A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection

Ocean Modelling

Volumn 86, Issue 1, 2015, Pages 1-14

  Bachman, S D ^a   Fox Kemper, B ^b   Bryan, F O ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b BROWN UNIVERSITY   (United States)

^c NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Eddies; Eddy transport tensor; Flux gradient relation; Gent McWilliams; Parameterization; Pseudoinverse

Indexed keywords

ADVECTION; ANISOTROPY; DIFFUSION; LAGRANGE MULTIPLIERS; LINEAR SYSTEMS; OPTICAL ANISOTROPY; PARAMETERIZATION;

EDDIES; EDDY TRANSPORTS; FLUX GRADIENTS; GENT-MCWILLIAMS; PSEUDO-INVERSES;

TENSORS;

ADVECTION; DATA INVERSION; DIFFUSIVITY; EDDY; ERROR ANALYSIS; MATHEMATICAL ANALYSIS; PARAMETERIZATION; TRACER;

EID: 84937158515     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2014.11.006     Document Type: Article

References (57)

1. Abernathey R.P., Ferreira D., Klocker A. Diagnostics of isopycnal mixing in a circumpolar channel. Ocean Modell. 2013, 72:1-16.
2. Abernathey R.P., Marshall J. Global surface eddy diffusivities derived from satellite altimetry. J. Geophys. Res.: Oceans 2013, 118(2):901-916.
3. Andrews D.G., McIntyre M.E. Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci. 1976, 33(11):2031-2048.
4. Andrews D.G., McIntyre M.E. Generalized Eliassen-Palm and Charney-Drazin theorems for waves on axisymmetric mean flows in compressible atmospheres. J. Atmos. Sci. 1978, 35(2):175-185.
5. Bachman S.D., Fox-Kemper B. Eddy parameterization challenge suite I: Eady spindown. Ocean Modell. 2013, 64:12-28.
6. Bishop S.P. Divergent eddy heat fluxes in the Kuroshio Extension at 144°-148°. Part 2: Spatiotemporal variability. J. Phys. Oceanography 2013, 43:2416-2431.
7. Bishop S.P., Bryan F.O. A comparison of mesoscale eddy heat fluxes from observations and a high-resolution ocean model simulation of the Kuroshio Extension. J. Phys. Oceanography 2013, 43:2563-2570.
8. Bratseth A.M. On the estimation of transport characteristics of atmospheric data sets. Tellus 1998, 50A:451-467.
9. Clark R.A., Ferziger J.H., Reynolds W.C. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 1979, 91(1):1-16.
10. Danilov S., Gurarie D. Rhines scale and spectra of the β-plane turbulence with bottom drag. Phys. Rev. E 2002, 65(6):067301.
11. Dukowicz J., Smith R. Stochastic theory of compressible turbulent fluid transport. Phys. Fluids 1997, 9:3523-3529.
12. Eckart C. An analysis of the stirring and mixing processes in incompressible fluids. J. Marine Res. 1948, 7:265-275.
13. Eden C. Eddy length scales in the North Atlantic Ocean. J. Geophys. Res. 2007, 112(C6).
14. Eden C., Greatbatch R.J., Olbers D. Interpreting eddy fluxes. J. Phys. Oceanography 2007, 37(5):1282-1296.
15. Eldén L. A weighted pseudoinverse, generalized singular values, and constrained least squares problems. BIT Numer. Math. 1982, 22(4):487-502.
16. Ferrari R., Nikurashin M. Suppression of eddy diffusivity across jets in the Southern Ocean. J. Phys. Oceanography 2010, 40(7):1501-1519.
17. Fox-Kemper B., Ferrari R., Pedlosky J. On the indeterminacy of rotational and divergent eddy fluxes. J. Phys. Oceanography 2003, 33(2):478-483.
18. Fox-Kemper B., Lumpkin R., Bryan F.O. Lateral transport in the ocean interior. Ocean Circulation and Climate: A 21st Century Perspective 2013, vol. 103:185-209. Academic Press, Ch. 8 (Elsevier Online). G. Siedler, S.M. Griffies, J. Gould, J.A. Church (Eds.).
19. Gent P.R., McWilliams J.C. Isopycnal mixing in ocean circulation models. J. Phys. Oceanography 1990, 20:150-155.
20. Gent P.R., Willebrand J., McDougall T.J., McWilliams J.C. Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanography 1995, 25:463-474.
21. Gille S.T., Davis E.E. The influence of mesoscale eddies on coarsely resolved density: An examination of sub- grid-scale parameterization. J. Phys. Oceanography 1999, 29:1109-1123.
22. Greatbatch R.J. A framework for mesoscale eddy parameterization based on density-weighted averaging at fixed height. J. Phys. Oceanography 2001, 31(9):2797-2806.
23. 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 ocean simulation. Ocean Modell. 2009, 29(4):248-260.
24. Griffies S.M. The Gent-McWilliams skew flux. J. Phys. Oceanography 1998, 28(5):831-841.
