- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Persistence and material coherence of a mesoscale ocean eddy

Michael C. Denes*, Gary Froyland, and Shane R. Keating

  • School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia

  • *m.denes@unsw.edu.au
PDF

Phys. Rev. Fluids 7, 034501 – Published 29 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.034501

Abstract

Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit at least two timescales: an Eulerian lifetime associated with persistent identifiable signatures in gridded fields such as vorticity or sea-surface height and multiple Lagrangian or material coherence timescales that are typically much shorter. We propose a method to study the multiple-timescale material transport, leakage, and entrainment by eddies with their surroundings by constructing sequences of finite-time coherent sets, computed as superlevel sets of dominant eigenfunctions of dynamic Laplace operators. The dominant eigenvalues of dynamic Laplace operators defined on time intervals of varying length allows us to identify a maximal coherence timescale that minimizes the rate of mass loss over a domain per unit flow time. We apply the method to examine the persistence and material coherence of an Agulhas ring, an ocean eddy in the South Atlantic ocean, using particle trajectories derived from a 0.1∘ global numerical ocean simulation. Using a sequence of sliding windows, the method is able to identify and track a persistent eddy feature for a time much longer than the maximal coherence timescale and with considerably larger material transport than the corresponding eddy feature identified from purely Eulerian information. Furthermore, the median residence times of fluid in the identified feature far exceed the timescale over which fully material motion is guaranteed. Through residence time calculations, we find that this particular eddy does not exhibit a long-lived coherent inner core and that the bulk of material transport is performed by the quasi-coherent outer ring of the eddy.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (68)

