Advertisement

The European Physical Journal Special Topics

, Volume 223, Issue 13, pp 2723–2743 | Cite as

Chaotic Lagrangian transport and mixing in the ocean

  • S. V. Prants
Review
Part of the following topical collections:
  1. Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.)

Abstract

Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.

Keywords

Lyapunov Exponent European Physical Journal Special Topic Stagnation Point Unstable Manifold Anticyclonic Eddy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V.I. Arnold, C. R. Hebd. Seances Acad. Sci. 261, 17 (1965)Google Scholar
  2. 2.
    M. Henon, C. R. Hebd. Seances Acad. Sci. 262, 312 (1966)Google Scholar
  3. 3.
    H. Aref, J. Fluid Mech. 143, 1 (1984)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    H. Aref, Phys. Fluids 14, 1315 (2002)ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    J.M. Ottino, The kinematics of mixing: stretching, chaos, and transport (Cambridge University Press, Cambridge, 1989)Google Scholar
  6. 6.
    M. Budyansky, M. Uleysky, S. Prants, Physica D 195, 369 (2004)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    M.V. Budyansky, M.Yu. Uleysky, S.V. Prants, J. Exp. Theor. Phys. 99, 1018 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    S. Wiggins, Annu. Rev. Fluid Mech. 37, 295 (2005)ADSCrossRefMathSciNetGoogle Scholar
  9. 9.
    K.V. Koshel, S.V. Prants, Phys. – Usp. 49, 1151 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    S. Abdullaev, G. Zaslavsky, Usp. Fiz. Nauk 8, 1 (1991)CrossRefGoogle Scholar
  11. 11.
    D.V. Makarov, M.Yu. Uleysky, S.V. Prants, Chaos 14, 79 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    D. Makarov, S. Prants, A. Virovlyansky, G. Zaslavsky, Ray and wave chaos in ocean acoustics: chaos in waveguides (World Scientific, Singapore, 2010)Google Scholar
  13. 13.
    A.L. Virovlyansky, D.V. Makarov, S.V. Prants, Phys.–Usp. 55, 18 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    R.M Samelson, J. Phys. Oceanogr. 22, 431 (1992)ADSCrossRefGoogle Scholar
  15. 15.
    S.V. Prants, M.V. Budyansky, M.Yu. Uleysky, G. M. Zaslavsky, Chaos 16, 033117 (2006)ADSCrossRefMathSciNetGoogle Scholar
  16. 16.
    M.Yu. Uleysky, M.V. Budyansky, S.V. Prants, Chaos 17, 024703 (2007)CrossRefGoogle Scholar
  17. 17.
    M.Yu. Uleysky, M.V. Budyansky, S.V. Prants, J. Phys. A 41, 215102 (2008)ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    M.V. Budyansky, M.Yu. Uleysky, S.V. Prants, Phys. Rev. E 79, 056215 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    R.T. Pierrehumbert, Geophys. Astrophys. Fluid Dyn. 58, 285 (1991)ADSCrossRefGoogle Scholar
  20. 20.
    R.T. Pierrehumbert, Chaos, Solit. Fract. 4, 1091 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    D. Del-Castillo-Negrete, P.J. Morrison, Phys. Fluids A 5, 948 (1993)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    V.F. Kozlov, K.V. Koshel, Izvestiya Akad. Nauk Fiz. Atmosferi i Okeana 35, 137 (1999)Google Scholar
  23. 23.
    I.I. Rypina, M.G. Brown, F.J. Beron-Vera, H. Kozak, M.J. Olascoaga, I.A. Udovydchenkov, J. Atmos. Sci. 64, 3595 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    K.V. Koshel, M.A. Sokolovskiy, P.A. Davies, Fluid Dyn. Res. 40, 695 (2008)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  25. 25.
    E.A. Ryzhov, K.V. Koshel, D.V. Stepanov, Theor. Comput. Fluid Dyn. 24, 59 (2010)CrossRefzbMATHGoogle Scholar
  26. 26.
    M.Yu. Uleysky, M.V. Budyansky, S.V. Prants, Phys. Rev. E 81, 017202 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    M.Yu. Uleysky, M.V. Budyansky, S.V. Prants, J. Exp. Theor. Phys. 111, 1039 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    V.V. Zhmur, E.A. Ryzhov, K.V. Koshel, J. Mar. Res. 69, 435 (2011)CrossRefGoogle Scholar
  29. 29.
    M.A. Sokolovskiy, K.V. Koshel, X. Carton, Geophys. Astrophys. Fluid Dyn. 105, 505 (2011)ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    E.A. Ryzhov, K.V. Koshel, Izvestiya, Atmos. Oceanic Phys. 47, 241 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    K.V. Koshel, M.A. Sokolovskiy, J. Verron, J. Fluid Mech. 717, 255 (2013)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  32. 32.
