Advertisement

Diagnosing and Parameterizing the Effects of Oceanic Eddies

  • Alexa GrieselEmail author
  • Julia Dräger-Dietel
  • Kerstin Jochumsen
Chapter
Part of the Mathematics of Planet Earth book series (MPE, volume 1)

Abstract

Oceanic eddies, fluctuations on scales on the order of one km to hundreds of km, derive their energy primarily from baroclinic instability processes. Currently, climate models do not incorporate the space and time variability of the effects of eddies and sub-mesoscale processes in an energy-consistent way. Eddy diffusivities are specified without connection to the energy budget and, more fundamentally, it is unclear to what extent, where and on what scales the downgradient eddy diffusion model is appropriate at all. Rotational components of the eddy fluxes associated with the advective terms in the eddy variance equation are generally large, so that production and dissipation of eddy energy do not balance locally. We will review here the current understanding of the spatial and temporal variability of eddy diffusivities and eddy–mean flow interactions that have been inferred in both observations and eddying ocean models. A focus will be on Lagrangian particle statistics as an ideal tool to describe the effects of eddies on a time mean transport and to assess the limits and validities of the eddy diffusion model. Eddy diffusivity diagnostics and the current state of eddy parameterizations in ocean models will be discussed as well as prospects for energy-consistent parameterizations.

References

  1. Abernathey, R., Cessi, P.: Topographic enhancement of eddy efficiency in baroclinic equilibration. J. Phys. Oceanogr. 44, 2107–2126 (2014)CrossRefGoogle Scholar
  2. Abernathey, R., Marshall, J.: Global surface eddy diffusivities derived from satellite altimetry. J. Geophys. Res. 118, 901–916 (2013)CrossRefGoogle Scholar
  3. Abernathey, R., Marshall, J., Mazloff, M., Shuckburgh, E.: Enhanced isopycnal mixing at steering levels in the Southern Ocean. J. Phys. Oceanogr. 40, 170–184 (2010)CrossRefGoogle Scholar
  4. Abernathey, R., Ferreira, D., Klocker, A.: Diagnostics of eddy mixing in a circumpolar channel. Ocean Model. 72, 1–16 (2013)CrossRefGoogle Scholar
  5. Andrews, D.G., Holton, J.R., Leovy, C.B.: Middle Atmosphere Dynamics. Academic Press (1987)Google Scholar
  6. Arbic, B.K., et al.: Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high-resolution models. J. Geophys. Res. 114, C02024 (2009)CrossRefGoogle Scholar
  7. Bates, M., Tulloch, R., Marshall, J., Ferrari, R.: Rationalizing the spatial distribution of mesoscale eddy diffusivity in terms of mixing length theory. J. Phys. Oceanogr. 44, 1523–1540 (2014)CrossRefGoogle Scholar
  8. Bauer, S., Swenson, M.S., Griffa, A., Mariano, A.J., Owens, K.: Eddy-mean flow decomposition and eddy-diffusivity estimates in the tropical Pacific Ocean. 1. Methodology. J. Geophys. Res. 103, 30855–30871 (1998)CrossRefGoogle Scholar
  9. Bell, T.H.: Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320–327 (1975)CrossRefGoogle Scholar
  10. Bennett, A.F.: Relative dispersion: local and nonlocal dynamics. J. Atmos. Sci. 41, 1881–1886 (1984)CrossRefGoogle Scholar
  11. Berloff, P.S., McWilliams, J.C.: Material transport in oceanic gyres. Part I: phenomenology. J. Phys. Oceanogr. 32, 764–796 (2002)CrossRefGoogle Scholar
  12. Bischoff, T., Thompson, A.: Configuration of a Southern Ocean storm track. J. Phys. Oceanogr. 44 (2014)CrossRefGoogle Scholar
  13. Bouchaud, J.P., Georges, A.: Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–129 (1990)MathSciNetCrossRefGoogle Scholar
  14. Bratseth, A.M.: On the estimation of transport characteristics of atmospheric data sets. Tellus 50A, 451–467 (1998)CrossRefGoogle Scholar