  1. R. Abernathey and G. Haller, Transport by Lagrangian vortices in the Eastern Pacific, J. Phys. Oceanogr. 48, 667 (2018).
  2. M. R. Allshouse and T. Peacock, Lagrangian based methods for coherent structure detection, Chaos 25, 097617 (2015).
  3. F. Andrade-Canto, D. Karrasch, and F. J. Beron-Vera, Genesis, evolution, and apocalypse of loop current rings, Phys. Fluids 32, 116603 (2020).
  4. F. Antown, G. Froyland, and O. Junge, Linear response for the dynamic Laplacian and finite-time coherent sets, Nonlinearity 34, 3337 (2021).
  5. R. Banisch and P. Koltai, Understanding the geometry of transport: Diffusion maps for Lagrangian trajectory data unravel coherent sets, Chaos 27, 035804 (2017).
  6. L. M. Beal, W. P. De Ruijter, A. Biastoch, and R. Zahn, On the role of the Agulhas system in ocean circulation and climate, Nature 472, 429 (2011).
  7. F. J. Beron-Vera, A. Hadjighasem, Q. Xia, M. J. Olascoaga, and G. Haller, Coherent Lagrangian swirls among submesoscale motions, Proc. Natl. Acad. Sci. USA 116, 18251 (2018).
  8. F. J. Beron-Vera, M. J. Olascoaga, and G. J. Goni, Oceanic mesoscale eddies as revealed by Lagrangian coherent structures, Geophys. Res. Lett. 35, L12603 (2008).
  9. F. J. Beron-Vera, M. J. Olascoaga, G. Haller, M. Farazmand, J. Triñanes, and Y. Wang, Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean, Chaos 25, 087412 (2015).
  10. F. J. Beron-Vera, Y. Wang, M. J. Olascoaga, G. J. Goni, and G. Haller, Objective detection of oceanic eddies and the Agulhas leakage, J. Phys. Oceanogr. 43, 1426 (2013).
  11. A. Biastoch, C. W. Böning, and J. R. Lutjeharms, Agulhas leakage dynamics affects decadal variability in Atlantic overturning circulation, Nature 456, 489 (2008).
  12. A. Biastoch, J. R. Lutjeharms, C. W. Böning, and M. Scheinert, Mesoscale perturbations control inter-ocean exchange south of Africa, Geophys. Res. Lett. 35, L20602 (2008).
  13. C. Blachut and C. González-Tokman, A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems, J. Comput. Dyn. 7, 369 (2020).
  14. C. Blachut, C. González-Tokman, and G. Hernandez-Duenas, A patch in time saves nine: Methods for the identification of localised dynamical behaviour and lifespans of coherent structures, arXiv:2109.09970.
  15. A. Chaigneau, and O. Pizarro, Eddy characteristics in the eastern South Pacific, J. Geophys. Res. 110, C06005 (2005).
  16. D. Chelton, P. Gaube, M. Schlax, J. Early, and R. Samelson, The influence of nonlinear mesoscale eddies on near-surface oceanic chlorophyll, Science 334, 328 (2011).
  17. D. B. Chelton, M. G. Schlax, and R. M. Samelson, Global observations of nonlinear mesoscale eddies, Prog. Oceanogr. 91, 167 (2011).
  18. D. B. Chelton, M. G. Schlax, R. M. Samelson, and R. A. de Szoeke, Global observations of large oceanic eddies, Geophys. Res. Lett. 34, L15606 (2007).
  19. W. P. De Ruijter, A. Biastoch, S. S. Drijfhout, J. R. Lutjeharms, R. P. Matano, T. Pichevin, P. J. Van Leeuwen, and W. Weijer, Indian-Atlantic interocean exchange: Dynamics, estimation and impact, J. Geophys. Res. [Oceans] 104, 20885 (1999).
  20. P. Delandmeter and E. van Sebille, The Parcels v2.0 Lagrangian framework: New field interpolation schemes, Geosci. Model Dev. 12, 3571 (2019).
  21. M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. Sen Gupta, Seasonal variability of the subpolar gyres in the southern ocean: A numerical investigation based on transfer operators, Nonlin. Processes Geophys. 16, 655 (2009).
  22. M. F. Demers and L.-S. Young, Escape rates and conditionally invariant measures, Nonlinearity 19, 377 (2005).
  23. A. Denner, O. Junge, and D. Matthes, Computing coherent sets using the Fokker-Planck equation, J. Comput. Dynam. 3, 163 (2016).
  24. J. J. Early, R. M. Samelson, and D. B. Chelton, The evolution and propagation of quasigeostrophic ocean eddies, J. Phys. Oceanogr. 41, 1535 (2011).
  25. H. Edelsbrunner, D. Kirkpatrick, and R. Seidel, On the shape of a set of points in the plane, IEEE Trans. Inf. Theory 29, 551 (1983).
  26. F. Fang and R. Morrow, Evolution, movement and decay of warm-core Leeuwin Current eddies, Deep Sea Res., Part II 50, 2245 (2003).
  27. G. Froyland, An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems, Physica D 250, 1 (2013).
  28. G. Froyland, Dynamic isoperimetry and the geometry of Lagrangian coherent structures, Nonlinearity 28, 3587 (2015).
  29. G. Froyland, C. Horenkamp, V. Rossi, N. Santitissadeekorn, and A. S. Gupta, Three-dimensional characterization and tracking of an Agulhas Ring, Ocean Model. 52-53, 69 (2012).
  30. G. Froyland, C. Horenkamp, V. Rossi, and E. van Sebille, Studying an Agulhas ring's long-term pathway and decay with finite-time coherent sets, Chaos 25, 083119 (2015).
  31. G. Froyland and O. Junge, Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories, SIAM J. Appl. Dyn. Syst. 17, 1891 (2018).
  32. G. Froyland and P. Koltai, Detecting the birth and death of finite-time coherent sets, arXiv:2103.16286.
  33. G. Froyland and E. Kwok, A Dynamic Laplacian for Identifying Lagrangian Coherent Structures on Weighted Riemannian Manifolds, J. Nonlinear Sci. 30, 1889 (2020).
