Spurious dianeutral mixing and the role of momentum closure

Ocean Modelling

Volumn 45-46, Issue , 2012, Pages 37-58

  Ilicak, Mehmet ^a   Adcroft, Alistair J ^a   Griffies, Stephen M ^a   Hallberg, Robert W ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Cabbeling; Exchange flow; Momentum transport; Ocean models; Overflows; Reference potential energy; Spurious dianeutral transport; Tracer advection

Indexed keywords

CABBELING; EXCHANGE-FLOW; MOMENTUM TRANSPORT; OCEAN MODEL; OVERFLOWS; SPURIOUS DIANEUTRAL TRANSPORT;

ADVECTION; EQUATIONS OF STATE; FRICTION; GOLD; MIXING; MOMENTUM TRANSFER; OCEAN HABITATS; POTENTIAL ENERGY; REYNOLDS NUMBER; SEAWATER;

COMPUTER SIMULATION;

ADVECTION; CLIMATE MODELING; COMPUTER SIMULATION; FLOW FIELD; MESOSCALE EDDY; MIXING; MOMENTUM TRANSFER; POTENTIAL ENERGY; REYNOLDS NUMBER; SEAWATER; TRACER; VISCOSITY;

EID: 84857031091     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2011.10.003     Document Type: Article

References (63)