  15. Brüggemann, N., Eden, C.: Evaluating different parameterizations for mixed layer eddy fluxes induced by baroclinic instability. J. Phys. Oceanogr. 44, 2525–2546 (2014)CrossRefGoogle Scholar
  16. Capet, X., McWilliams, J.C., Molemaker, M.J., Shchepetkin, A.F.: Mesoscale to submesoscale transition in the california current system. Part i: flow structure, eddy flux, and observational tests. J. Phys. Oceanogr. 38, 29–43 (2008a)CrossRefGoogle Scholar
  17. Capet, X., McWilliams, J.C., Molemaker, M.J., Shchepetkin, A.F.: Mesoscale to submesoscale transition in the california current system. Part ii: frontal processes. J. Phys. Oceanogr. 38, 44–64 (2008b)CrossRefGoogle Scholar
  18. Capet, X., McWilliams, J.C., Molemaker, M.J., Shchepetkin, A.F.: Mesoscale to submesoscale transition in the california current system. Part iii: energy balance and flux. J. Phys. Oceanogr. 38, 2256–2269 (2008c)CrossRefGoogle Scholar
  19. Chapman, C., Hogg, A., Kiss, A., Rintoul, S.: The dynamics of Southern Ocean storm tracks. J. Phys. Oceanogr. 45, 884–903 (2015)CrossRefGoogle Scholar
  20. Chelton, D.B., Schlax, M.G., Samelson, R.M.: Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167–216 (2011)CrossRefGoogle Scholar
  21. Chen, R., Flierl, G., Wunsch, C.: A description of local and nonlocal eddy-mean flow interaction from an eddying state estimate. J. Phys. Oceanogr. 44, 2336–2352 (2014a)CrossRefGoogle Scholar
  22. Chen, R., McClean, J.L., Gille, S.T., Griesel, A.: Isopycnal eddy diffusivities and critical layers in the Kuroshio extension from an eddying ocean circulation model. J. Phys. Oceanogr. 44, 2191–2211 (2014b)CrossRefGoogle Scholar
  23. Chen, R., Gille, S., McClean, J., Flierl, G., Griesel, A.: A multi-wavenumber theory for eddy diffusivities and its application to the southeast Pacific (DIMES) region. J. Phys. Oceanogr. (2015).  https://doi.org/10.1175/JPO-D-14-0229.1CrossRefGoogle Scholar
  24. Cole, S.T., Wortham, C., Kunze, E., Owens, W.B.: Eddy stirring and horizontal diffusivity from argo float observations: geographic and depth variability. Geophys. l Res. Lett. 42, 3989–3997 (2015).  https://doi.org/10.1002/2015GL063827CrossRefGoogle Scholar
  25. Cushman-Roisin, B.: Beyond eddy diffusivity: an alternative model for turbulet disperion. Env. Fluid. Mech. 8, 543–549 (2008)CrossRefGoogle Scholar
  26. Danilov, S., Juricke, S., Kutsenko, A., Oliver, M.: Toward consistent subgrid momentum closures in ocean models (This volume, Chapter 5) (2019)Google Scholar
  27. Danabasoglu, G., Marshall, J.: Effects of vertical variations of thickness diffusivity in an ocean general circulation model. Ocean Model. 18, 122–141 (2007)CrossRefGoogle Scholar
  28. Davis, R.: Modelling eddy transport of passive tracers. J. Mar. Res. 45, 635–666 (1987)CrossRefGoogle Scholar
  29. Davis, R.E.: Observing the general circulation with floats. Deep sea research Part A. Oceanogr. Res. Pap. 38, S531–S571 (1991).  https://doi.org/10.1016/S0198-0149(12)80023-9CrossRefGoogle Scholar
  30. Draeger, J., Klafter, J.: Strong anomaly in diffusion generated by an iterated map. Phys. Rev. Lett. 84, 5998–6001 (2000)CrossRefGoogle Scholar
  31. Draeger-Dietel, J., Jochumsen, K., Griesel, A., Badin, G.: Relative dispersion of surface drifters in the Benguela upwelling region. J. Phys. Oceanogr. 48 (10), 2325–2341 (2018).  https://doi.org/10.1175/JPO-D-18-0027.1CrossRefGoogle Scholar
  32. Eden, C.: Parameterizing meso-scale eddy momentum fluxes based on potential vorticity mixing and a gauge term. Ocean Model. 32, 58–71 (2010)CrossRefGoogle Scholar
  33. Eden, C.: Thickness diffusivity in the Southern Ocean. Geophys. Res. Lett. 33 (2006).  https://doi.org/10.1029/2006GL026157.
