Free Access
Issue |
ESAIM: M2AN
Volume 49, Number 3, May-June 2015
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Page(s) | 875 - 919 | |
DOI | https://doi.org/10.1051/m2an/2014061 | |
Published online | 16 April 2015 |
- P. Azerad and F. Guillén–González, Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics. SIAM J. Math. Anal. 33 (2001) 847–859. [CrossRef] [MathSciNet] [Google Scholar]
- J.T. Beale, Large-time regularity of viscous surface waves. Arch. Rat. Mech. Anal. 84 (1984) 307–352. [CrossRef] [Google Scholar]
- F.J. Beron–Vera, J. Ochoa and P. Ripa, A note on boundary conditions for salt and freshwater balances. Ocean Modelling 1 (1999) 111–118. [CrossRef] [Google Scholar]
- V. Bjerknes, Das problem von der wettervorhersage, betrachtet vom standpunkt der mechanik und der physik. Meteor. Z. 21 (1904) 1–7. [Google Scholar]
- O. Besson and M.R. Laydi, Some estimates for the anisotropic Navier–Stokes equations and for the hydrostatic approximation. RAIRO: M2AN-Mod. Math. Anal. Numér. 26 (1992) 855–865. [Google Scholar]
- R. Bleck and D.B. Boudra, Wind-driven spin-up eddy resolving ocean models formulated in isopycnic and isobaric coordinates. J. Geophys. Res. 91 (1986) 7611–7621. [CrossRef] [Google Scholar]
- A.F. Blumberg and G.L. Mellor, A description of a three-dimensional coastal ocean circulation model, in vol. 4 Three-Dimensional Coastal Ocean Models. Edited by N. Heaps. American Geophysical Union (1987) 1–16. [Google Scholar]
- D. Bresch, A. Kazhikhov and J. Lemoine, On the two-dimensional hydrostatic Navier–Stokes equations. SIAM. J. Math. Anal. 36 (2004) 796–814. [Google Scholar]
- K. Bryan, A numerical method for the study of the circulation of the world ocean. J. Comput. Phys. 135 (1969) 154–169. [CrossRef] [Google Scholar]
- K. Bryan and M.D. Cox, An approximate equation of state for numerical models of ocean circulation. J. Phys. Oceanogr. 2 (1972) 510–514. [CrossRef] [Google Scholar]
- C. Cao and E.S. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Ann. Math. 166 (2007) 245–267. [CrossRef] [Google Scholar]
- M.D. Cox, A primitive equation, three-dimensional model of the ocean. GFDL Ocean Group Technical Report 1 (1984). [Google Scholar]
- W.P. Crowley, A global numerical ocean model. J. Comput. Phys. 3 (1968) 111–147. [CrossRef] [Google Scholar]
- W.P. Crowley, A numerical model for viscous, free-surface, barotropic wind driven ocean circulations. J. Comput. Phys. 5 (1970) 139–168. [CrossRef] [Google Scholar]
- J.K. Dukowicz and R.D. Smith, Implicit free-surface method for the Bryan-Cox-Semtner ocean model. J. Geophys. Research 99 (1994) 7991–8014. [CrossRef] [Google Scholar]
- S.M. Griffies et al., Developments in ocean climate modelling. Ocean Modelling 2 (2000) 123–192. [CrossRef] [Google Scholar]
- S.M. Griffies, R.C. Pacanowski, M. Schmidt and V. Balaji, Tracer concentration with an explicit free surface method for z-coordinate ocean models. Mon. Wea. Rev. 5 (2001) 1081–1098. [CrossRef] [Google Scholar]
- S.M. Griffies, Fundamentals of Ocean Climate Models. Princeton University Press, Princeton (2004). [Google Scholar]
- F. Guillén–González and M.A. Rodríguez–Bellido, On the strong solutions of the primitive equations in 2D domains. Nonlinear Anal. 50 (2002) 621–646. [CrossRef] [MathSciNet] [Google Scholar]
- F. Guillén–González and M.A. Rodríguez–Bellido, A review on the improved regularity for the primitive equations, in Regularity and other aspects of the Navier–Stokes equations, edited by P. Mucha, P. Penel, M. Wiegner and W. Zajaczkowski. In vol. 70 of Banach Center (2005) 85–103. [Google Scholar]
- F. Guillén–González, N. Masmoudi and M.A. Rodríguez–Bellido, Anisotropic estimates and strong solutions of the Primitive Equations. Differ. Int. Eq. 14 (2001) 1381–1408. [Google Scholar]
- H. Hasumi, CCSR Ocean Component Model (COCO) Version 2.1, CCSR Report No. 13 (2000). [Google Scholar]
- H. Honda, Small-time Existence of a Strong Solution of Primitive Equations for the Ocean and the Atmosphere. Ph.D. thesis, Keio University, Japan (2011). [Google Scholar]
- H. Honda and A. Tani, Small-time existence of a strong solution of primitive equations of the coupled atmosphere and the ocean. Sūrikaisekikenkyūsho Kōkyūroku 1631 (2009) 12–33. [Google Scholar]
- H. Honda and A. Tani, Small-time existence of a strong solution of primitive equations for the atmosphere. Adv. Math. Sci. Appl. 20 (2010) 547–583. [MathSciNet] [Google Scholar]
- H. Honda and A. Tani, Small-time existence of a strong solution of primitive equations for the ocean. Tokyo J. Math. 35 (2012) 97–138. [CrossRef] [MathSciNet] [Google Scholar]
- C. Hu, Asymptotic analysis of the primitive equations under the small depth assumption. Nonlin. Anal. 61 (2005) 425–460. [CrossRef] [Google Scholar]
