Rationalizing the spatial distribution of mesoscale eddy diffusivity in terms of mixing length theory

Journal of Physical Oceanography

Volumn 44, Issue 6, 2014, Pages 1523-1540

  Bates, Michael ^a,b   Tulloch, Ross ^a   Marshall, John ^a   Ferrari, Raffaele ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b GRIFFITH UNIVERSITY   (Australia)

Author keywords

Circulation Dynamics; Eddies; Mixing; Models and modeling; Parameterization; Subgrid scale processes

Indexed keywords

EDDY CURRENTS; KINETICS; MIXING; OCEANOGRAPHY; PARAMETERIZATION;

EDDIES; EDDY DIFFUSIVITIES; EDDY KINETIC ENERGY; MERIDIONAL HEAT TRANSPORTS; MIXING LENGTH THEORIES; OVERTURNING STREAMFUNCTION; PROPAGATION SPEED; SUB-GRID SCALE PROCESS;

DIFFUSION;

DIFFUSIVITY; KINETIC ENERGY; MESOSCALE EDDY; MIXING; OCEANIC CIRCULATION; PARAMETERIZATION; SPATIAL DISTRIBUTION;

EID: 84901624736     PISSN: 00223670     EISSN: 15200485     Source Type: Journal    
DOI: 10.1175/JPO-D-13-0130.1     Document Type: Article

References (74)