  34. Eden, C.: A closure for meso-scale eddy fluxes based on linear instability theory. Ocean Model. 39, 362–369 (2011)CrossRefGoogle Scholar
  35. Eden, C., Greatbatch, R.J.: Towards a mesoscale eddy closures. Ocean Model. 20, 223–239 (2008)CrossRefGoogle Scholar
  36. Eden, C., Greatbatch, R.J., Olbers, D.: Interpreting eddy fluxes. J. Phys. Oceanogr. 37, 1282–1296 (2007a)CrossRefGoogle Scholar
  37. Eden, C., Greatbatch, R.J., Willebrand, J.: A diagnosis of thickness fluxes in an eddy-resolving model. J. Phys. Oceanogr. 37, 727–742 (2007b)CrossRefGoogle Scholar
  38. Farneti, R., et al.: An assessment of Antarctic Circumpolar Current and Southern Ocean meridional overturning circulation during 1958–2007 in a suite of interannual CORE-II simulations. Ocean Model. 93, 84–120 (2015)CrossRefGoogle Scholar
  39. Ferrari, R., Nikurashin, M.: Suppression of eddy mixing across jets in the Southern Ocean. J. Phys. Oceanogr. 40, 1501–1519 (2010)CrossRefGoogle Scholar
  40. Ferreira, D., Marshall, J., Heimbach, P.: Estimating eddy stresses by fitting dynamics to observations using a residual-mean ocean circulation model and its adjoint. J. Phys. Oceanogr. 35, 1891–1910 (2005)CrossRefGoogle Scholar
  41. Fox-Kemper, B., Lumpkin, R., Bryan, F.: Lateral transport in the ocean interior. In: Ocean Circulation and Climate: A 21st century perspective, vol. 103, pp. 185–209 (2013)Google Scholar
  42. Franzke, C.L.E., Oliver, M., Rademacher, J.D.M., Badin, G.: Multi-scale methods for geophysical flows (2019) (This volume, Chapter 1)Google Scholar
  43. Gabrielski, A., Badin, G., Kaleschke, L.: Anomalous dispersion of sea ice in the Fram Strait region. J. Geophys. Res. 120, 1809–1824 (2015)CrossRefGoogle Scholar
  44. Gent, P., Danabasoglu, G.: Response to increasing Southern Hemisphere winds in CCSM4. J. Clim. 24, 4992–4998 (2011).  https://doi.org/10.1175/JCLI-D-10-05011.1CrossRefGoogle Scholar
  45. Gent, P.R., McWilliams, J.C.: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 20, 150–155 (1990)CrossRefGoogle Scholar
  46. Greatbatch, R.J.: A framework for mesoscale eddy parameterization based on density-weighted averaging at fixed height. J. Phys. Oceanogr. 31, 2797–2806 (2011)CrossRefGoogle Scholar
  47. Green, J.S.: Transfer properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. R. Meteorol. Soc. 96, 157–185 (1970)CrossRefGoogle Scholar
  48. Griesel, A., Gille, S.T., Sprintall, J., McClean, J.L., Maltrud, M.E.: Assessing eddy heat flux and its parameterization: a wavenumber perspective from a 1/10\(^\circ \) ocean simulation. Ocean Model. 29, 248–260 (2009).  https://doi.org/10.1016/j.ocemod.2009.05.004CrossRefGoogle Scholar
  49. Griesel, A., Gille, S.T., Sprintall, J., McClean, J.L., LaCasce, J.H., Maltrud, M.E.: Isopycnal diffusivities in the Antarctic Circumpolar Current inferred from Lagrangian floats in an eddying model. J. Geophys. Res. 115 (2010).  https://doi.org/10.1029/2009JC005821
  50. Griesel, A., McClean, J.L., Gille, S.T., Sprintall, J., Eden, C.: Eulerian and Lagrangian isopycnal eddy diffusivities in the Southern Ocean of an eddying model. J. Phys. Oceanogr. 44, 644–661 (2014)CrossRefGoogle Scholar
