Internal gravity waves in the ocean with shear flows excited by non-stationary sources

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The problem of internal gravity wave generation by a localized oscillating disturbance source in the ocean of finite depth with background shear currents is considered. Model representations of the buoyancy frequency and the shear current distribution by depth are used to construct analytical solutions in the linear approximation. Under the Miles–Howard assumption, an integral representation of the solution is constructed as a sum of wave modes. Using the stationary phase method, an asymptotic representation of the solution for an individual mode is obtained. The spatial transformation of the phase structures of wave fields is studied depending on the oscillation frequency of the disturbance source and the main characteristics of the shear currents. Experimentally measured shear flows in abyssal channels are shown and compared with the results of laboratory modeling.

Full Text

Restricted Access

About the authors

V. V. Bulatov

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences

Author for correspondence.
Email: internalwave@mail.ru
Russian Federation, Moscow

I. Yu. Vladimirov

Shirshov Oceanology Institute, Russian Academy of Sciences

Email: iyuvladimirov@rambler.ru
Russian Federation, Moscow

Е. G. Morozov

Shirshov Oceanology Institute, Russian Academy of Sciences

Email: egmorozov@mail.ru
Russian Federation, Moscow

References

  1. Арнольд А. И. Волновые фронты и топологии кривых. М.: Фазис, 2002. 118 с.
  2. Булатов В. В., Владимиров Ю. В. Волны в стратифицированных средах. М.: Наука, 2015. 735 с.
  3. Булатов В. В., Владимиров И. Ю., Морозов Е. Г. Генерация внутренних гравитационных волн в океане при набегании фонового сдвигового течения на подводную возвышенность // Доклады РАН. Науки о Земле. 2022. Т. 505. № 2. С. 192–195.
  4. Гаврильева А. Г., Губарев Ю. Г., Лебедев М. П. Теорема Майлса и новые частные решения уравнения Тейлора–Гольдштейна // Ученые записки Казанского университета. Серия физико–математические науки. 2016. Т. 158(2). С. 156–171.
  5. Миропольский Ю. З. Динамика внутренних гравитационных волн в океане. Л.: Гидрометеоиздат, 1981. 302 с.
  6. Слепышев А. А. Вертикальный перенос импульса инерционно–гравитационными внутренними волнами на двумерном сдвиговом течении // Морской гидрофизический журнал. 2021. Т. 37. № 4. С. 279–287.
  7. Baines P. G. Mixing in downslope flows in the ocean – plumes versus gravity currents // Atmosphere–Ocean. 2008. V. 46(4). P. 405–419.
  8. Baines P. G., Hoinka K. P. Stratified flow over two–dimensional topography in fluid of infinite depth: a laboratory simulation // J. Atmospheric Sciences. 1985. V. 42 (15). P. 1614–1630.
  9. Bulatov V. V., Vladimirov Yu. V. Dynamics of internal gravity waves in the ocean with shear flows // Russian J. Earth Sciences. 2020. V. 20. ES4004.
  10. Fabrikant A. L., Stepanyants Yu. A. Propagation of waves in shear flows. World Scientific Publishing, 1998. 304 p.
  11. Howland C. J., Taylor J. R., Caulfield C. P. Shear–induces breaking of internal gravity waves // J. Fluid Mechanics. 2021. V. 921. A24.
  12. Kravtsov Yu., Orlov Yu. Caustics, catastrophes and wave fields. Berlin: Springer, 1999. 210 p.
  13. Long R. R. Some aspects of the flow of stratified fluids II I. Continuous density gradients // Tellus. 1955. V. 7. P. 341–357.
  14. Miles J. W. On the stability of heterogeneous shear flow // J. Fluid Mech. 1961. V. 10 (4). Р. 495–509.
  15. Meunier P., Dizиs S., Redekopp L., Spedding G. Internal waves generated by a stratified wake: experiment and theory // J. Fluid Mech. 2018. V. 846. P. 752–788.
  16. Morozov E. G. Oceanic internal tides. Observations, analysis and modeling. Berlin: Springer, 2018. 317 p.
  17. Morozov E. G., Frey D. I., Zuev O. A., Makarenko N. I., Seliverstova A. M., Mekhova O. S., Krechik V. A. Antarctic Bottom Water in the Vema Fracture Zone // J. Geophys. Res. 2023. V. 128. e2023JC019967.
  18. Morozov E. G., Kozlov I. E., Shchuka S. A., Frey D. I. Internal tide in the Kara Gates Strait // Oceanology. 2017. V. 57 (1). P. 8–18.
  19. 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. P. 7.
  20. Vallis G. K. Atmospheric and oceanic fluid dynamics. Cambridge University Press, 2006. 758 p.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Wave pattern of waves propagating from a source in the positive direction of the axis, two wave fronts at

Download (48KB)
Indexing metadata
3. Fig. 2. Waves from a source in all directions; two wave fronts at , two wave fronts at

Download (83KB)
Indexing metadata
4. Fig. 3. Measured velocity field along the Vema abyssal rift in the tropical Atlantic Ocean with bottom water flowing around a transverse submarine ridge. The numbers on the upper axis indicate the numbers of the current profiling stations with a down-slope Doppler current profiler. The maximum flow velocities to the east (from left to right) are observed after the current has rolled down the slope.

Download (192KB)
Indexing metadata
5. Fig. 4. Laboratory modeling (top) and numerical calculation (bottom) of flow around an underwater obstacle for values ​​of the parameter close to those observed in the ocean.

Download (324KB)
Indexing metadata

Note

Presented by Academician of the RAS M.V. Flint August 12, 2024


Copyright (c) 2025 Russian Academy of Sciences