1. Abernathey, R., and J. C. Marshall, 2013: Global surface eddy diffusivities derived from satellite altimetry. J. Geophys. Res. Oceans, 118, 901-916, doi: 10. 1002/jgrc. 20066.
2. Abernathey, R., J. C. Marshall, M. Mazloff, and E. Shuckburgh, 2010: Enhancement of mesoscale eddy stirring at steering levels in the Southern Ocean. J. Phys. Oceanogr., 40, 170-184, doi: 10. 1175/2009JPO4201. 1.
3. Abernathey, R., D. Ferreira, and A. Klocker, 2013: Diagnostics of isopycnal mixing in a circumpolar channel. Ocean Modell., 72, 1-16, doi: 10. 1016/j. ocemod. 2013. 07. 004.
4. Bower, A. S., 1991: A simple kinematic mechanism for mixing fluid parcels across a meandering jet. J. Phys. Oceanogr., 21, 173-180, doi: 10. 1175/1520-0485(1991)021<0173: ASKMFM>2. 0. CO;2.
5. Bower, A. S., and M. S. Lozier, 1994: A closer look at particle exchange in the Gulf Stream. J. Phys. Oceanogr., 24, 1399-1418, doi: 10. 1175/1520-0485(1994)024<1399: ACLAPE>2. 0. CO;2.
6. Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc., 92, 325-334, doi: 10. 1002/qj. 49709239302.
7. Cerovečki, I., R. A. Plumb, and W. Heres, 2009: Eddy transport and mixing in a wind-and buoyancy-driven jet on the sphere. J. Phys. Oceanogr., 39, 1133-1149, doi: 10. 1175/2008JPO3596. 1.
8. Charney, J. G., and M. E. Stern, 1962: On the stability of internal baroclinic jets in a rotating atmosphere. J. Atmos. Sci., 19, 159-172, doi: 10. 1175/1520-0469(1962)019<0159: OTSOIB>2. 0. CO;2.
9. Chelton, D. B., M. G. Schlax, and R. M. Samelson, 2011: Global observations of nonlinear mesoscale eddies. Prog. Oceanogr., 91, 167-216, doi: 10. 1016/j. pocean. 2011. 01. 002.
10. Danabasoglu, G., and J. C. Marshall, 2007: Effects of vertical variations of thickness diffusivity in an ocean general circulation model. Ocean Modell., 18, 122-141, doi: 10. 1016/j. ocemod. 2007. 03. 006.
11. Danabasoglu, G., J. C. McWilliams, and P. R. Gent, 1994: The role of mesoscale tracer transports in the global ocean circulation. Science, 264, 1123-1126, doi: 10. 1126/science. 264. 5162. 1123.
12. Davis, R. E., 1991: Observing the general circulation with floats. Deep-Sea Res., 38A (Suppl. 1), S531-S571, doi: 10. 1016/S0198-0149(12)80023-9.
13. Döös, K., and D. J. Webb, 1994: The Deacon cell and the other meridional cells of the Southern Ocean. J. Phys. Oceanogr., 24, 429-442, doi: 10. 1175/1520-0485(1994)024<0429: TDCATO>2. 0. CO;2.
14. Eden, C., and R. J. Greatbatch, 2008: Diapycnal mixing by meso-scale eddies. OceanModell., 23, 113-120, doi: 10. 1016/j. ocemod. 2008. 04. 006.
15. Ferrari, R., and K. L. Polzin, 2005: Finescale structure of the T-S relation in the eastern North Atlantic. J. Phys. Oceanogr., 35, 1437-1454, doi: 10. 1175/JPO2763. 1.
16. Ferrari, R., and M. Nikurashin, 2010: Suppression of eddy diffusivity across jets in the Southern Ocean. J. Phys. Oceanogr., 40, 1501-1519, doi: 10. 1175/2010JPO4278. 1.
17. Ferrari, R., S. M. Griffies, A. J. G. Nurser, and G. K. Vallis, 2010: A boundary-value problem for the parameterized mesoscale eddy transport. Ocean Modell., 32, 143-156, doi: 10. 1016/j. ocemod. 2010. 01. 004.
18. Ferreira, D., J. C. Marshall, and P. Heimbach, 2005: Estimating eddy stresses by fitting dynamics to observations using a residual-mean ocean circulation model and its adjoint. J. Phys. Oceanogr., 35, 1891-1910, doi: 10. 1175/JPO2785. 1.
19. Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150-155, doi: 10. 1175/1520-0485(1990)020<0150: IMIOCM>2. 0. CO;2.
20. Greatbatch, R. J., 1998: Exploring the relationship between eddyinduced transport velocity, vertical momentum transfer, and the isopycnal flux of potential vorticity. J. Phys. Oceanogr., 28, 422-432, doi: 10. 1175/1520-0485(1998)028<0422: ETRBEI>2. 0. CO;2.
21. Green, J. S. A., 1970: Transfer properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. Roy. Meteor. Soc., 96, 157-185, doi: 10. 1002/qj. 49709640802.
22. Griffies, S. M., and Coauthors, 2009: Coordinated Ocean-Ice Reference Experiments (COREs). Ocean Modell., 26, 1-46, doi: 10. 1016/j. ocemod. 2008. 08. 007.
23. Haine, T. W. N., and J. C. Marshall, 1998: Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr., 28, 634-658, doi: 10. 1175/1520-0485(1998)028<0634: GSABIO>2. 0. CO;2.
24. Holloway, G., 1986: Estimation of oceanic eddy transports from satellite altimetry. Nature, 323, 243-244, doi: 10. 1038/323243a0.