  51. Griesel, A., Eden, C., Koopmann, N., Yulaeva, E.: Comparing isopycnal eddy diffusivities in the Southern Ocean with predictions from linear theory. Ocean Model. 94, 33–45 (2015).  https://doi.org/10.1016/j.ocemod.2015.08.001CrossRefGoogle Scholar
  52. Griffies, S.M.: The Gent-McWilliams skew flux. J. Phys. Oceanogr. 28, 831–841 (1998)CrossRefGoogle Scholar
  53. Hofmann, M., Morales, M.: The response of Southern Ocean eddies to increased midlatitude westerlies: a non-eddy resolving model study. Geophys. Res. Lett. 38 (2011).  https://doi.org/10.1029/2010GL045972CrossRefGoogle Scholar
  54. Jochum, M., Eden, C.: The connection between Southern Ocean winds, the Atlantic Meridional Overturning circulation, and Indo-Pacific upwelling. J. Clim. 28, 9250–9257 (2015)CrossRefGoogle Scholar
  55. Kämpf, J., Cox, D.: Towards improved numerical schemes of turbulent lateral dispersion. Ocean Modell. 106, 1–11 (2016)CrossRefGoogle Scholar
  56. Killworth, P.D.: On the parameterization of eddy transfer. Part I. Theory. J. Mar. Res. 55, 1171–1197 (1997)CrossRefGoogle Scholar
  57. Klingbeil, K., Burchard, H., Danilov, S., Goetz, C., Iske, A.: Reducing spurious diapycnal mixing in ocean models (2019) (This volume, Chapter 8)Google Scholar
  58. Klocker, A., Abernathey, R.: Global patterns of mesoscale eddy properties and diffusivities. J. Phys. Oceanogr. 44, 1030–1046 (2014)CrossRefGoogle Scholar
  59. Klocker, A., Ferrari, R., LaCasce, J.H.: Estimating suppression of eddy mixing by mean flows. J. Phys. Oceanogr. 9, 1566–1576 (2012a)CrossRefGoogle Scholar
  60. Klocker, A., Ferrari, R., LaCasce, J.H., Merrifield, S.T.: Reconciling float-based and tracer-based estimates of eddy diffusivities. J. Mar. Res 70, 569–602 (2012b)CrossRefGoogle Scholar
  61. Kolmogorov, A.N.: Dissipation of energy in the locally-isotropic turbulence. Proc. Math. Phys. Sci. 434, 15–17 (1941)MathSciNetzbMATHCrossRefGoogle Scholar
  62. Koszalka, I.M., LaCasce, J.H., Orvik, K.A.: Relative dispersion in the Nordic Seas. J. Mar. Res. 67 (2009)CrossRefGoogle Scholar
  63. Krauss, W., Böning, C.: Lagrangian properties of eddy fields in the northern North Atlantic as deduced from satellite-tracked buoys. J. Mar. Res. 45, 259–291 (1987)CrossRefGoogle Scholar
  64. LaCasce, J.H.: Lagrangian statistics from oceanic and atmospheric observations. In: Weiss, J.B., Provenzale, A. (eds.) Transport and Mixing in Geophysical Flows. Springer, Berlin (2008)Google Scholar
  65. LaCasce, J.H., Bower, A.: Relative dispersion in the subsurface North Atlantic. J. Mar. Res. 58, 863–894 (2000)CrossRefGoogle Scholar
  66. LaCasce, J.H., Ferrari, R., Marshall, J., Tulloch, R., Balwada, D., Speer, K.: Float-derived isopycnal diffusivities in the DIMES experiment. J. Phys. Oceanogr. 44, 764–780 (2014)CrossRefGoogle Scholar
  67. Koszalka, I., LaCasce, J.H., Andersson, M., Orvik, K.A., Mauritzen, C.: Surface circulation in the Nordic Seas from clustered drifters. Deep Sea Res. 58, 468–485 (2011)CrossRefGoogle Scholar
