Evaluation of the Temporal Dynamics of Oceanic Eddies with Initial Peripheral Rate Shift

  • Alexander Aleхeyevich Solovyev
  • Dmitry Alexandrovich Solovyev
Conference paper
Part of the Springer Geology book series (SPRINGERGEOL)

Abstract

We consider the problem of the development of two-dimensional vortex with initial vorticity in the peripheral ring area of the circularly rotating incompressible viscous fluid. As a mechanism for the generation of vortex motion, we propose the model of plain circular rotation of incompressible viscous fluid with initial perturbation localized at the peripheral ring zone with rate shift. Based on the analytical solution axisymmetric nonstationary equation of plain evolution of vortex in viscous fluid we obtained the resulting integral for the vorticity in the whole area of rotating fluid. This allowed us to study the dynamic characteristics of oceanic vortex formations and the time duration of the vortex motion conservation in a viscous liquid. The presented calculations given here show that the process of vorticity generation is characterized by the complex of interacting movements from the main vortex in the center of the rotating system and from the peripheral secondary perturbations. Vortex formation occurs in such direction that the central vorticity intensifies due to the secondary perturbations, as a result forming two areas – vortex and potential – of the rotating system. The obtained calculation results for the vorticity generation time in rings forming at the meanders of Gulf Stream jets, when compared to the observational data, show that lifespan of rings of different scales distributes rather variously according to their sizes and viscosity, the value of which correspond to turbulent regimes of jet streams. We discuss the prospect of its possible applications for predictive analysis of the development dynamics of large-scale ocean eddies.

Keywords

Eddy growth Vortex line stretching Finite-time singularities 

Notes

Acknowledgment

The work was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 14.616.21.0035, unique identifier of the project RFMEFI61615X0035).

References

  1. 1.
    North, G.R., Pyle, J.A., Zhang, F.: Encyclopedia of Atmospheric Sciences. Elsevier (2014)Google Scholar
  2. 2.
    Fedorov, K.N.: The Physical Nature and Structure of Oceanic Fronts. Springer, New York (1986)CrossRefGoogle Scholar
  3. 3.
    Shevchenko, I., Berloff, P.: On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics. Ocean Model. 111, 55–65 (2017).  https://doi.org/10.1016/j.ocemod.2017.02.003 ADSCrossRefGoogle Scholar
  4. 4.
    Uchida, T., Abernathey, R., Smith, S.: Seasonality of eddy kinetic energy in an eddy permitting global climate model. Ocean Model. 118, 41–58 (2017).  https://doi.org/10.1016/j.ocemod.2017.08.006 ADSCrossRefGoogle Scholar
  5. 5.
    Monin, A.S., Zhikharev, G.M.: Ocean vortexes. Phys. Usp. 160, 1–47 (1990)CrossRefGoogle Scholar
  6. 6.
    Nekrasov, A.N.: Diffusion of the vortex. Coll. op. T.1, pp. 92–116. The USSR Academy of Sciences Publishing House, Moscow (1961)Google Scholar
  7. 7.
    Terazawa, K.: On the decay of vortical motion in viscous fluid. Report of the Aeronautical Research Institute. Tokyo Imperial University, vol. 1 (1922)Google Scholar
  8. 8.
    Maddison, J.R., Marshall, D.P., Shipton, J.: On the dynamical influence of ocean eddy potential vorticity fluxes. Ocean Model. 92, 169–182 (2015).  https://doi.org/10.1016/j.ocemod.2015.06.003 ADSCrossRefGoogle Scholar
  9. 9.
    Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  10. 10.
    Solovyev, A.A., Solovyev, D.A.: The barotropic instability of the oceanic jet currents. Atmos. Ocean. Sci. 2, 80–84 (2017). Science Publishing Group, New York.  https://doi.org/10.11648/j.aos.20170203.13
  11. 11.
    Gulev, S., Freeman, E.: Tracking progress in marine climatology (2017)Google Scholar
  12. 12.
    Alekseev, V.V., Kisileva, S.V., Lappo, S.S.: Laboratory models of the physical processes in the atmosphere and ocean. Nauka, Moscow (2005)Google Scholar
  13. 13.
    Zhang, Y., Afanasyev, Y.D.: Baroclinic turbulence on the polar $β$-plane in the rotating tank: down to submesoscale. Ocean Model. 107, 151–160 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Polyanin, A.D., Manzhirov, A.V.: Handbook of Integral Equations. CRC Press, Boca Raton (2002)MATHGoogle Scholar
  15. 15.
    Smirnov, V.I.: A Course of Higher Mathematics. Elsevier (2014)Google Scholar
  16. 16.
    Barton, K.W., Sano, M.H.: Anticyclonic warm-core Gulf Stream rings off the northeastern United States during 1985. NAFO SCR Doc. 86, 77 (1986)Google Scholar
  17. 17.
    Chelton, D.B., Schlax, M.G., Samelson, R.M., de Szoeke, R.A.: Global observations of large oceanic eddies. Geophys. Res. Lett. 34 (2007).  https://doi.org/10.1029/2007gl030812
  18. 18.
    Auer, S.J.: Five-year climatological survey of the gulf stream system and its associated rings. J. Geophys. Res. Ocean 92, 11709–11726 (1987).  https://doi.org/10.1029/JC092iC11p11709 ADSCrossRefGoogle Scholar
  19. 19.
    Lai, D.Y., Richardson, P.L.: Distribution and movement of gulf stream rings. J. Phys. Oceanogr. 7, 670–683 (1977).  https://doi.org/10.1175/1520-0485(1977)007<0670:DAMOGS>2.0.co;2
  20. 20.
    Leterme, S.C., Pingree, R.D.: The Gulf stream, rings and North Atlantic eddy structures from remote sensing (Altimeter and SeaWiFS). J. Mar. Syst. 69, 177–190 (2008).  https://doi.org/10.1016/j.jmarsys.2005.11.022 ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of GeographyM.V.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Shirshov Institute of Oceanology, Russian Academy of SciencesMoscowRussia

Personalised recommendations