1. Adcroft A., Campin J. Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models. Ocean Modell. 2004, 7:269-284.
2. Adcroft A., Hill C., Marshall J. Representation of topography by shaved cells in a height coordinate ocean model. Mon. Weather Rev. 1997, 125:2293-2315.
3. Adcroft A., Hallberg R., Harrison M. A finite volume discretization of the pressure gradient force using analytic integration. Ocean Modell. 2008, 22:106-113.
4. Anderson D.A., Tannehill J.C., Pletcher R.H. Computational Fluid Mechanics and Heat Transfer 1984, McGraw-Hill Book Company.
5. Benjamin T.B. Gravity currents and related phenomena. J. Fluid Mech. 1968, 31:209-248.
6. Bryan K., Manabe S., Pacanowski R.C. A global ocean-atmosphere climate model. Part II. Ocean. Circul. 1975, 5:30-46.
7. Burchard H., Rennau H. Comparative quantification of physically and numerically induced mixing in the ocean models. Ocean Modell. 2008, 20:293-311.
8. 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. 2008, 38:29-43.
9. Colella P., Woodward P.R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 1984, 54:174-201.
10. Daru V., Tenaud C. High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations. J. Comput. Phys. 2004, 193:563-594.
11. Delworth, T.L., Broccoli, A.J., Rosati, A., Stouffer, R.J., Balaji, V., Beesley, J.A., Cooke, W.F., Dixon, K.W., Dunne, J., Dunne, K.A., Durachta, J.W., Findell, K.L., Ginoux, P., Gnanadesikan, A., Gordon, C., Griffies, S. M., Gudgel, R., Harrison, M.J., Held, I.M., Hemler, R.S., Horowitz, L.W., Klein, S.A., Knutson, T.R., Kushner, P.J., Langenhorst, A.L., Lee, H.-C., Lin, S., Lu, L., Malyshev, S.L., Milly, P., Ramaswamy, V., Russell, J., Schwarzkopf, M.D., Shevliakova, E., Sirutis, J., Spelman, M., Stern, W. F., Winton, M., Wittenberg, A.T., Wyman, B., Zeng, F., Zhang, R., 2006. GFDL's CM2 global coupled climate models - Part 1: Formulation and simulation characteristics. J. Climate 19, 643-674.
12. Delworth, T.L., Rosati, A., Anderson, W., Adcroft, A.J., Balaji, V., Benson, R., Dixon, K., Griffies, S.M., Lee, H.-C., Pacanowski, R.C., Vecchi, G.A., Wittenberg, A.T., Zeng, F., Zhang, R., 2011. Simulated climate and climate change in the GFDL CM2.5 high-resolution coupled climate model. J. Climate accepted for publication.
13. Dunne, J.P., John, J.G., Hallberg, R.W., Griffies, S.M., Shevliakova, E.N., Stouffer, R.J., Krasting, J.P., Sentman, L.A., Milly, P.C.D., Malyshev, S.L., Adcroft, A.J., Cooke, W., Dunne, K.A., Harrison, M.J., Levy, H., Samuels, B.L., Spelman, M., Winton, M., Wittenberg, A.T., Phillips, P.J., Zadeh, N., in press. GFDLs ESM2 global coupled climate-carbon Earth system models Part I: Physical formulation and baseline simulation characteristics, J. Climate, submitted for publication.
14. Gent P.R., McWilliams J.C. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 1990, 20:150-155.
15. Getzlaff J., Nurser G., Oschlies A. Diagnostics of diapycnal diffusivity in z-level ocean models part I: 1-Dimensional case studies. Ocean Modell. 2010, 35:173-186.
16. Gnanadesikan A., Slater R.D., Swathi P.S., Vallis G.K. The energetics of ocean heat transport. J. Climate 2005, 18:2604-2616.
17. Gregg M., Sanford T., Winkel D. Reduced mixing from the breaking of internal waves in equatorial waters. Nature 2003, 422:513-515.
18. Griffies S.M. Fundamentals of Ocean Climate Models 2004, Princeton University Press, Princeton, USA, 518+xxxiv pages.
19. Griffies, S.M., 2009. Elements of MOM4p1: GFDL ocean group Technical Report No. 6. NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, USA, pp. 444.
20. Griffies S.M., Hallberg R.W. Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Mon. Weather. Rev. 2000, 128:2935-2946.
21. Griffies S.M., Pacanowski R.C., Hallberg R.W. Spurious diapycnal mixing associated with advection in a z-coordinate ocean model. Mon. Weather. Rev. 2000, 128:538-564.
22. Haidvogel D.B., Beckmann A. Numerical Ocean Circulation Modeling 1999, Imperial College Press.
23. Hallberg R., Adcroft A. Reconciling estimates of the free surface height in Lagrangian vertical coordinate ocean models with mode-split time stepping. Ocean Modell. 2009, 29:15-26.
24. Hill, C., Ferreira, D., Campin, J.M., Marshall, J., Abernathey, R., Barrier, N., 2011. Controlling spurious diapycnal mixing in eddy-resolving heigh-coordinate ocean models-insights from virtual deliberate tracer release experiments. Ocean Modell. accepted for publication.
25. Ili{dotless}cak M., Özgökmen T.M., özsoy E., Fischer P.F. Non-hydrostatic modeling of exchange flows across complex geometries. Ocean Modell. 2009, 29:159-175.
26. Ili{dotless}cak M., Legg S., Adcroft A., Hallberg R. Dynamics of a dense gravity current flowing over a corrugation. Ocean Model. 2011, 38:71-84.
27. IOC, SCOR, IAPSO, 2010. The international thermodynamic equation of seawater-2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO, available from, pp. 196. http://www.TEOS-10.org.
28. Iudicone D., Madec G., McDougall T.J. Water-mass transformations in a neutral density framework and the key role of light penetration. J. Phys. Oceanogr. 2008, 38:1357-1376.
29. Jackson L., Hallberg R., Legg S. A parameterization of shear-driven turbulence for ocean climate models. J. Phys. Oceanogr. 2008, 38:1033.