  68. LaCasce, J.H., Ohlmann, C.: Relative dispersion at the surface of the Gulf of Mexico. J. Mar. Res. 61, 285–312 (2003)CrossRefGoogle Scholar
  69. Liu, C., Köhl, A., Stammer, D.: Adjoint-based estimation of eddy-induced tracer mixing parameters in the global ocean. J. Phys. Oceanogr. 42, 1186–1206 (2012)CrossRefGoogle Scholar
  70. Lumpkin, R., Treguier, A.-M., Speer, K.: Lagrangian eddy scales in the Northern Atlantic Ocean. J. Phys. Oceanogr. 32, 2425–2440 (2001)CrossRefGoogle Scholar
  71. Mak, J., Marshall, D.P., Maddison, J.R., Bachmann, S.D.: Emergent eddy saturation from an energy constrained eddy parameterisation. Ocean Model. 112, 125–138 (2017)CrossRefGoogle Scholar
  72. Mandelbrot, B.: The Fractal Geometry of Nature. ISBN 0-7167-1186-9. W.H. Freeman & Co (1982)Google Scholar
  73. Marshall, J., Shutts, G.: A note on rotational and divergent eddy fluxes. J. Phys. Oceanogr. 11, 1677–1680 (1981)CrossRefGoogle Scholar
  74. Marshall, J., Shuckburgh, E., Jones, H., Hill, C.: Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport. J. Phys. Oceanogr. 36, 1806–1821 (2006)CrossRefGoogle Scholar
  75. Marshall, D.P., Maddison, J.R., Berloff, P.S.: A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr. 42, 539–557 (2012)CrossRefGoogle Scholar
  76. Medvedev, A.S., Greatbatch, R.J.: On advection and diffusion in the mesosphere and lower thermosphere: the role of rotational fluxes. J. Geophys. Res. 109, D07104 (2004).  https://doi.org/10.1029/2003JD003931CrossRefGoogle Scholar
  77. Molemaker, M.J., McWilliams, J.C., Yavneh, I.: Baroclinic instability and loss of balance. J. Phys. Oceanogr. 35, 1505–1517 (2005)MathSciNetCrossRefGoogle Scholar
  78. Molemaker, M.J., McWilliams, J.C., Capet, X.: Balanced and unbalanced routes to dissipation in an equilibrated Eady flow. J. Fluid Mech. 654, 35–63 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  79. Montroll, E.W., Weiss, G.H.: Random walks on lattices. J. Math. Phys. 6 (1965).  https://doi.org/10.1063/1.1704269MathSciNetzbMATHCrossRefGoogle Scholar
  80. Munday, D.R., Johnson, H.L., Marshall, D.P.: Eddy saturation of equilibrated circumpolar currents. J. Phys. Oceanogr. 43, 507–532 (2013).  https://doi.org/10.1175/JPO-D-12-095.1CrossRefGoogle Scholar
  81. Nakamura, M., Chao, Y.: On the eddy isopycnal thickness diffusivity of the Gent-McWilliams subgrid mixing parameterization. J. Clim. 13, 502–510 (2000)CrossRefGoogle Scholar
  82. Nakamura, N.: A new look at eddy diffusivity as a mixing diagnostic. J. Atmos. Sci. 58, 3685–3702 (2001)CrossRefGoogle Scholar
  83. Naveira Garabato, A.C., Ferrari, R., Polzin, K.L.: Eddy stirring in the Southern Ocean. J. Geophys. Res. 116, C09019 (2011).  https://doi.org/10.1029/2010JC006818CrossRefGoogle Scholar
  84. Nikurashin, M., Ferrari, R.: Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett. 38, L08610 (2011)CrossRefGoogle Scholar
  85. Oh, S.I., Zhurbas, V., Park, W.S.: Estimating horizontal diffusivity in the East Sea (Sea of Japan) and the northwest Pacific from satellite-tracked drifter data. J. Geophys. Res. 105, 6483–6492 (2000)CrossRefGoogle Scholar