25. Griffies S.M., Gnanadesikan A., Pacanowski R.C., Larichev V.D., Dukowicz J.K., Smith R.D. Isoneutral diffusion in a z-coordinate ocean model. J. Phys. Oceanography 1998, 28(5):805-830.
26. Held I.M., Larichev V.D. A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane. J. Atmos. Sci. 1996, 53(7):946-952.
27. Holloway G., Kristmannsson S.S. Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech. 1984, 141:27-50.
28. Lau N.C., Wallace J.M. On the distribution of horizontal transports by transient eddies in the Northern Hemisphere wintertime circulation. J. Atmos. Sci. 1979, 36(10):1844-1861.
29. Lee M.M., Marshall D.P., Williams R.G. On the eddy transfer of tracers: Advective or diffusive?. J. Marine Res. 1997, 55(3):483-505.
30. Leonard A. Energy cascade in large-eddy simulations of turbulent fluid flows. Turbulent Diffusion Environ. Pollut. 1974, 1:237-248.
31. Marshall J., Shutts G. A note on rotational and divergent eddy fluxes. J. Phys. Oceanography 1981, 11(12):1677-1680.
32. McDougall T.J. Neutral surfaces. J. Phys. Oceanography 1987, 17:1950-1964.
33. McDougall T.J., McIntosh P.C. The temporal-residual-mean velocity. Part I: Derivation and the scalar conservation equations. J. Phys. Oceanography 1996, 26(12):2653-2665.
34. McDougall T.J., McIntosh P.C. The temporal-residual-mean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. J. Phys. Oceanography 2001, 31:1222-1246.
35. Medvedev A.S., Greatbatch R.J. On advection and diffusion in the mesosphere and lower thermosphere: The role of rotational fluxes. J. Geophys. Res.: Atmospheres (1984-2012) 2004, 109(D7).
36. Moore E.H. On the reciprocal of the general algebraic matrix. Bull. Am. Math. Soc. 1920, 26(9):394-395.
37. Müller P., Garrett C. From stirring to mixing in a stratified ocean. Oceanography 2002, 15:12-19.
38. Nakamura N. Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate. J. Atmos. Sci. 1996, 53(11):1524-1537.
39. Nakamura Y. Advanced Robotics: Redundancy and Optimization 1990, Addison-Wesley Longman Publishing Co., Inc.
40. Okubo A. Oceanic Diffusion Diagrams. Deep Sea Research and Oceanographic Abstracts 1971, vol. 18. Elsevier, (No. 8, pp. 789-802).
41. Penrose R. A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 1955, 51:406-413.
42. Plumb R.A. Eddy fluxes of conserved quantities by small-amplitude waves. J. Atmos. Sci. 1979, 36(9):1699-1704.
43. Plumb R.A., Mahlman J.D. The zonally averaged transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci. 1987, 44:298-327.
44. Plumb R.A., Ferrari R. Transformed Eulerian-mean theory. Part I: Nonquasigeostrophic theory for eddies on a zonal-mean flow. J. Phys. Oceanography 2005, 35(2):165-174.
45. Richardson, L.F., 1926. Atmospheric diffusion shown on a distance-neighbour graph. In: Proceedings of the 807 Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, pp. 709-737.
46. Rypina I.I., Kamenkovich I., Berloff P., Pratt L.J. Eddy-induced particle dispersion in the near-surface North Atlantic. J. Phys. Oceanography 2012, 42(12):2206-2228.
47. Redi M.H. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanography 1982, 12:1154-1158.
48. Sagaut P. Large Eddy Simulation for Incompressible Flows 2002, Springer-Verlag, Heidelberg.
49. Scott R.B., Wang F. Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanography 2005, 35(9):1650-1666.
50. Shuckburgh E., Jones H., Marshall J., Hill C. Robustness of an effective diffusivity diagnostic in oceanic flows. J. Phys. Oceanography 2009, 39(9):1993-2009.
51. Smith K. Tracer transport along and across coherent jets in two-dimensional turbulent flow. J. Fluid Mech. 2005, 544:133-142.
52. Smith R.D., Gent P.R. Anisotropic Gent-McWilliams parameterization for ocean models. J. Phys. Oceanography 2004, 34(11):2541-2564.
53. Sukoriansky S., Dikovskaya N., Galperin B. On the arrest of inverse energy cascade and the Rhines scale. J. Atmos. Sci. 2007, 64(9):3312-3327.
54. Taylor G.I. Diffusion by continuous movements. Proc. London Math. Soc. 1921, 20:196-211.
55. Taylor G.I. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. Roy. Soc. London Ser. A. Math. Phys. Sci. 1953, 219(1137):186-203.
56. Vallis G.K. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation 2006, Cambridge University Press.
57. Wunsch C. Discrete Inverse and State Estimation Problems: With Geophysical Fluid Applications 2006, vol. 2. Cambridge University Press, Cambridge.