30. Jochum M., Danabasoglu G., Holland M., Kwon Y.-O., Large W.G. Ocean viscosity and climate. J. Geophys. Res. 2008, 113:C06017.
31. Klocker A., McDougall T.J. Influence of the nonlinear equation of state on global estimates of dianeutral advection and diffusion. J. Phys. Oceanogr. 2010, 40:1690-1709.
32. Kunze E., Sanford T.B. Abyssal mixing: where it is not. J. Phys. Oceanogr. 1996, 26:2286-2296.
33. Kunze E., Firing E., Hummon J.M., Chereskin T.K., Thurnherr A.M. Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr. 2006, 36:1553-1576.
34. Large W.G., McWilliams J.C., Doney S.C. Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 1994, 32:363-403.
35. Leclair M., Madec G. z̃-Coordinate, an Arbitrary Lagrangian-Eulerian coordinate separating high and low frequency motions. Ocean Modell. 2011, 37:139-152.
36. Ledwell J.R., Watson A.J., Law C.S. Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature 1993, 364:701-703.
37. Ledwell J.R., St. Laurent L., Girton J., Toole J. Diapycnal mixing in the Antarctic circumpolar current. J. Phys. Oceanogr. 2011, 41:241-246.
38. Lee M.-M., Coward A.C., Nurser A.G. Spurious diapycnal mixing of deep waters in an eddy-permitting global ocean model. J. Phys. Oceanogr. 2002, 32:1522-1535.
39. Legg S., Hallberg R.W., Girton J.B. Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and non-hydrostatic models. Ocean Modell. 2006, 11:69-97.
40. Legg S., Jackson L., Hallberg R.W. Eddy-resolving modeling of overflows. Geophysical Monograph 2008, vol. 177:63-82. American Geophysical Union, Washington, DC. M.W. Hecht, H. Hasumi (Eds.).
41. Legg S., Briegleb B., Chang Y., Chassignet E.P., Danabasoglu G., Ezer T., Gordon A.L., Grii{dotless}̈ňčes S.M., Hallberg R.W., Jackson L., Large W., özg̈okmen T.M., Peters H., Price J., Riemenschneider U., Wu W., Xu X., Yang J. Improving oceanic overni{dotless}̈ňćow representation in climate models: The Gravity Current Entrainment Climate Process Team. BAMS 2009, 90:657-670.
42. Lin S. A "vertically Lagrangian" finite-volume dynamical core for global models. Mon. Weather Rev. 2004, 132:2293-2307.
43. Maqueda M.M., Holloway G. Second-order moment advection scheme applied to arctic ocean simulation. Ocean Modell. 2006, 14:197-221.
44. Marchesiello P., Debreu L., Couvelard X. Spurious diapycnal mixing in terrain-following coordinate models: the problem and a solution. Ocean Modell. 2009, 26:156-169.
45. Margolin L., Smolarkiewicz P. Antidiffusive velocities for multipass donor cell advection. SIAM J. Sci. Comput. 1998, 20:907-929.
46. Marsh R. Cabbeling due to isopycnal mixing in isopycnic coordinate models. J. Phys. Oceanogr. 2000, 30:1757-1775.
47. Marshall J., Adcroft A., Hill C., Perelman L., Heisey C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res. 1997, 102:5753-5766.
48. McDougall T.J. Thermobaricity, cabbeling, and water-mass conversion. J. Geophys. Res. 1987, 92:5448-5464.
49. Merryfield W.J., Holloway G. Application of an accurate advection algorithm to sea-ice modelling. Ocean Modell. 2003, 5:1-15.
50. Munk W., Wunsch C. Abyssal recipes II: energetics of tidal and wind mixing. Deep. Sea. Res. Pt.1 1998, 45:1977-2010.
51. Özgökmen T.M., Iliescu T., Fischer P.F. Large eddy simulation of stratified mixing in a three-dimensional lock-exchange system. Ocean Modell. 2009, 26:134-155.
52. Pacanowski R.C., Gnanadesikan A. Transient response in a Z-level ocean model that resolves topography with partial cells. Mon. Weather Rev. 1998, 126:3248-3270.
53. Prather M. Numerical advection by conservation of second-order moments. J. Geophys. Res. 1986, 91:6671-6681.
54. Shchepetkin A.F., McWilliams J.C. Quasi-monotone advection schemes based on explicit locally adaptive dissipation. Mon. Weather. Rev. 1998, 126:1541-1580.
55. Shchepetkin A.F., McWilliams J.C. The regional oceanic modeling system (roms): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell. 2005, 9:347-404.
56. Simmons H.L., Jayne S.R., St. Laurent L.C., Weaver A.J. Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell. 2004, 6:245-263.
57. Smagorinsky J. General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weather. Rev. 1963, 91:99-164.
58. Smagorinsky J. Some historical remarks on the use of nonlinear viscosities. Large Eddy Simulation of Complex Engineering and Geophysical Flows 1993, 3-36. Cambridge University Press. B. Galperin, S.A. Orszag (Eds.).
59. Stacey M.W., Pond S., Nowak Z.P. A numerical model of the circulation in Knight Inlet, British Columbia, Canada. J. Phys. Oceanogr. 1995, 25:1037-1062.
60. Tatebe H., Hasumi H. Formation mechanism of the pacific equatorial thermocline revealed by a general circulation model with a high accuracy tracer advection scheme. Ocean Modell. 2010, 35:245-252.
61. Winters K.B., Lombard P.N., Riley J.J., D'Asaro E.A. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 1995, 289:115-128.
62. Winton M., Hallberg R., Gnanadesikan A. Simulation of density-driven frictional downslope flow in Z-coordinate ocean models. J. Phys. Oceanogr. 1998, 28:2163-2174.
63. Wunsch C., Ferrari R. Vertical mixing, energy, and the general circulation of the ocean. Ann. Rev. Fluid Mech. 2004, 36:281-314.