  86. Ohlmann, J.C., Niiler, P.: A two-dimensional response to a tropical storm on the Gulf of Mexico shelf. Prog. Oceanogr. 29 (2005)CrossRefGoogle Scholar
  87. Okubo, A.: Oceanic diffusion diagrams. Deep-Sea Res. 18 (1971)CrossRefGoogle Scholar
  88. Olbers, D., Willebrand, J., Eden, C.: Ocean Dynamics. Springer, Berlin (2012)zbMATHCrossRefGoogle Scholar
  89. Ollitraut, M., Gabillet, C., de Verdiere, A.C.: Open ocean regimes of relative dispersion. J. Fluid Mech. 533 (2005)Google Scholar
  90. Osborn, T.R., Cox, C.S.: Oceanic fine structure. Geol. Astron. Fluid Dyn. 3 (1972)CrossRefGoogle Scholar
  91. Poje, A.C., et al.: The nature of surface dispersion near the Deepwater Horizon oil spill. Proc. Nat. Acad. Sci. USA 111, 12693–12698 (2014)CrossRefGoogle Scholar
  92. Richardson, L.F.: Atmospheric diffusion shown on a distance-neighbor graph. Proc. R. Soc. A. Bd 110, 709–737 (1926)CrossRefGoogle Scholar
  93. Riha, S., Eden, C.: Lagrangian and Eulerian lateral diffusivities in zonal jets. Ocean Modell. 39, 114–124 (2011)CrossRefGoogle Scholar
  94. Roach, C.J., Balwada, D., Speer, K.: Horizontal mixing in the Southern Ocean from Argo float trajectories. J. Geophys. Res. 5570–5586 (2016).  https://doi.org/10.1002/2015JC011440Google Scholar
  95. Sallée, J.B., Speer, K., Morrow, R., Lumpkin, R.: An estimate of Lagrangian eddy statistics and diffusion in the mixed layer of the Southern Ocean. J. Mar. Res. 66, 441–463 (2008)CrossRefGoogle Scholar
  96. Sallée, J.B., Speer, K., Rintoul, S.R.: Mean-flow and topographic control on surface eddy-mixing in the Southern Ocean. J. Mar. Res. 69, 753–777 (2011)CrossRefGoogle Scholar
  97. Salmon, R.: Lectures on Geophysical Fluid Dynamics. Oxford University Press, Oxford (1998)Google Scholar
  98. Shlesinger, M.F., Zaslavsky, G.M., Klafter, J.: Strange kinetics. Nature (1993)Google Scholar
  99. Shuckburgh, E., Jones, H., Marshall, J., Hill, C.: Understanding the regional variability of eddy diffusivity in the Pacific sector of the Southern Ocean. J. Phys. Oceanogr. 39, 2011–2023 (2009)CrossRefGoogle Scholar
  100. Smith, K.: The geography of linear baroclinic instability in the Earth’s Ocean. J. Mar. Res. 65, 655–683 (2007)CrossRefGoogle Scholar
  101. Smith, K., Marshall, J.: Evidence for deep eddy mixing in the Southern Ocean. J. Phys. Oceanogr. 39, 50–69 (2009)CrossRefGoogle Scholar
  102. Stone, P.H.: On non-geostrophic baroclinic instability. J. Atmos. Sci. 27, 390–400 (1966)CrossRefGoogle Scholar
  103. Stone, P.H.: A simplified radiative-dynamical model for the static stability of rotating atmospheres. J. Atmos. Sci. 29, 405–418 (1972)CrossRefGoogle Scholar
  104. Tanaka, Y., Hasumi, H., Endoh, M.: The distribution of the thickness diffusivity inferred from a high-resolution ocean model. In: Ohfuchi, W., Hamilton, K. (eds.) High Resolution Numerical Modeling of the Atmosphere and Ocean. Springer, Berlin (2007)Google Scholar
  105. Taylor, G.I.: Diffusion by continuous movements. Proc. R. Soc. A 64, 476–490 (1921)zbMATHGoogle Scholar
