MODE STRUCTURE OF INTERNAL GRAVITY WAVES GENERATED BY LOCALIZED SOURCES IN A STRATIFIED OCEAN WITH SHEARS FLOWS

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

The aim of the work is to study the mode structure of solutions describing the generation of internal gravity waves in stratified media with model distributions of the buoyancy frequency and background shear currents, which allows us to determine the main qualitative characteristics of the behavior of dispersion relations at small wave numbers depending on the mode number. The problem of constructing solutions describing the generation of linear internal gravity waves in a layer of a stratified medium of finite depth with model distributions of the buoyancy frequency and background shear current is considered. Under the assumption of the Miles–Howard stability for the Richardson number, the corresponding dispersion dependences are studied. It is shown that, depending on the parameters of the linear shear current, the dispersion curves of the wave modes can have qualitatively different asymptotic representations at small wave numbers. The dispersion curves of a finite number of modes describing waves with a limited length, at small values of the wave number, admit expansions in even powers of a small parameter. The dispersion curves of the remaining modes, corresponding to waves with an arbitrarily large length, are expanded in a series in odd powers of small wave numbers. The phase structure of the wave fields is studied depending on the mode number and the main characteristics of the shear currents. Analytical estimates are obtained that make it possible, depending on the parameters of the model flow, to find the number of the wave mode that divides the entire existing set of wave modes into limited and long-wave ones.

Авторлар туралы

V. Bulatov

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences

Email: internalwave@mail.ru
Moscow, Russia

I. Vladimirov

Shirshov Oceanology Institute, Russian Academy of Sciences

Moscow, Russia

Әдебиет тізімі

  1. Арнольд В. И. Волновые фронты и топология кривых. М.: Фазис, 2002. 120 с.
  2. Булатов В. В., Владимиров Ю. В. Волны в стратифицированных средах. М.: Наука, 2015. 735 с.
  3. Булатов В. В., Владимиров Ю. В. Дальние поля внутренних гравитационных волн при произвольных скоростях движения источника возмущений // Изв. РАН. Физика атмосферы и океана. 2015. Т. 51. № 6. С. 684–689.
  4. Булатов В. В., Владимиров Ю. В. Внутренние гравитационные волны в океане с разнонаправленными сдвиговыми течениями // Изв. РАН. Физика атмосферы и океана. 2020. Т. 56. № 1. С. 104–111.
  5. Булатов В. В., Владимиров Ю. В., Владимиров И. Ю. Внутренние гравитационные волны от осциллирующего источника возмущений в океане // Изв. РАН. Физика атмосферы и океана. 2021. Т. 57. № 3. С. 362–373.
  6. Булатов В. В., Владимиров И. Ю. Внутренние гравитационные волны, возбуждаемые нестационарными источниками возмущений в стратифицированном океане с фоновыми сдвиговыми течениями // Изв. РАН. Физика атмосферы и океана. 2024. Т. 60. № 5. С. 567–581.
  7. Лайпхил Дж. Волны в жидкостях. М.: Мир, 1981. 598 с.
  8. Миропольский Ю. З. Динамика внутренних гравитационных волн в океане. Л.: Гидрометеоиздат, 1981. 302 с.
  9. Свиркунов П. Н., Калашник М. В. Фазовые картины диспергирующих волн от движущихся локализованных источников // УФН. 2014. Т. 184. № 1. С. 89–100.
  10. Слепышев А. А., Лактинова Н. В. Вертикальный перенос импульса внутренними волнами в сдвиговом потоке // Изв. РАН. Физика атмосферы и океана. 2019. Т. 55. № 6. С. 194–200.
  11. Borovikov V.A., Kinber B.Ye. Geometrical theory of diffraction. London: Institution of Electrical Engineers, 1994. 390 p. (IEE Electromagnetic Waves Series, V. 37).
  12. Bournet-Aubertot P.I., Thorpe S.A. Numerical experiments of internal gravity waves an accelerating shear flow // Dyn. Atm. Oceans. 1999. V. 29. P. 41–63.
  13. Broutman D., Brandt L., Rotman J., Taylor C. A WKB derivation for internal waves generated by a horizontally moving body in a thermocline // Wave Motion. 2021. V. 105. 102759.
  14. Bulatov V.V., Vladimirov Yu.V. Dynamics of internal gravity waves in the ocean with shear flows // Russian J. Earth Sciences. 2020. V. 20. E54004.
  15. Bulatov V., Vladimirov Yu. Analytical approximations of dispersion relations for internal gravity waves equation with shear flows // Symmetry. 2020. V. 12 (11). 1865.
  16. Carpenter J.R., Balmforth N.J., Lawrence G.A. Identifying unstable modes in stratified shear layers // Phys. Fluids. 2010. V. 22. 054104.
  17. Churilov S. On the stability analysis of sharply stratified shear flows // Ocean Dynamics. 2018. V. 68. P. 867–884.
  18. Fabrikant A.L., Stepanyants Yu.A. Propagation of waves in shear flows. World Scientific Publishing, 1998. 304 p.
  19. Fraternale F., Domenicale L., Staffilan G., Tordella D. Internal waves in sheared flows: lower bound of the vorticity growth and propagation discontinuities in the parameter space // Phys. Re V. 2018. V. 97. № 6. 063102.
  20. Frey D.I., Novigatsky A.N., Kravchishina M.D., Morozov E.G. Water structure and currents in the Bear Island Trough in July-August 2017 // Russian J. Earth Sciences. 2017. V. 17. E53003.
  21. Gavrilova A.A., Gubarev Yu.G., Lebedev M.P. The Miles theorem and the first boundary value problem for the Taylor–Goldstein equation // J. Applied and Industrial Mathematics. 2019. V. 13 (3). P. 460–471.
  22. Gnevyshev V., Badulin S. Wave patterns of gravity–capillary waves from moving localized sources // Fluids. 2020. V. 5. 219.
  23. Gordey A.S., Frey D.I., Drozd I.D., Krechik V.A., Smirnova D.A., Gladyshev S.V., Morozov E.G. Spatial variability of water mass transports in the Bransfield Strait based on direct current measurements // Deep Sea Res. Part I: Oceanographic Res. Papers. 2024. V. 207. 104284.
  24. Hirota M., Morrison P.J. Stability boundaries and sufficient stability conditions for stably stratified, monotonic shear flows // Physics Letters A. 2016. V. 380 (21). P. 1856–1860.
  25. Howland C.J., Taylor J.R., Caulfield C.P. Shear-induces breaking of internal gravity waves // J. Fluid Mechanics. 2021. V. 921. A24.
  26. Klimchenko E.E., Frey D.I., Morozov E.G. Tidal internal waves in the Bransfield Strait, Antarctica // Russ. J. Earth. Science. 2020. V. 20. ES2006.
  27. Kravtsov Yu., Orlov Yu. Caustics, catastrophes and wave fields. Berlin: Springer, 1999. 210 p.
  28. Miles J.W. On the stability of heterogeneous shear flow // J. Fluid Mech. 1961. V. 10 (4). P. 495–509.
  29. Meunier P., Dizus S., Redekopp L., Spedding G. Internal waves generated by a stratified wake: experiment and theory // J. Fluid Mech. 2018. V. 846. P. 752–788.
  30. Morozov E.G. Oceanic internal tides. Observations, analysis and modeling. Berlin: Springer, 2018. 317 p.
  31. Morozov E.G., Parrilla-Barrera G., Velarde M.G., Scherbinin A.D. The Straits of Gibraltar and Kara Gates: a comparison of internal tides // Oceanologica Acta. 2003. V. 26 (3). P. 231–241.
  32. Morozov E.G., Tarakanov R.Yu., Frey D.I., Demidova T.A., Makarenko N.I. Bottom water flows in the tropical fractures of the Northern Mid-Atlantic Ridge // Journal of Oceanography. 2018. V. 74 (2). P. 147–167.
  33. Morozov E.G., Tarakanov R.Yu., Frey D.I. Bottom gravity currents and overflow in deep channels of the Atlantic ocean. Cham: Springer, 2021. 483 p.
  34. Pedlosky J. Waves in the ocean and atmosphere: introduction to wave dynamics. Berlin; Heildelberg: 2010. 260 p.
  35. Shugan I., Chen Y.-Y. Kinematics of the ship’s wake in the presence of a shear flow // J. Mar. Sci. Eng. 2021. V. 9. 7.
  36. Siepyshev A.A., Vorotnikov D.I. Generation of vertical fine structure by internal waves in a shear flows // Open J. Fluid Mechanics. 2019. V. 9. P. 140–157.
  37. Sutherland B.R. Internal gravity waves. Cambridge: Cambridge University Press, 2010. 394 p.
  38. Talipova T., Pelinovsky E., Didenkulova E. Internal tsunami waves in a stratified ocean induced by explosive volcano eruption: a parametric source // Phys. Fluids. 2024. V. 36. 042110
  39. Vlasenko V., Stashenuk N., Hutter K. Baroclinic tides. N.Y.: Cambridge University Press, 2005. 372 p.
  40. Voelker G.S., Akylas T.R., Achatz U. An application of WKBJ theory for triad interactions of internal gravity waves in varying background flows // Q. J.R. Meteorol. Soc. 2021. V. 147. P. 1112–1134.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу


Creative Commons License
Бұл мақала лицензия бойынша қол жетімді Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).