Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques

Didier Bresch; Thierry Huck; Mamadou Sy

Annales mathématiques Blaise Pascal (2002)

  • Volume: 9, Issue: 2, page 181-212
  • ISSN: 1259-1734

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Bresch, Didier, Huck, Thierry, and Sy, Mamadou. "Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques." Annales mathématiques Blaise Pascal 9.2 (2002): 181-212. <http://eudml.org/doc/79249>.

@article{Bresch2002,
author = {Bresch, Didier, Huck, Thierry, Sy, Mamadou},
journal = {Annales mathématiques Blaise Pascal},
language = {fre},
number = {2},
pages = {181-212},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques},
url = {http://eudml.org/doc/79249},
volume = {9},
year = {2002},
}

TY - JOUR
AU - Bresch, Didier
AU - Huck, Thierry
AU - Sy, Mamadou
TI - Circulation thermohaline et équations planétaires géostrophiques : propriétés physiques, numériques et mathématiques
JO - Annales mathématiques Blaise Pascal
PY - 2002
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 9
IS - 2
SP - 181
EP - 212
LA - fre
UR - http://eudml.org/doc/79249
ER -

References

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  1. [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. Zbl0147.44202MR1486265
  2. [2] J. Boussinesq. Théorie analytique de la chaleur, Vol. 2. Gauthier-Villars, Paris, 1903. 
  3. [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. Zbl1068.76551MR1986703
  4. [4] A.P. Burger. Scale considerations of planetary motions of the atmosphere. Tellus, 10: 195-205, 1958. 
  5. [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. Zbl1035.37043MR1934620
  6. [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. Zbl1023.76593MR1751425
  7. [7] A. Colin de Verdière . Buoyancy driven planetary flows. J. Mar. Res., 46: 215-265, 1988. 
  8. [8] A. Colin de Verdière. On the interaction of wind and buoyancy driven gyres. J. Mar. Res., 47: 595-633, 1989. 
  9. [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. [10] A. Colin de Verdièreet T. Huck. Baroclinic instability: an oceanic wavemaker for interdecadal variability. J. Phys. Oceanogr., 29: 893-910, 1999. MR1790179
  11. [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. Zbl1051.86004
  12. [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. [13] P. Fabrie. Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieux poreux. Acta Applicandae Mathematicae, 7: 45-77, 1986. Zbl0609.76091MR855105
  14. [14] B.F. Farrell et P.J. Ioannou. Generalized stability theory. part i: Autonomous operators. J. Atmos. Sci., 53: 2025-2040, 1996. MR1409987
  15. [15] B.F. Farrell et P.J. Ioannou. Generalized stability theory. part ii: Nonautonomous operators. J. Atmos. Sci., 53: 2041-2053, 1996. MR1409988
  16. [16] P.R. Gent et J.C. McWilliams. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20: 150-155, 1990. 
  17. [17] S.M. Griffies et al. Developments in ocean climate modelling. Ocean Modelling, 2: 123-192, 2000. 
  18. [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. [19] R. Haney. Surface thermal boundary condition for ocean circulation models. J. Phys. Oceanogr., 1: 241-248, 1971. 
  20. [20] T. Huck. Modélisation de la circulation thermohaline : Analyse de sa variabilité interdécennale. Thèse de doctorat, Université de Bretagne Occidentale, Brest, France, 1997. 
  21. [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. [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. [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. [24] P. Killworth. A two-level wind and buoyancy driven thermocline model. J. Phys. Oceanogr., 15: 1414-1432, 1985. MR489985
  25. [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. [26] J. Marotzke. Instabilities and multiple equilibria of the thermohaline circulation. Ph.D. thesis dissertation, Institut fur Meereskunde, Kiel, 126pp, 1990. 
  27. [27] J. Marotzke et J. Willebrand. Multiple equilibria of the global thermohaline circulation. J. Phys. Oceanogr., 21: 1372-1385, 1991. 
  28. [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. [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. [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. [31] N.A. Philipps. Geostrophic motion. Rev. Geophys. Space Phys., 1: 123-176, 1963. 
  32. [32] M. Redi. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12: 1154-1158, 1982. 
  33. [33] A. Robinson et H. Stommel. The oceanic thermocline and the associated thermohaline circulation. Tellus, XI: 295-308, 1959. MR107596
  34. [34] R. Salmon. A simplified linear ocean circulation theory. J. Mar. Res., 44:695-711, 1986. 
  35. [35] R. Salmon. Linear ocean circulation theory with realistic bathymetry. J. Mar. Res., 56: 833-884, 1998. 
  36. [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. Zbl1027.86002MR1671567
  37. [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. Zbl0979.35118MR1811946
  38. [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. [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. [40] G.A. Schmidt et L.A. Mysak. The stability of a zonally averaged thermohaline circulation model. Tellus, 48: 158-178, 1996. 
  41. [41] H. Stommel. Thermohaline convection with two stable regimes of flow. Tellus, XIII: 224-230, 1961. 
  42. [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. [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. [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. [45] P. Vadasz. Coriolis effect on gravity-driven convection in a rotating porous layer heated from below. J. Fluid Mech, 1376: 351-375, 1998. Zbl0943.76033MR1658958
  46. [46] P. Welander. An advective model of the ocean thermocline. Tellus, XI: 309-318, 1959. 
  47. [47] M. Winton. Numerical investigations of steady and oscillating thermohaline circulation. Ph.D. thesis, University of Washington, 1993. 
  48. [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. [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. [50] M. Ziane. Regularity results for the stationary primitive equations of the atmosphere and the ocean. Nonlinear Anal, 28: 289-313, 1997. Zbl0863.35085MR1418137

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