  106. Theiss, J.: Equatorward energy cascade, critical latitude and the predominance of cyclonic vortices in geostrophic turbulence. J. Phys. Oceanogr. 34, 1663–1678 (2004).  https://doi.org/10.1002/2015JC011440Google Scholar
  107. Treguier, A.M.: Evaluating eddy mixing coefficients from eddy-resolving ocean models: a case study. J. Mar. Res. 57, 89–108 (1999)CrossRefGoogle Scholar
  108. Tulloch, R., Ferrari, R., Jahn, O., Klocker, A., LaCasce, J.H., Ledwell, J.R., Marshall, J., Messias, M.-J., Speer, K., Watson, A.: Direct estimate of lateral eddy diffusivity upstream of Drake Passage. J. Phys. Oceanogr. 44, 2593–2616 (2014)CrossRefGoogle Scholar
  109. Vallis, G.K.: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, Cambridge, UK (2006)zbMATHCrossRefGoogle Scholar
  110. Veneziani, M., Griffa, A., Reynolds, A.M., Garraffo, Z.D., Chassignet, E.P.: Parameterizations of lagrangian spin statistics and particle dispersion in presence of coherent vortices. J. Mar. Res. 63, 1057–1083 (2005)CrossRefGoogle Scholar
  111. Viebahn, J., Eden, C.: Towards the impact of eddies on the response of the southern ocean to climate change. Ocean Model. 34 (2010).  https://doi.org/10.1016/j.ocemod.2010.05.005CrossRefGoogle Scholar
  112. Visbeck, M., Marshall, J., Haine, T.: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr. 27, 381–402 (1997)CrossRefGoogle Scholar
  113. Vollmer, L., Eden, C.: A global map of meso-scale eddy diffusivitie based on linear stability analysis. Ocean Modell. 72, 198–209 (2013)CrossRefGoogle Scholar
  114. von Storch, J.-S., Eden, C., Fast, I., Haak, H., Hernandez-Deckers, D., Maier-Reimer, E., Marotzke, J., Stammer, D.: An estimate of the Lorenz energy cycle for the World Ocean based on the 1/10\(^o\) STORM/NCEP simulation. J. Phys. Oceanogr. 42, 2185–2205 (2012)CrossRefGoogle Scholar
  115. von Storch, J.-S., Badin, G., Oliver, M.: The interior energy pathway: inertial gravity wave emission by oceanic flows, p. 2 (2019) (This volume, Chapter 2)Google Scholar
  116. Wilson, C., Williams, R.G.: Why are eddy fluxes of potential vorticity difficult to parameterize? J. Phys. Oceanogr. 34, 142–155 (2004)MathSciNetCrossRefGoogle Scholar
  117. Wilson, C., Williams, R.G.: When are eddy tracer fluxes directed downgradient? J. Phys. Oceanogr. 36, 189–201 (2006)CrossRefGoogle Scholar
  118. Zhurbas, V., Lyzhkov, D., Kuzmina, N.: Drifter-derived estimates of lateral eddy diffusivity in the World Ocean with emphasis on the Indian Ocean and problems of parameterization. Deep Sea Res. I 83, 1–11 (2014)CrossRefGoogle Scholar
  119. Zhurbas, V., Oh, S.I.: Drifter-derived maps of lateral diffusivity in the Pacific and Atlantic Oceans in relation to surface circulation patterns. J. Geophys. Res. 109, C05015 (2003).  https://doi.org/10.1029/2003JC002241

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexa Griesel
    • 1
    Email author
  • Julia Dräger-Dietel
    • 1
  • Kerstin Jochumsen
    • 2
  1. 1.Center for Earth System Research and Sustainability (CEN), Universität HamburgHamburgGermany
  2. 2.Federal Maritime and Hydrographic AgencyHamburgGermany

Personalised recommendations