Evolution of Hydrodynamic Parameters of an Ellipsoidal Vortex in a Baroclinic Background Flow
Abstract and keywords
Abstract (English):
This study examines the behavior of a circular ellipsoidal ocean vortex in an external baroclinic flow with vertical shear. It is established that the vortex lifetime under fixed initial parameter conditions strongly depends on the external shear parameter. Depending on the vortex lifetime, the representative point in the parameter space may reside in one of three zones: (1) the survival zone, where the vortex lifetime tends to infinity, (2) the finite lifetime zone, and (3) the stretching zone, where the vortex lifetime approaches zero. At a certain shear velocity value, the infinite vortex lifetime becomes finite. This shear value, corresponding to the boundary between zones (1) and (2), is characterized as critical. The critical shear, in turn, depends on the initial geometric parameters of the vortex core. The work also investigates the vortex energy evolution. It is shown that during vortex stretching by the baroclinic flow, the total mechanical energy decreases both for the core and the entire vortex. Furthermore, the quasi-geostrophic balance remains valid for all three behavioral regimes.

Keywords:
ellipsoidal vortex, vortex lifetime, critical shear, vortex energy, Rossby number
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References

1. Arutyunyan D. A. i Zhmur V. V. Rezhimy povedeniya kvazigeostroficheskogo ellipsoidal'nogo vihrya na gorizontal'nom potoke s vertikal'nym sdvigom // Okeanologiya. — 2025. — T. 65, № 4. — S. 14—34. — https://doi.org/10.31857/S0030157425040024. — EDN: https://elibrary.ru/XMHRAH. EDN: https://elibrary.ru/YSPPSG

2. Zhmur V. V. Mezomasshtabnye vihri v okeane. — Moskva : GEOS, 2011. — S. 290.

3. Zhmur V. V. i Arutyunyan D. A. Pereraspredelenie energii pri gorizontal'nom vytyagivanii okeanskih vihrey barotropnymi techeniyami // Okeanologiya. — 2023. — T. 63, № 1. — S. 3—19. — https://doi.org/10.31857/S0030157423010185. — EDN: https://elibrary.ru/AFRQHI.

4. Zhmur V. V., Belonenko T. V., Novoselova E. V. i dr. O vytyagivanii mezomasshtabnyh vihrey v filamenty i raspredelenii ih na poverhnosti okeana // Izvestiya vuzov. Radiofizika. — 2023a. — T. 66, № 2/3. — S. 104—121. — https://doi.org/10.52452/00213462_2023_66_02_104. EDN: https://elibrary.ru/DCIBNC

5. Zhmur V. V., Belonenko T. V., Novoselova E. V. i dr. Prilozhenie k real'nomu okeanu teorii transformacii mezomasshtabnogo vihrya v submezomasshtabnuyu vihrevuyu nit' pri vytyagivanii ego neodnorodnym barotropnym techeniem // Okeanologiya. — 2023b. — T. 63, № 2. — S. 211—223. — https://doi.org/10.31857/S0030157423020156. — EDN: https://elibrary.ru/MAWHPW.

6. Zhmur V. V. i Pankratov K. K. Dinamika ellipsoidal'nogo pripoverhnostnogo vihrya v neodnorodnom potoke // Okeanologiya. — 1989. — T. 29, № 2. — S. 205—211.

7. Zhmur V. V., Travkin V. S., Belonenko T. V. i dr. Transformaciya kineticheskoy i potencial'noy energii pri vytyagivanii mezomasshtabnogo vihrya // Morskoy gidrofizicheskiy zhurnal. — 2022. — T. 38, 5 (227). — S. 466—480. — https://doi.org/10.22449/0233-7584-2022-5-466-480. EDN: https://elibrary.ru/MJMZVU

8. Zhmur V. V. i Schepetkin A. F. Evolyuciya ellipsoidal'nogo vihrya v stratificirovannom okeane v priblizhenii f-ploskosti // Izvestiya AN SSSR. FAO. — 1991. — T. 27, № 5. — S. 492—503. — URL: https://istina.ipmnet.ru/publications/article/394868173/.

9. Monin A. S. i Ozmidov R. V. Okeanskaya turbulentnost'. — Leningrad : Gidrometeoizdat, 1981. — S. 376. — URL: https://rusneb.ru/catalog/000199_000009_001036846/.

10. Tihonov A. N. i Samarskiy A. A. Uravneniya matematicheskoy fiziki. — 5-e. — Moskva : Nauka, 1977. — S. 736. — URL: https://biblioclub.ru/index.php?page=book&id=468275.

11. Chaplygin S. A. O pul'siruyuschem cilindricheskom vihre // Trudy otdeleniya fizicheskih nauk Obschestva lyubiteley estestvoznaniya / pod red. N. E. Zhukovskogo i P. V. Preobrazhenskogo. — Moskva, 1899. — T. 10, № 1. — S. 13—22. — URL: https://rusneb.ru/catalog/000199_000009_009791811/.

12. Dritschel D. G., Reinaud J. N. and McKiver W. J. The quasi-geostrophic ellipsoidal vortex model // Journal of Fluid Mechanics. — 2004. — Vol. 505. — P. 201–223. — https://doi.org/10.1017/S0022112004008377. EDN: https://elibrary.ru/XRPTJK

13. Kida S. Motion of an elliptic vortex in uniform shear flow // Journal of the Physical Society of Japan. — 1981. — Vol. 50, no. 10. — P. 3517–3520. — https://doi.org/10.1143/JPSJ.50.3517.

14. Kirchhoff G. Vorlesungen über mathematische Physik: Mechanik. — Leipzig : Taubner, 1876. — URL: https://archive.org/details/vorlesungenberm02kircgoog/page/n18/mode/2up.

15. McKiver W. J. and Dritschel D. G. The motion of a fluid ellipsoid in a general linear background flow // Journal of Fluid Mechanics. — 2003. — Vol. 474. — P. 147–173. — https://doi.org/10.1017/S0022112002002859. EDN: https://elibrary.ru/SZPBJB

16. McKiver W. J. and Dritschel D. G. The stability of a quasi-geostrophic ellipsoidal vortex in a background shear flow // Journal of Fluid Mechanics. — 2006. — Vol. 560. — P. 1–17. — https://doi.org/10.1017/S0022112006000462. EDN: https://elibrary.ru/XSVDKX

17. McKiver W. J. and Dritschel D. G. Balanced solutions for an ellipsoidal vortex in a rotating stratified flow // Journal of Fluid Mechanics. — 2016. — Vol. 802. — P. 333–358. — https://doi.org/10.1017/jfm.2016.462. EDN: https://elibrary.ru/WSNSXF

18. Meacham S. P., Pankratov K. K., Shchepetkin A. F., et al. The interaction of ellipsoidal vortices with background shear flows in a stratified fluid // Dynamics of Atmospheres and Oceans. — 1994. — Vol. 21, no. 2/3. — P. 167–212. — https://doi.org/10.1016/0377-0265(94)90008-6. EDN: https://elibrary.ru/PSCJZF

19. Polvani L. M. and Flierl G. R. Generalized Kirchhoff vortices // Physics of Fluids. — 1986. — Vol. 29. — P. 2376–2379. — https://doi.org/10.1063/1.865530.


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