Regular and Chaotic Dynamics

, Volume 21, Issue 3, pp 335–350 | Cite as

A Lagrangian study of eddies in the ocean

Article

Abstract

A brief review of our results on the application of the Lagrangian approach to study observed and simulated eddies in the ocean is presented. It is shown by a few examples of mesoscale vortex structures in the North Western Pacific how to compute and analyze maps of specific Lagrangian indicators in order to study the birth, formation, evolution, metamorphoses and death of ocean eddies. The examples involve two-dimensional eddies observed in satellitederived velocity fields in the deep ocean and three-dimensional ones simulated in a regional numerical model of circulation with a high resolution.

Keywords

ocean eddies Lagrangian analysis Lyapunov exponent 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fu, L.-L., Pattern and Velocity of Propagation of the Global Ocean Eddy Variability, J. Geophys. Res. Oceans, 2009, vol. 114, C11017, 14 pp.Google Scholar
  2. 2.
    Chelton, D. B., Schlax, M. G., and Samelson, R. M., Global Observations of Nonlinear Mesoscale Eddies, Progr. Oceanogr., 2011, vol. 91, no. 2, pp. 167–216.CrossRefGoogle Scholar
  3. 3.
    Olson, D. B., Rings in the Ocean, Annu. Rev. Earth Planet. Sci., 1991, vol. 19, no. 1, pp. 283–311.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Shen, C. Y. and Evans, Th. E., Inertial Instability and Sea Spirals, Geophys. Res. Lett., 2002, vol. 29, no. 23, 39-1-39-4, 4 pp.CrossRefGoogle Scholar
  5. 5.
    Dugan, J. P., Mied, R.P., Mignerey, P.C., and Schuetz, A. F., Compact, Intrathermocline Eddies in the Sargasso Sea, J. Geophys. Res. Oceans, 1982, vol. 87, no.C1, pp. 385–394.CrossRefGoogle Scholar
  6. 6.
    Gordon, A. L., Giulivi, C. F., Lee, C. M., Furey, H.H., Bower, A., and Talley, L., Japan/East Sea Intrathermocline Eddies, J. Phys. Oceanogr., 2002, vol. 32, no. 6, pp. 1960–1974.CrossRefGoogle Scholar
  7. 7.
    Hormazabal, S., Combes, V., Morales, C. E., Correa-Ramirez, M. A., Di Lorenzo, E., and Nuez, S., Intrathermocline Eddies in the Coastal Transition Zone off Central Chile (31-41S), J. Geophys. Res. Oceans, 2013, vol. 118, no. 10, pp. 4811–4821.CrossRefGoogle Scholar
  8. 8.
    Sokolovskiy, M. A., Filyushkin, B.N., and Carton, X. J., Dynamics of Intrathermocline Vortices in a Gyre Flow over a Seamount Chain, Ocean Dynam., 2013, vol. 63, no. 7, pp. 741–760.CrossRefGoogle Scholar
  9. 9.
    Sokolovskiy, M. A. and Verron, J., Finite-Core Hetons: Stability and Interactions, J. Fluid Mech., 2000, vol. 423, pp. 127–154.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Sokolovskiy, M. A. and Carton, X. J., Baroclinic Multipole Formation from Heton Interaction, Fluid Dynam. Res., 2010, vol. 42, no. 4, 045501, 31 pp.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Aref, H., Stirring by Chaotic Advection, J. Fluid Mech., 1984, vol. 143, pp. 1–21.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Samelson, R.M., Fluid Exchange across a Meandering Jet, J. Phys. Oceanogr., 1992, vol. 22, no. 4, pp. 431–444.CrossRefGoogle Scholar
  13. 13.
    Koshel, K.V. and Prants, S.V., Chaotic Advection in the Ocean, Physics–Uspekhi, see also: Uspekhi Fiz. Nauk, 2006, vol. 176, no. 11, pp. 1177–1206.Google Scholar
  14. 14.
    Uleysky, M.Yu., Budyansky, M. V., and Prants, S.V., Effect of Dynamical Traps on Chaotic Transport in a Meandering Jet Flow, Chaos, 2007, vol. 17, no. 4, 043105.CrossRefMATHGoogle Scholar
  15. 15.
    Budyansky, M. V., Uleysky, M.Yu., and Prants, S.V., Detection of Barriers to Cross-Jet Lagrangian Transport and Its Destruction in a Meandering Flow, Phys. Rev. E, 2009, vol. 79, no. 5, 056215, 11 pp.CrossRefGoogle Scholar
  16. 16.