  34. G. Froyland and K. Padberg-Gehle, Almost-invariant and finite-time coherent sets: Directionality, duration, and diffusion, in Ergodic Theory, Open Dynamics, and Coherent Structures, Springer Proceedings in Mathematics & Statistics, Vol. 70, pp. 171-216 (2014).
  35. G. Froyland, N. Santitissadeekorn, and A. Monahan, Transport in time-dependent dynamical systems: Finite-time coherent sets, Chaos 20, 043116 (2010).
  36. L.-L. Fu, Pathways of eddies in the South Atlantic Ocean revealed from satellite altimeter observations, Geophys. Res. Lett. 33, L14610 (2006).
  37. A. L. Gordon, Interocean exchange of thermocline water, J. Geophys. Res. 91, 5037 (1986).
  38. J. Haddad and M. Montenegro, On differentiability of eigenvalues of second order elliptic operators on non-smooth domains, J. Diff. Equ. 259, 408 (2015).
  39. A. Hadjighasem, M. Farazmand, D. Blazevski, G. Froyland, and G. Haller, A critical comparison of Lagrangian methods for coherent structure detection, Chaos 27, 053104 (2017).
  40. G. Haller, Lagrangian coherent structures, Annu. Rev. Fluid Mech. 47, 137 (2015).
  41. G. Haller and F. J. Beron-Vera, Coherent Lagrangian vortices: The black holes of turbulence, J. Fluid Mech. 731, R4 (2013).
  42. G. Haller, A. Hadjighasem, M. Farazmand, and F. Huhn, Defining coherent vortices objectively from the vorticity, J. Fluid Mech. 795, 136 (2016).
  43. J. Isern-Fontanet, E. García-Ladona, and J. Font, Identification marine eddies from altimetric maps, J. Atmos. Ocean. Technol. 20, 772 (2003).
  44. J. Isern-Fontanet, E. García-Ladona, and J. Font, Vortices of the Mediterranean Sea: An altimetric perspective, J. Phys. Oceanogr. 36, 87 (2006).
  45. D. Karrasch and N. Schilling, A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit, arXiv:2102.04777.
  46. A. E. Kiss, A. McC Hogg, N. Hannah, F. Boeira Dias, G. B. Brassington, M. A. Chamberlain, C. Chapman, P. Dobrohotoff, C. M. Domingues, E. R. Duran, M. H. England, R. Fiedler, S. M. Griffies, A. Heerdegen, P. Heil, R. M. Holmes, A. Klocker, S. J. Marsland, A. K. Morrison, J. Munroe, M. Nikurashin, P. R. Oke, G. S. Pilo et al. ACCESS-OM2 v1.0: A global ocean-sea ice model at three resolutions, Geosci. Model Dev. 13, 401 (2020).
  47. M. Lange and E. van Sebille, Parcels v0.9: Prototyping a Lagrangian ocean analysis framework for the petascale age, Geosci. Model Dev. 10, 4175 (2017).
  48. T. Liu, R. Abernathey, A. Sinha, and D. Chen, Quantifying Eulerian Eddy Leakiness in an Idealized Model, J. Geophys. Res. [Oceans] 124, 8869 (2019).
  49. M. Ndour, K. Padberg-Gehle, and M. Rasmussen, Spectral early-warning signals for sudden changes in time-dependent flow patterns, Fluids 6, 49 (2021).
  50. A. Okubo, Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences, Deep-Sea Res. Oceanogr. Abstr. 17, 445 (1970).
  51. P. J. Olver, Introduction to Partial Differential Equations (Springer International, Cham, 2014).
  52. A. R. Robinson, ed., Eddies in Marine Science (Springer, Berlin, 1983).
  53. C. P. Rock (private communication, 2021).
  54. C. Schneide, P. P. Vieweg, J. Schumacher, and K. Padberg-Gehle, Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows, Chaos 32, 013123 (2022).
  55. A. Sinha, D. Balwada, N. Tarshish, and R. Abernathey, Modulation of lateral transport by submesoscale flows and inertia-gravity waves, J. Adv. Model. Earth Syst. 11, 1039 (2019).
  56. Y. Wang, F. J. Beron-Vera, and M. J. Olascoaga, The life cycle of a coherent Lagrangian Agulhas ring, J. Geophys. Res. [Oceans] 121, 3944 (2016).
  57. Y. Wang, M. J. Olascoaga, and F. J. Beron-Vera, Coherent water transport across the South Atlantic, Geophys. Res. Lett. 42, 4072 (2015).
  58. W. Weijer, W. P. De Ruijter, A. Sterl, and S. S. Drijfhout, Response of the Atlantic overturning circulation to South Atlantic sources of buoyancy, Glob. Planet. Change 34, 293 (2002).
  59. J. Weiss, The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D 48, 273 (1991).
  60. M. Serra and G. Haller, Forecasting long-lived Lagrangian vortices from their objective Eulerian footprints, J. Fluid Mechanics 813, 436 (2017).
  61. S. C. Shadden, F. Lekien, and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D: Nonlinear Phenomena 212, 271 (2005).
  62. W. Zhang, C. L. P. Wolfe, and R. Abernathey, Role of surface-layer coherent eddies in potential vorticity transport in quasigeostrophic turbulence driven by eastward shear, Fluids 5, 2 (2019).
  63. See, www.cosima.org.au.
  64. G. Froyland, C. P. Rock, and K. Sakellariou, Sparse eigenbasis approximation: Multiple feature extraction across spatiotemporal scales with application to coherent set identification, Communs. Nonlin. Sci. Numer. Simul. 77, 81 (2019).
  65. See, www.github.com/michaeldenes/FEMDLpy.
  66. See, www.github.com/COSIMA/access-om2.
  67. doi: 10.4225/41/5a2dc8543105a.
  68. See, www.github.com/OceanParcels/parcels.

Outline

Information

Phys. Rev. Fluids 7, 034501– Published 29 March, 2022
  • Received 16 November 2021
  • Accepted 23 February 2022
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation