Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques
Annales mathématiques Blaise Pascal, Volume 9 (2002) no. 2, p. 181-212
@article{AMBP_2002__9_2_181_0,
     author = {Bresch, Didier and Huck, Thierry and Sy, Mamadou},
     title = {Circulation thermohaline et \'equations plan\'etaires g\'eostrophiques : propri\'et\'es physiques, num\'eriques et math\'ematiques},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Laboratoires de Math\'ematiques Pures et Appliqu\'ees de l'Universit\'e Blaise Pascal},
     volume = {9},
     number = {2},
     year = {2002},
     pages = {181-212},
     zbl = {02081310},
     mrnumber = {1969078},
     language = {fr},
     url = {http://www.numdam.org/item/AMBP_2002__9_2_181_0}
}
Bresch, Didier; Huck, Thierry; Sy, Mamadou. Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques. Annales mathématiques Blaise Pascal, Volume 9 (2002) no. 2, pp. 181-212. http://www.numdam.org/item/AMBP_2002__9_2_181_0/

[1] A. Arakawa. Computational design for long-term numerical integration of the equations of fluid motions: two dimensional incompressible flow. part 1. J. Comput. Phys., 1: 119-143, 1966. | MR 1486265 | Zbl 0147.44202

[2] J. Boussinesq. Théorie analytique de la chaleur, Vol. 2. Gauthier-Villars, Paris, 1903.

[3] D. Bresch et M. Sy. Convection in rotating porous media: The planetary geostrophic equations, used in geophysical fluid dynamics, revisited. Cont. Mech. Thermodyn., To appear 2003. | MR 1986703 | Zbl 02034136

[4] A.P. Burger. Scale considerations of planetary motions of the atmosphere. Tellus, 10: 195-205, 1958.

[5] C. Cao et E.S. Titi. Global well posedness and finite dimensional global attractor for a 3-d planetary geostrophic viscous model. Comm. Pure Appl. Math., page , To appear 2003. | MR 1934620 | Zbl 1035.37043

[6] T. Colin et P. Fabrie. Rotating fluid at high rossby number driven by a surface stress: existence and convergence. Adv. Differential Equations, 2: 715-751, 1997. | MR 1751425 | Zbl 1023.76593

[7] A. Colin De Verdière . Buoyancy driven planetary flows. J. Mar. Res., 46: 215-265, 1988.

[8] A. Colin De Verdière. On the interaction of wind and buoyancy driven gyres. J. Mar. Res., 47: 595-633, 1989.

[9] A. Colin De Verdière. On the oceanic thermohaline circulation. in modelling oceanic climate interactions. J. Willebrand and D. L. T. AndersonEds, Springer-Verlag: 151-183, 1993.

[10] A. Colin De Verdièreet T. Huck. Baroclinic instability: an oceanic wavemaker for interdecadal variability. J. Phys. Oceanogr., 29: 893-910, 1999. | MR 1790179

[11] H.A. Dijkstra, H. Oksuzoglu, F.W. Wubs, et E.F.F. Bott. A fully implicit model of the three-dimensional thermohaline ocean circulation. J. Comput. Phys., 173: 1-31, 2001. | Zbl 1051.86004 | Zbl 01708366

[12] N.R. Edwards et J.G. Shepherd. Multiple thermohaline states due to variable diffusivity in a hierarchy of simple models. Ocean Modelling, 3: 67-94, 2001.

[13] P. Fabrie. Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieux poreux. Acta Applicandae Mathematicae, 7: 45-77, 1986. | MR 855105 | Zbl 0609.76091

[14] B.F. Farrell et P.J. Ioannou. Generalized stability theory. part i: Autonomous operators. J. Atmos. Sci., 53: 2025-2040, 1996. | MR 1409987

[15] B.F. Farrell et P.J. Ioannou. Generalized stability theory. part ii: Nonautonomous operators. J. Atmos. Sci., 53: 2041-2053, 1996. | MR 1409988

[16] P.R. Gent et J.C. Mcwilliams. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20: 150-155, 1990.

[17] S.M. Griffies et al. Developments in ocean climate modelling. Ocean Modelling, 2: 123-192, 2000.

[18] R. Hallberg et P. Rhines. Buoyancy-driven circulation in an ocean-basin with isopycnals intersecting the sloping boundary. J. Phys. Oceanogr., 26: 913-940, 1996.

[19] R. Haney. Surface thermal boundary condition for ocean circulation models. J. Phys. Oceanogr., 1: 241-248, 1971.

[20] T. Huck. Modélisation de la circulation thermohaline : Analyse de sa variabilité interdécennale. Thèse de doctorat, Université de Bretagne Occidentale, Brest, France, 1997.

[21] T. Huck, G.K. Vallis, et A. Colin De Verdière. On the robustness of the interdecadal modes of the thermohaline circulation. J. Climate, 14: 940-963, 2001.

[22] T. Huck et G.K. Vallis. Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations. Tellus, 53A: 526-545, 2001.