25. Holloway, G., and S. S. Kristmannsson, 1984: Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech., 141, 27-50, doi: 10. 1017/S0022112084000720.
26. Hughes, C. W., 2005: Nonlinear vorticity balance of the Antarctic Circumpolar Current. J. Geophys. Res., 110, C11008, doi: 10. 1029/2004JC002753.
27. Hughes, C. W., M. S. Jones, and S. Carnochan, 1998: Use of transient features to identify eastward currents in the Southern Ocean. J. Geophys. Res., 103, 2929, doi: 10. 1029/97JC02442.
28. Jackson, J. D., 1998: Classical Electrodynamics. 3rd ed. Wiley, 808 pp.
29. Killworth, P. D., 1997: On the parameterization of eddy transfer. Part I. Theory. J. Mar. Res., 55, 1171-1197, doi: 10. 1357/0022240973224102.
30. Klocker, A., and R. P. Abernathey, 2014: Global patterns of mesoscale eddy properties and diffusivities. J. Phys. Oceanogr., 44, 1030-1046, doi: 10. 1175/JPO-D-13-0159. 1.
31. Klocker, A., R. Ferrari, and J. H. LaCasce, 2012a: Estimating suppression of eddy mixing by mean flows. J. Phys. Oceanogr., 42, 1566-1576, doi: 10. 1175/JPO-D-11-0205. 1.
32. Klocker, A., R. Ferrari, J. H. LaCasce, and S. Merrifield, 2012b: Reconciling float-based and tracer-based estimates of eddy diffusivities. J. Mar. Res., 70, 569-602, doi: 10. 1357/002224012805262743.
33. Lagerloef, G. S. E., G. T. Mitchum, R. B. Lukas, and P. P. Niiler, 1999: Tropical Pacific near-surface currents estimated from altimeter, wind, and drifter data. J. Geophys. Res., 104, 23 313-23 326, doi: 10. 1029/1999JC900197.
34. Large, W. G., G. Danabasoglu, S. C. Doney, and J. C. McWilliams, 1997: Sensitivity to surface forcing and boundary layer mixing in a global ocean model: Annual-mean climatology. J. Phys. Oceanogr., 27, 2418-2447, doi: 10. 1175/1520-0485(1997)027<2418: STSFAB>2. 0. CO;2.
35. Larichev, V. D., and I. M. Held, 1995: Eddy amplitudes and fluxes in a homogeneous model of fully developed baroclinic instability. J. Phys. Oceanogr., 25, 2285-2297, doi: 10. 1175/1520-0485(1995)025<2285: EAAFIA>2. 0. CO;2.
36. Ledwell, J. R., A. J. Watson, and C. S. Law, 1998: Mixing of a tracer in the pycnocline. J. Geophys. Res., 103, 21 499-21 529, doi: 10. 1029/98JC01738.
37. Lozier, M. S., and D. Bercovici, 1992: Particle exchange in an unstable jet. J. Phys. Oceanogr., 22, 1506-1516, doi: 10. 1175/1520-0485(1992)022<1506: PEIAUJ>2. 0. CO;2.
38. Marshall, D. P., J. R. Maddison, and P. S. Berloff, 2012: A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr., 42, 539-557, doi: 10. 1175/JPO-D-11-048. 1.
39. Marshall, J. C., 1981: On the parameterization of geostrophic eddies in the ocean. J. Phys. Oceanogr., 11, 257-271, doi: 10. 1175/1520-0485(1981)011<0257: OTPOGE>2. 0. CO;2.
40. Marshall, J. C., and T. Radko, 2003: Residual-mean solutions for the Antarctic Circumpolar Current and its associated overturning circulation. J. Phys. Oceanogr., 33, 2341-2354, doi: 10. 1175/1520-0485(2003)033<2341: RSFTAC>2. 0. CO;2.
41. Marshall, J. C., and K. Speer, 2012: Closure of the meridional overturning circulation through Southern Ocean upwelling. Nat. Geosci., 5, 171-180, doi: 10. 1038/ngeo1391.
42. Marshall, J. C., E. Shuckburgh, H. Jones, and C. Hill, 2006: Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport. J. Phys. Oceanogr., 36, 1806-1821, doi: 10. 1175/JPO2949. 1.
43. Menemenlis, D., J.-M. Campin, P. Heimbach, C. Hill, T. Lee, A. Nguyen, M. Schodlok, and H. Zhang, 2008: ECCO2: High resolution global ocean and sea ice data synthesis. Mercator Ocean Quarterly Newsletter, No. 31, Mercator Ocean, Ramonville Saint-Agne, France, 13-21.
44. Nakamura, N., 1996: Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate. J. Atmos. Sci., 53, 1524-1537, doi: 10. 1175/1520-0469(1996)053<1524: TDMEFA>2. 0. CO;2.
45. Naveira Garabato, A. C., R. Ferrari, and K. L. Polzin, 2011: Eddy stirring in the Southern Ocean. J. Geophys. Res., 116, C09019, doi: 10. 1029/2010JC006818.
46. Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn., 3, 321-345, doi: 10. 1080/03091927208236085.
47. Plumb, R. A., and J. D. Mahlman, 1987: The zonally averaged transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci., 44, 298-327, doi: 10. 1175/1520-0469(1987)044<0298: TZATCO>2. 0. CO;2.
48. Poulain, P.-M., and P. P. Niiler, 1989: Statistical analysis of the surface circulation in the California Current system using satellite-tracked drifters. J. Phys. Oceanogr., 19, 1588-1603, doi: 10. 1175/1520-0485(1989)019<1588: SAOTSC>2. 0. CO;2.
49. Prandtl, L., 1925: Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech., 5, 136-139.
50. Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 1154-1158, doi: 10. 1175/1520-0485(1982)012<1154: OIMBCR>2. 0. CO;2.
51. Rhines, P. B., and W. R. Holland, 1979: A theoretical discussion of eddy-driven mean flows. Dyn. Atmos. Oceans, 3, 289-325, doi: 10. 1016/0377-0265(79)90015-0.
52. Rhines, P. B., and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid Mech., 122, 347-367, doi: 10. 1017/S0022112082002250.
53. Sallée, J. B., K. Speer, R. Morrow, and R. Lumpkin, 2008: An estimate of Lagrangian eddy statistics and diffusion in the mixed layer of the Southern Ocean. J. Mar. Res., 66, 441-463, doi: 10. 1357/002224008787157458.
54. Sallée, J. B., K. Speer, and S. R. Rintoul, 2011: Mean-flow and topographic control on surface eddy-mixing in the Southern Ocean. J. Mar. Res., 69, 753-777, doi: 10. 1357/002224011799849408.
55. Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 378 pp.
56. Smith, K. S., 2007: The geography of linear baroclinic instability in Earth's oceans. J. Mar. Res., 65, 655-683, doi: 10. 1357/002224007783649484.
57. Smith, K. S., and J. C. Marshall, 2009: Evidence for enhanced eddy mixing at middepth in the Southern Ocean. J. Phys. Oceanogr., 39, 50-69, doi: 10. 1175/2008JPO3880. 1.
58. Stewart, R., and R. E. Thomson, 1977: Re-examination of vorticity transfer theory. Proc. Roy. Soc., 354, 1-8, doi: 10. 1098/rspa. 1977. 0053.
59. Stone, P. H., 1972: A simplified radiative-dynamical model for the static stability of rotating atmospheres. J. Atmos. Sci., 29, 405-418, doi: 10. 1175/1520-0469(1972)029<0405: ASRDMF>2. 0. CO;2.
60. Swenson, M. S., and P. P. Niiler, 1996: Statistical analysis of the surface circulation of the California Current. J. Geophys. Res., 101, 22 631-22 645, doi: 10. 1029/96JC02008.
61. Taylor, G. I., 1922: Diffusion by continuous movements. Proc. London Math. Soc., s2-20, 196-212, doi: 10. 1112/plms/s2-20. 1. 196.
62. Thompson, A. F., and W. R. Young, 2006: Scaling baroclinic eddy fluxes: Vortices and energy balance. J. Phys. Oceanogr., 36, 720-738, doi: 10. 1175/JPO2874. 1.
63. Thomson, R. E., and R. Stewart, 1977: The balance and redistribution of potential vorticity within the ocean. Dyn. Atmos. Oceans, 1, 299-321, doi: 10. 1016/0377-0265(77)90019-7.
64. Treguier, A.-M., I. M. Held, and V. D. Larichev, 1997: Parameterization of quasigeostrophic eddies in primitive equation ocean models. J. Phys. Oceanogr., 27, 567-580, doi: 10. 1175/1520-0485(1997)027<0567: POQEIP>2. 0. CO;2.
65. Tulloch, R., J. C. Marshall, and K. S. Smith, 2009: Interpretation of the propagation of surface altimetric observations in terms of planetary waves and geostrophic turbulence. J. Geophys. Res., 114, C02005, doi: 10. 1029/2008JC005055.
66. Tulloch, R., J. C. Marshall, C. Hill, and K. S. Smith, 2011: Scales, growth rates, and spectral fluxes of baroclinic instability in the ocean. J. Phys. Oceanogr., 41, 1057-1076, doi: 10. 1175/2011JPO4404. 1.
67. Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, 745 pp.
68. Visbeck, M., J. C. Marshall, T. W. N. Haine, and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27, 381-402, doi: 10. 1175/1520-0485(1997)027<0381: SOETCI>2. 0. CO;2.
69. Welander, P., 1973: Lateral friction in the oceans as an effect of potential vorticity mixing. Geophys. Fluid Dyn., 5, 173-189, doi: 10. 1080/03091927308236114.
70. White, A. A., 1977: The surface flow in a statistical climate model-A test of a parameterization of large-scale momentum fluxes. Quart. J. Roy. Meteor. Soc., 103, 93-119, doi: 10. 1002/qj. 49710343506.
71. Wunsch, C., 2011: The decadal mean ocean circulation and Sverdrup balance. J. Mar. Res., 69, 417-434, doi: 10. 1357/002224011798765303.
72. Wunsch, C., P. Heimbach, R. M. Ponte, I. Fukumori, and ECCOGODAE Consortium Members, 2009: The global general circulation of the ocean estimated by the ECCO-Consortium. Oceanography, 22, 88-103, doi: 10. 5670/oceanog. 2009. 41.
73. Young, W. R., 2012: An exact thickness-weighted average formulation of the Boussinesq equations. J. Phys. Oceanogr., 42, 692-707, doi: 10. 1175/JPO-D-11-0102. 1.
74. Zhurbas, V., and I. S. Oh, 2004: Drifter-derived maps of lateral diffusivity in the Pacific and Atlantic Oceans in relation to surface circulation patterns. J. Geophys. Res., 109, C05015, doi: 10. 1029/2003JC002241.