On the structure of the attractors of the finite-dimensional approximations of the barotropic vorticity equation on a rotating sphere

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 12, Issue 1, 1997, Pages 13-32

  Dymnikov, V P ^a   Gritsun, A S ^a  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002962312     PISSN: 09276467     EISSN: None     Source Type: Journal    
DOI: 10.1515/rnam.1997.12.1.13     Document Type: Article

References (20)

1. P. Cehelsky and K. K. Tung, Theories of multiple equilibria and weather regimes - a critical reexamination. Part II: Baroclinic two-layer models. J. Atmos. Sci. (1987) 44, 3282-3303.
2. F. Demengel and J. M. Ghidaylia, Inertial manifolds for partial differential evolution equations under time-discretization: existence, convergence, and applications. J. Math. Anal. Appl. (1991) 155, 177-225.
3. V. P. Dymnikov and A. N. Filatov, Foundations of Mathematical Climate Theory. VINITI, Moscow, 1994 (in Russian).
4. V. P. Dymnikov and E. V. Kazantsev, On the structure of the attractor generated by the system of barotropic atmosphere equation. Izv. Ross. Akad. Nauk, Ser. Fiz, Atmos. Okean (1993) 5 (in Russian).
5. V. P. Dymnikov and A. S. Gritsun, Lyapunov indices and the attractor dimension in a two-layer baroclinic model of atmospheric circulation. Doklady Ross. Akad. Nauk (1996) 347, No. 4, 535-538 (in Russian).
6. J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attract ors. Rev. Modern Phys. (1985) 57, 617-656.
7. J. S. Frederiksen, M. R. Dix, and S. M. Kepert, Systematic energy errors and the tendency toward canonical equilibrium in Atmospheric circulation models. J. Atmos. Sci. (1995) 53, No. 6, 887-904.
8. A. S. Gorelov and A. N. Filatov, Inertial manifolds in the barotropic atmosphere equations. Doklady Akad. Nauk SSSR (1991) 318, No. 6, 535-538 (in Russian).
9. A. S. Gorelov, Attractor dimension of a baroclinic model. Doklady Ross. Akad. Nauk (1995) 342, No. 1, 101-104 (in Russian).
10. R. Grotjahn, Three-dimensional linear instability on a sphere: resolution experiments with a model using vertical orthogonal basis functions. J. Atmos. Sci. (1987) 44, No. 24, 3734-3752.
11. A. A. Ilin and A. N. Filatov, Navier-Stokes equations on a sphere. Stability of stationary solutions. In: Mat. Fiz. Mezhvuz. Sb. Nauch. Trudov. Leningrad, 1987, pp. 128-146 (in Russian).
12. A. A. Ilin, Partially dissipative semigroups generated by the Navier-Stokes system on two-dimensional manifolds, and their attractors. Mat. Sbornik (1993) 184, No. 1, 55-58 (in Russian).
13. L. V. Kapitansky and I. N. Kostin, Attractors of nonlinear evolutionary equations and their approximations. Algebra Analiz (1990)2, No. 1, 114-140 (in Russian).
14. J. L. Kaplan and J. A. Yorke, Chaotic Behaviour in Multidimensional Difference Equations. In: Lecture Notes in Mathematics, 1979.
15. B. Legras and M. Gill, Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci. (1985) 42, No. 5, 433-471.
16. V. I. Oseledets, Multiplicative ergodic theorem, the lyapunov characteristic indices of dynamical systems. Trudy Mosk. Mat. Obshch. (1969) 19, 179-210 (in Russian).
17. Ya. B. Pesin, Lyapunov characteristic indices and the smooth ergodic theory. Uspehi Mat. Nauk (1977) 32, No. 1, 4-55 (in Russian).
18. I. Shimada and T. Nagashima, A numerical approach to ergodic problem of dissipative dynamic systems. Prog. Theor. Phys. (1979) 61, 1605-1616.
19. J. M. Wallace, X. Cheng, and D. Sun, Does low-frequency atmospheric variability exhibit regime-like behaviour? Tellus (1991) 43AB, 16-26.
20. J. I. Yano and H. Mukougawa, The attractor dimension of a quasi-geostrophic two-layer system. Geophys. Astrophys. Fluid Dynamics (1992) 65, 77-91.