. SIDDIES Corridor: A Major East-West Pathway of Long-Lived Surface and Subsurface Eddies Crossing the Subtropical South Indian Ocean / A. F. Dilmahamod [et al.] // Journal of Geophysical Research: Oceans. 2018. Vol. 123, iss. 8. P. 5406–5425. https://doi.org/10.1029/2018JC013828
50. Sutyrin G. G. How baroclinic vortices intensify resulting from erosion of their cores and/or changing environment // Ocean Modelling. 2020. Vol. 156. 101711. https://doi.org/10.1016/j.ocemod.2020.101711
51. Pegliasco C., Chaigneau A., Morrow R. Main eddy vertical structures observed in the four major Eastern Boundary Upwelling Systems // Journal of Geophysical Research: Oceans. 2015. Vol. 120, iss. 9. P. 6008–6033. https://doi.org/10.1002/2015JC010950
52. Burgess B. H., Dritschel D. G., Scott R. K. Vortex scaling ranges in two-dimensional turbulence // Physics of Fluids. 2017. Vol. 29, iss. 11. 111104. https://doi.org/10.1063/1.4993144
53. Sutyrin G. G. Azimutal'nye volny i simmetrizatsiya intensivnogo vikhrya // Doklady Akademii nauk SSSR. 1989. T. 304, № 5. S. 1086–1091. URL: http://www.mathnet.ru/links/8a31183a00e5c592d7d0ebfc624dda46/dan48505.pdf (data obrashcheniya: 30.10.2020).
54. Sutyrin G. G. On the vortex intensification due to stretching out of weak satellites // Physics of Fluids. 2019. Vol. 31, iss. 7. 075103. https://doi.org/10.1063/1.5098068
55. Sutyrin G. G., Radko T. On the peripheral intensification of two-dimensional vortices in smaller-scale randomly forcing flow // Physics of Fluids. 2019. Vol. 31, iss. 10. 101701. https://doi.org/10.1063/1.5118752
56. Benilov E. S. Stability of vortices in a two-layer ocean with uniform potential vorticity in the lower layer // Journal of Fluid Mechanics. 2004. Vol. 502. P. 207–232. doi:10.1017/S0022112003007547
57. Sutyrin G. Generation of deep eddies by a turning baroclinic jet // Deep Sea Research Part I: Oceanographic Research Papers. 2015. Vol. 101. P. 1–6. doi:10.1016/j.dsr.2015.02.011
58. Sutyrin G. G., Radko T. Stabilization of Isolated Vortices in a Rotating Stratified Fluid // Fluids. 2016. Vol. 1, iss 3. 26. doi:10.3390/fluids1030026
59. Sutyrin G. Why compensated cold-core rings look stable // Geophysical Research Letters. 2015. Vol. 42, iss. 13. P. 5395–5402. doi:10.1002/2015GL064378
60. Sutyrin G. G. On sharp vorticity gradients in elongating baroclinic eddies and their stabilization with a solid-body rotation // Geophysical Research Letters. Vol. 43, iss. 11. P. 5802–5811. doi:10.1002/2016GL069019.
61. Legras B., Dritschel D. Vortex stripping and the generation of high vorticity gradients in twodimensional flows // Applied Scientific Research. 1993. Vol. 51. P. 445–455. doi.org/10.1007/BF01082574
62. Mariotti A., Legras B., Dritschel D. G. Vortex stripping and the erosion of coherent structures in two-dimensional flows // Physics of Fluids. 1994. Vol. 6, iss. 12. 3954. https://doi.org/10.1063/1.868385
63. Legras B., Dritschel D. D., Caillol P. The erosion of a distributed two-dimensional vortex in a background straining flow // Journal of Fluid Mechanics. 2001. Vol. 441. P. 369–398. https://doi.org/10.1017/S002211200100502X
64. Sutyrin G., Carton X. Vortex interaction with a zonal Rossby wave in a quasi-geostrophic model // Dynamics of Atmospheres and Oceans. 2006. Vol. 41, iss. 2. P. 85–102. doi:10.1016/j.dynatmoce.2005.10.004
65. Sutyrin G. G. Maintenance of quick fluid rotation in the cores of long-lived Arctic eddies // Journal of Marine Systems. 1992. Vol. 3, iss. 6. P. 489–496 doi:10.1016/0924-7963(92)90019-5
События
-
Журнал «Современная наука и инновации» принят в DOAJ >>>
28 июл 2025 | 08:36 -
К платформе Elpub присоединились 4 журнала КФУ >>>
24 июл 2025 | 08:39 -
Журнал «Advanced Engineering Research (Rostov-on-Don)» вошел в Russian Science Citation Index >>>
23 июл 2025 | 08:38 -
Журнал «Літасфера» присоединился к Elpub! >>>
22 июл 2025 | 11:00 -
К платформе Elpub присоединился журнал «Труды НИИСИ» >>>
21 июл 2025 | 10:43