Abstract
The dynamic stochastic approach to the study of mathematical models of thermohydrodynamic, large-scale fields is developed in which the mathematical image of stochasticity is the strange attractor of the real atmosphere.
In this part, a way of formulating the problem of forecasting flow fields on a two-dimensional spherical surface, using group formalism (Lie's group) is outlined, and the limit of deterministic forecast is estimated for selected fields. Having outlined methods of analysing non-linear dynamic systems and the statistical dynamics of their attractors, the interaction of baroclinic waves and zonal flow is studied. The response of this model to external periodic effects is sought; representations defined on a circle and the existence of quasiperiodic motions on diffeomorphism defined on a circle play an important part here. We are also interested in the bifurcation analysis of the two-parameter model of large-scale geophysical hydrodynamics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold V. I.: Ann. Inst. Fourier1 (1966) 319.
Horák J.: Systems of the fluid mechanical type: applications and connections. Academia, Prague, 1990.
Arnold V. I.: Mathematical methods of classical mechanics. Nauka, Moscow, 1979 (In Russian).
Horák J.:In: Proc. Seminar “Physics and Mathematics” (Eds. M. RůŽička, J. Roskovec). JčSMF, Prague, 1987 (In Czech).
Peixoto M.: Topology1 (1962) 101.
Eckmann J. P.: Rev. Mod. Phys.4 (1981) 643.
Horák J.: Acta Technica čSAV1 (1990) 116.
Bowen P.: Methods of symbolic dynamics. Mir, Moscow, 1979 (In Russian).
Arnold V. I.: Additional chapters to the theory of ordinary differential equations. Nauka, Moscow, 1979 (In Russian).
Marek M., Schreiber I.: Stochastic behaviour of deterministic systems. Academia, Prague, 1984 (In Czech).
Cvitanovich P., Jensen M. H., Kandoff Z. P., Procaccia I.: Phys. Rev. Lett.4 (1985) 343.
Farmer J. D., Satija I.: Phys. Rev. A31 (1985) 3520.
Schuster H. G.: Deterministic Chaos. Physik-Verlag, Weinheim, 1984.
Busse F. H.:In: Hydrodynamics instabilities and the transition to turbulence (Eds. H. L. Swinney, J. P. Gollub). Springer-Verlag, Berlin, 1981.
Aheers G., Behringer R.: Phys. Rev. Lett.40 (1987) 712.
Lichtenberg A. J., Lieberman M. A.: Regular and stochastic motion. Spriner-Verlag, New York-Heidelberg-Berlin, 1983.
Anishchenko V. S., Letford T. E., Sonechkin D. M.: Zh. Tekh. Fiz.5 (1988) 849.
Lorenz E. N.: J. Atm. Sci.1 (1962) 39.
Lorenz E. N.: J. Atm. Sci.5 (1963) 448.
Lorenz E. N.: J. Atm. Sci.20 (1963) 130.
Sonechkin D. M.: Stochasticity in model of general atmospheric circulation. Gidrometeoizdat, Leningrad, 1984 (In Russian).
Barnsley M.: Fractals everywhere. Academic Press, Boston-San Diego-New York-Berkley-London-Sydney-Tokyo-Toronto, 1988.
Wilson K. G.: Cesk. Cas. Fyz. A34 (1984) 97.
Neimark Yu. I., Landa P. S.: Stochastic and chaotic oscillations. Nauka, Moscow, 1987 (In Russian).
Mandelbrot B. B.: Fractals: form, change, and dimension. Freeman, San Francisco, 1977.
Holodniok M., Klíč A., Kubíček M., Marek M.: Methods of analysing non-linear dynamic model. Academia, Prague, 1986 (In Czech).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Horák, J. Non-linear models of geophysical hydrodynamics and the problem of forecasting stream patterns II. Czech J Phys 42, 713–739 (1992). https://doi.org/10.1007/BF01598731
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01598731