    Pierrehumbert, R. T., Chaotic Mixing of Tracer and Vorticity by Modulated Travelling Rossby Waves, Geophys. Astrophys. Fluid Dyn., 1991, vol. 58, nos. 1–4, pp. 285–319.CrossRefGoogle Scholar
  17. 17.
    del-Castillo-Negrete, D. and Morrison, P. J., Chaotic Transport by Rossby Waves in Shear Flow, Phys. Fluids A, 1993, vol. 5, no. 4, pp. 948–965.MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Rypina, I. I., Brown, M. G., Beron-Vera, F. J., Ko¸cak, H., Olascoaga, M. J., and Udovydchenkov, I. A., On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex, J. Atmos. Sci., 2007, vol. 64, no. 10, pp. 3595–3610.CrossRefGoogle Scholar
  19. 19.
    Koshel, K.V., Sokolovskiy, M. A., and Davies, P.A., Chaotic Advection and Nonlinear Resonances in an Oceanic Flow above Submerged Obstacle, Fluid Dynam. Res., 2008, vol. 40, no. 10, pp. 695–736.MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Uleysky, M.Yu., Budyansky, M. V., and Prants, S.V., Mechanism of Destruction of Transport Barriers in Geophysical Jets with Rossby Waves, Phys. Rev. E, 2010, vol. 81, no. 1, 017202, 4 pp.CrossRefGoogle Scholar
  21. 21.
    Uleysky, M.Yu., Budyansky, M. V., and Prants, S.V., Chaotic Transport across Two-Dimensional Jet Streams, Zh. Eksp. Teor. Fiz., 2010, vol. 138, no. 6, pp. 1175–1188.Google Scholar
  22. 22.
    Sudre, J. and Morrow, R. A., Global Surface Currents: A High-Resolution Product for Investigating Ocean Dynamics, Ocean Dynam., 2008, vol. 58, no. 2, pp. 101–118.CrossRefGoogle Scholar
  23. 23.
    Lehahn, Y., D’ovidio, F., Lévy, M., and Heifetz, E., Stirring of the Northeast Atlantic Spring Bloom: A Lagrangian Analysis Based on Multisatellite Data, J. Geophys. Res. Oceans, 2007, vol. 112, no.C8, C08005, 15 pp.CrossRefGoogle Scholar
  24. 24.
    D’ovidio, F., Isern-Fontanet, J., López, C., Hernández-García, E., and García-Ladona, E., Comparison between Eulerian Diagnostics and Finite-Size Lyapunov Exponents Computed from Altimetry in the Algerian Basin, Deep Sea Res. Part 1 Oceanogr. Res. Pap., 2009, vol. 56, no. 1, pp. 15–31.CrossRefGoogle Scholar
  25. 25.
    Prants, S.V., Budyansky, M. V., and Uleysky, M.Yu., Lagrangian Study of Surface Transport in the Kuroshio Extension Area Based on Simulation of Propagation of Fukushima-Derived Radionuclides, Nonlinear Proc. Geophys., 2014, vol. 21, no. 1, pp. 279–289.CrossRefGoogle Scholar
  26. 26.
    Prants, S.V., Budyansky, M. V., and Uleysky, M.Yu., Lagrangian Fronts in the Ocean, Izv. Atmos. Ocean. Phys., 2014, vol. 50, no. 3, pp. 284–291CrossRefMATHGoogle Scholar
  27. 27.
    Prants, S.V., Budyansky, M. V., and Uleysky, M.Yu., Identifying Lagrangian Fronts with Favourable Fishery Conditions, Deep Sea Res. Part 1 Oceanogr. Res. Pap., 2014, vol. 90, pp. 27–35.CrossRefGoogle Scholar
  28. 28.
    Makarov, D., Uleysky, M., Budyansky, M., and Prants, S., Clustering in Randomly Driven Hamiltonian Systems, Phys. Rev. E, 2006, vol. 73, no. 6, 066210, 10 pp.MathSciNetMATHGoogle Scholar
  29. 29.
    Beron-Vera, F. J., Wang, Y., Olascoaga, M. J., Goni, G. J., and Haller, G., Objective Detection of Oceanic Eddies and the Agulhas Leakage, J. Phys. Oceanogr., 2013, vol. 43, no. 7, pp. 1426–1438.CrossRefGoogle Scholar
  30. 30.
    Prants, S.V., Budyansky, M. V., Ponomarev, V. I., and Uleysky, M.Yu., Lagrangian Study of Transport and Mixing in a Mesoscale Eddy Street, Ocean Model., 2011, vol. 38, nos. 1–2, pp. 114–125.CrossRefGoogle Scholar
  31. 31.
    Prants, S.V., Uleysky, M.Yu., and Budyansky, M. V., Lagrangian Coherent Structures in the Ocean Favorable for Fishery, Dokl. Earth Sci., 2012, vol. 447, no. 1, pp. 93–97.CrossRefGoogle Scholar
  32. 32.
    Haller, G., Lagrangian Coherent Structures from Approximate Velocity Data, Phys. Fluids, 2002, vol. 14, no. 6, pp. 1851–1861.MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Prants, S.V., Ponomarev, V. I., Budyansky, M. V., Uleysky, M.Yu., and Fayman, P.A., Lagrangian Analysis of Mixing and Transport of Water Masses in the Marine Bays, Izv. Atmos. Ocean. Phys., 2013, vol. 49, no. 1, pp. 91–106.CrossRefGoogle Scholar
  34. 34.
    Prants, S.V., Andreev, A.G., Budyansky, M. V., and Uleysky, M.Yu., Impact of Mesoscale Eddies on Surface Flow between the Pacific Ocean and the Bering Sea across the Near Strait, Ocean Model., 2013, vol. 72, pp. 143–152.CrossRefGoogle Scholar
  35. 35.
    Prants, S.V., Dynamical Systems Theory Methods to Study Mixing and Transport in the Ocean, Phys. Scr., 2013, vol. 87, no. 3, 038115, 5 pp.CrossRefGoogle Scholar
  36. 36.
    Prants, S.V., Uleysky, M.Yu., and Budyansky, M. V., Numerical Simulation of Propagation of Radioactive Pollution in the Ocean from the Fukushima Dai-Ichi Nuclear Power Plant, Dokl. Earth Sci., 2011, vol. 439, no. 6, pp. 811–814.Google Scholar
  37. 37.
    Prants, S.V., Chaotic Lagrangian Transport and Mixing in the Ocean, Eur. Phys. J. Spec. Top., 2014, vol. 223, no. 13, pp. 2723–2743.CrossRefGoogle Scholar
  38. 38.
    Budyansky, M. V., Goryachev, V.A., Kaplunenko, D. D., Lobanov, V.B., Prants, S.V., Sergeev, A.F., Shlyk, N. V., and Uleysky, M.Yu., Role of Mesoscale Eddies in Transport of Fukushima-Derived Cesium Isotopes in the Ocean, Deep Sea Res. Part 1 Oceanogr. Res. Pap., 2015, vol. 96, pp. 15–27.CrossRefGoogle Scholar
  39. 39.
    Prants, S.V., Ponomarev, V. I., Budyansky, M. V., Uleysky, M.Yu., and Fayman, P.A., Lagrangian Analysis of the Vertical Structure of Eddies Simulated in the Japan Basin of the Japan/East Sea, Ocean Model., 2015, vol. 86, pp. 128–140.CrossRefGoogle Scholar
  40. 40.
    Prants, S.V., Andreev, A.G., Budyansky, M. V., and Uleysky, M.Yu., Impact of the Alaskan Stream Flow on Surface Water Dynamics, Temperature, Ice Extent, Plankton Biomass, and Walleye Pollock Stocks in the Eastern Okhotsk Sea, J. Marine Syst., 2015, vol. 151, pp. 47–56.CrossRefGoogle Scholar
  41. 41.
    Takematsu, M., Ostrovski, A.G., and Nagano, Z., Observations of Eddies in the Japan Basin Interior, J. Oceanogr., 1999, vol. 55, no. 2, pp. 237–246.CrossRefGoogle Scholar
  42. 42.
    Talley, L., Min, D.-H., Lobanov, V., Luchin, V., Ponomarev, V., Salyuk, A., Shcherbina, A., Tishchenko, P., and Zhabin, I., Japan/East Sea Water Masses and Their Relation to the Sea’s Circulation, Oceanography, 2006, vol. 19, no. 3, pp. 32–49.CrossRefGoogle Scholar
  43. 43.
    Shapiro, N., Formation of a Circulation in the Quasiisopycnic Model of the Black Sea Taking into Account the Stochastic Nature of the Wind Stress, Phys. Oceanogr., 2000, vol. 10, no. 6, pp. 513–531.CrossRefGoogle Scholar
  44. 44.
    Samelson, R.M. and Wiggins, S., Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach, Interdiscip. Appl. Math., vol. 31, New York: Springer, 2006.Google Scholar
  45. 45.
    Peacock, Th. and Haller, G., Lagrangian Coherent Structures: The Hidden Skeleton of Fluid Flows, Phys. Today, 2013, vol. 66, no. 2, pp. 41–47.CrossRefGoogle Scholar
  46. 46.
    Olascoaga, M. J. and Haller, G., Forecasting Sudden Changes in Environmental Pollution Patterns, Proc. Natl. Acad. Sci., 2012, vol. 109, no. 13, pp. 4738–4743.CrossRefGoogle Scholar
  47. 47.
    Tew Kai, E., Rossi, V., Sudre, J., Weimerskirch, H., Lopez, C., Hernandez-Garcia, E., Marsac, F., and Garcon, V., Top Marine Predators Track Lagrangian Coherent Structures, Proc. Natl. Acad. Sci., 2009, vol. 106, no. 20, pp. 8245–8250.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Pacific Oceanological Institute of the Russian Academy of SciencesLaboratory of Nonlinear Dynamical SystemsVladivostokRussia

Personalised recommendations