    J. Sommeria, S.D. Meyers, H.L. Swinney, Nature 337, 58 (1989)ADSCrossRefGoogle Scholar
  33. 33.
    T.H. Solomon, W.J. Holloway, H.L. Swinney, Phys. Fluids A 5, 1971 (1993)ADSCrossRefGoogle Scholar
  34. 34.
    G. Haller, Phys. Fluids 14, 1851 (2002)ADSCrossRefMathSciNetGoogle Scholar
  35. 35.
    A.K.M.F. Hussain, Phys. Fluids 26, 2816 (1983)ADSCrossRefzbMATHGoogle Scholar
  36. 36.
    T. Peacock, G. Haller, Phys. Today 66(2), 41 (2013)CrossRefGoogle Scholar
  37. 37.
    R.M. Samelson, Ann. Rev. Mar. Sci. 5, 137 (2013)CrossRefGoogle Scholar
  38. 38.
    E.R. Abraham, M.M. Bowen, Chaos 12, 373 (2002)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  39. 39.
    F. d’Ovidio, V. Fernandez, E. Hernandez-Garcia, C. Lopez, Geophys. Res. Lett. 31, L17203 (2004)ADSCrossRefGoogle Scholar
  40. 40.
    S. Shadden, F. Lekien, J.E. Marsden, Physica D 212, 271 (2005)ADSCrossRefMathSciNetzbMATHGoogle Scholar
  41. 41.
    A.D. Jr. Kirwan, Prog. Ocean. 70, 448 (2006)CrossRefGoogle Scholar
  42. 42.
    Y. Lehahn, F. d’Ovidio, M. Levy, E. Heifetz, J. Geophys. Res. 112, C08005 (2007)ADSGoogle Scholar
  43. 43.
    F. Beron-Vera, M. Olascoaga, G. Goni, Geophys. Res. Lett. 35, L12603 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    E. Tew Kai, V. Rossi, J. Sudre, H. Weimerskirch, C. Lopez, E. Hernandez-Garcia, F. Marsac, V. Garcon, Proc. Nat. Ac. Sci. USA 106, 8245 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    S.V. Prants, M.V. Budyansky, V.I. Ponomarev, M.Yu. Uleysky, Ocean Modelling 38, 114 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    S.V. Prants, M.Yu. Uleysky, M.V. Budyansky, Doklady Earth Sciences 447, 1269 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    S.V. Prants, V.I. Ponomarev, M.V. Budyansky, M.Yu. Uleysky, P.A. Fyman, Izvestiya, Atmos. Oceanic Phys. 49, 82 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    S.V. Prants, Phys. Scr. 87, 038115 (2013)ADSCrossRefGoogle Scholar
  49. 49.
    S.V. Prants, A.G. Andreev, M.V. Budyansky, M.Yu. Uleysky, Ocean Model. 72, 143 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    S.V. Prants, M.V. Budyansky, M.Yu. Uleysky, Deep Sea Res. I 90, 27 (2014)CrossRefGoogle Scholar
  51. 51.
    S.V. Prants, M.V. Budyansky, M.Yu. Uleysky, Izv., Atmos. Oceanic Phys. 50, 284 (2014)ADSCrossRefGoogle Scholar
  52. 52.
    S.V. Prants, M.V. Budyansky, M.Yu. Uleysky, Nonlinear Proc. Geophys. 21, 279 (2014)ADSCrossRefGoogle Scholar
  53. 53.
    M.V. Budyansky, V.A. Goryachev, D.D. Kaplunenko, V.B. Lobanov, S.V. Prants, A.F. Sergeev, N.V. Shlyk, M.Yu. Uleysky, Deep Sea Res. I (in press)Google Scholar
  54. 54.
    S.V. Prants, A.G. Andreev, M.Yu. Uleysky, M.V. Budyansky. Ocean Dyn. 64, 771 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    S.V. Prants, M.Yu. Uleysky, M.V. Budyansky, Dok. Earth Sci. 439, 1179 (2011)ADSCrossRefGoogle Scholar
  56. 56.
    F. Huhn F, A. von Kameke, V. Perez Munuzuri, M.J. Olascoaga, F.J. Beron-Vera, Geophys. Res. Lett. 39, L06602 (2012)ADSCrossRefGoogle Scholar
  57. 57.
    J.H. Bettencourt, C. Lopez, E. Hernandez-Garcia, Ocean Modelling 51, 73 (2012)ADSCrossRefGoogle Scholar
  58. 58.
    F.J. Beron-Vera, Y. Wang, M.J. Olascoaga, G.J. Goni, G. Haller, J. Phys. Oceanogr. 43, 1426 (2013)ADSCrossRefGoogle Scholar
  59. 59.
    D.V. Makarov, M.Yu. Uleysky, M.V Budyansky, S.V. Prants, Phys. Rev. E 73, 066210 (2006)ADSCrossRefMathSciNetGoogle Scholar
  60. 60.
    A.M. Mancho, Des Small, S. Wiggins, Phys. Rep. 437, 55 (2006)ADSCrossRefGoogle Scholar
  61. 61.
    F. d’Ovidio, S. de Monti, A.D. Penna, C. Cotte, C. Guinet, J. Phys. A 46, 254023 (2013)ADSCrossRefMathSciNetGoogle Scholar
  62. 62.
    H. Kaeriyama, et al., Biogeosciences 10, 4287 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Laboratory of Nonlinear Dynamical SystemsPacific Oceanological Institute of the Russian Academy of SciencesVladivostokRussia

Personalised recommendations