[23] T. Huck, A.J. Weaver, et A. Colin De Verdière. On the influence of the parameterization of lateral boundary layers on the thermohaline circulation in coarse-resolution ocean models. J. Mar. Res., 57: 387-426, 1999.

[24] P. Killworth. A two-level wind and buoyancy driven thermocline model. J. Phys. Oceanogr., 15: 1414-1432, 1985. | MR 489985

[25] G. Madec, P. Delecluse, M. Imbard, et C. Lévy. OPA 8.1 ocean general circulation model reference manual. Note du Pôle de modélisation, Institut Pierre-Simon Laplace, 11:1-91, 1998.

[26] J. Marotzke. Instabilities and multiple equilibria of the thermohaline circulation. Ph.D. thesis dissertation, Institut fur Meereskunde, Kiel, 126pp, 1990.

[27] J. Marotzke et J. Willebrand. Multiple equilibria of the global thermohaline circulation. J. Phys. Oceanogr., 21: 1372-1385, 1991.

[28] A.M. Moore, J. Vialard, A.T. Weaver, D.L.T. Anderson, R. Kleeman, et J.R. Johnson. The role of air-sea interaction in controlling the optimal perturbations of low-frequency tropical coupled ocean-atmosphere modes. ECMWF Technical memorandum, Reading, UK, 351: 35pp, 2001.

[29] R. Pacanowski, K. Dixon, et A. Rosati. The GFDL Modular Ocean Model. Users Guide Version 1.0., GFDL Ocean Group Technical Report #2, 1991.

[30] Y.G. Park et K. Bryan. Comparison of thermally driven circulations from a depth-coordinate model and an isopycnal-layer model. part ii: The difference and structure of the circulations. J. Phys. Oceanogr., 31: 2612-2624, 2001.

[31] N.A. Philipps. Geostrophic motion. Rev. Geophys. Space Phys., 1: 123-176, 1963.

[32] M. Redi. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12: 1154-1158, 1982.

[33] A. Robinson et H. Stommel. The oceanic thermocline and the associated thermohaline circulation. Tellus, XI: 295-308, 1959. | MR 107596

[34] R. Salmon. A simplified linear ocean circulation theory. J. Mar. Res., 44:695-711, 1986.

[35] R. Salmon. Linear ocean circulation theory with realistic bathymetry. J. Mar. Res., 56: 833-884, 1998.

[36] R.M. Samelson, R. Temam, et S. Wang. Some mathematical properties of the planetary geostrophic equations for large scale ocean circulation. Appl. Anal., 70: 147-173, 1998. | MR 1671567 | Zbl 1027.86002 | Zbl 01463975

[37] R.M. Samelson, R. Temam, et S. Wang. Remarks on the planetary geostrophic model of gyre scale ocean circulation. Diff. Int. Eqs., 13: 1-14, 2000. | MR 1811946 | Zbl 0979.35118

[38] R.M. Samelson et G.K. Vallis. Large-scale circulation with small diapycnal diffusion: The two-thermocline limit. J. Mar. Res., 55: 223-275, 1997.

[39] R.M. Samelson et G.K. Vallis. A simple friction and diffusion scheme for planetary geostrophic basin models. J. Phys. Oceanogr., 27: 186-194, 1997.

[40] G.A. Schmidt et L.A. Mysak. The stability of a zonally averaged thermohaline circulation model. Tellus, 48: 158-178, 1996.

[41] H. Stommel. Thermohaline convection with two stable regimes of flow. Tellus, XIII: 224-230, 1961.

[42] H. Stommel et A.B. Arons. On the abyssal circulation of the world ocean. i: Stationary planetary flow patterns on a sphere. Deep Sea Res., 6: 140-154, 1960.

[43] H. Stommel et A.B. Arons. On the abyssal circulation of the world ocean. ii: An idealized model of the circulation pattern and amplitude in oceanic basins. Deep Sea Res., 6: 217-233, 1960.

[44] L.A. Te Raaet H.A. Dijkstra. Instability of the thermohaline ocean circulation on interdecadal time scales. J. Phys. Oceanogr., 32: 138-160, 2002.

[45] P. Vadasz. Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J. Fluid Mech, 1376: 351-375, 1998. | MR 1658958 | Zbl 0943.76033

[46] P. Welander. An advective model of the ocean thermocline. Tellus, XI: 309-318, 1959.

[47] M. Winton. Numerical investigations of steady and oscillating thermohaline circulation. Ph.D. thesis, University of Washington, 1993.

[48] M. Winton et E.S. Sarachik. Thermohaline oscillations induced by strong steady salinity forcing of ocean general circulation models. J. Phys. Oceanogr., 23: 1389-1410, 1993.

[49] S. Zhang, C.A. Lin, et R.J. Greatbatch. A thermocline model for ocean-climate studies. J. Mar. Res., 50: 99-124, 1992.

[50] M. Ziane. Regularity results for the stationary primitive equations of the atmosphere and the ocean. Nonlinear Anal, 28: 289-313, 1997. | MR 1418137 | Zbl 0863.35085