- C. Hu, R. Temam and M. Ziane, The primitive equations on the large scale ocean under small depth hypothesis. Discrete Contin. Dyn. Syst. 9 (2003) 97–131. [MathSciNet] [Google Scholar]
- J.H. Jones, Vertical mixing in the Equatorial Undercurrent. J. Phys. Oceanogr. 3 (1973) 286–296. [CrossRef] [Google Scholar]
- P.D. Killworth, D. Stainforth, D.J. Webb and S.M. Peterson, The Development of a Free-Surface Bryan-Cox-Semtner Ocean Model. J. Phys. Oceanogr. 21 (1991) 1333–1348. [CrossRef] [Google Scholar]
- E.B. Kraus and J.S. Turner, A one-dimensional model of the seasonal thermocline. Tellus 19 (1967) 98–106. [CrossRef] [Google Scholar]
- O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and Quasi-linear Equations of Parabolic Type. In vol. 23 of Transl. Math. Monogr. American Mathematical Society (1968). [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of atmosphere and applications. Nonlin. 5 (1992) 237–288. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, On the equations of the large-scale-ocean. Nonlin. 5 (1992) 1007–1053. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, Models for the coupled atmosphere and ocean. Comput. Mech. Adv. 1 (1993) 5–54. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, Numerical analysis of the coupled atmosphere and ocean models. Comput. Mech. Adv. 1 (1993) 55–120. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, Problemes a frontiere libre pour les modeles couples de l’Ocean et de l’Atmosphere. C. R. Acad. Sci. Paris 318 (1994) 1165–1171. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, Mathematical theory for the coupled atmosphere-ocean models. J. Math. Pures Appl. 74 (1995) 105–163. [Google Scholar]
- J.L. Lions, R. Temam and S. Wang, On mathematical problems for the primitive equations of the ocean: the mesoscale midlatitude case. Nonlinear Anal. 40 (2000) 439–482. [CrossRef] [MathSciNet] [Google Scholar]
- https://www.pik-potsdam.de/research/earth-system-analysis/models/climber/climber3/ocean.html [Google Scholar]
- http://www.gfdl.noaa.gov/ocean-model [Google Scholar]
- R.C. Pacanowski and S.H. Philander, Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr. 11 (1981) 1443–1451. [CrossRef] [Google Scholar]
- L.F. Richardson, Weather Prediction by Numerical Process. Cambridge University Press (1922). [Google Scholar]
- A.J. Semtner, A general circulation model for the world ocean. UCLA Dept. Meteorol. Tech. Report 8 (1974) 99–120. [Google Scholar]
- V.A. Solonnikov, Solvability of a problem of evolution of a viscous incompressible fluid bounded by a free surface in a finite time interval. St. Peters. Math. J. 3 (1992) 189–220. [Google Scholar]
- V.A. Solonnikov and A. Tani, Free boundary problem for a compressible flow with a surface tension, in Constantin Carathéodory: International Tribute, edited by Th. M. Rassias. World Scientific Publ. Co. (1991) 1270–1309. [Google Scholar]
- N. Tanaka, Two-phase free boundary problem for viscous incompressible thermo-capillary convection. Japan J. Math. 21 (1995) 1–42. [MathSciNet] [Google Scholar]
- V.A. Solonnikov, On Boundary Value Problems to the Linear Parabolic Systems of Differential Equations of General Form (Russian), in Trudy. Mat. Inst. Steklov. 83 (1965) 3–163. English Transl. Proc. Steklov. Math. Inst. 83 (1965) 1–184. [Google Scholar]
- N. Tanaka and A. Tani, Large-time existence of surface waves in incompressible viscous fluids with or without surface tension. Arch. Rat. Mech. Anal. 130 (1995) 303–314. [CrossRef] [Google Scholar]
- N. Tanaka and A. Tani, Surface waves for a compressible viscous fluid. J. Math. Fluid Mech. 5 (2003) 303–363. [CrossRef] [MathSciNet] [Google Scholar]
- R. Temam and M. Ziane, Some mathematical problems in geophysical fluid dynamics, in Handb. Math. Fluid Dyn., vol. III. Edited by S.J. Friedlander, D. Serre. North-Holland (2004) 535–657. [Google Scholar]
- UNESCO, 1981: Tenth report of the Joint Panel on Oceanographic Tables and Standards. Unesco Technical papers in marine science, No. 36, 25 pp. Sidney, B.C. (1980). [Google Scholar]
- W.M. Washington and C.L. Parkinson, An Introduction to Three-Dimensional Climate Modeling. Oxford University Press (1986). [Google Scholar]
- J. Wloka, Partielle Differentialgleichungen. B.G. Teubner (1982). [Google Scholar]
- M. Ziane, Regularity results for Stokes type systems. Appl. Anal. 58 (1995) 263–292. [CrossRef] [Google Scholar]
- M. Ziane, Regularity results for the stationary primitive equations of atmosphere and the ocean. Nonlinear Anal. 28 (1997) 289–313. [CrossRef] [MathSciNet] [Google Scholar]
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