Modélisation de la transition vers la turbulence
Séminaire Bourbaki (1982-1983)
- Volume: 25, page 179-197
- ISSN: 0303-1179
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topIooss, Gérard. "Modélisation de la transition vers la turbulence." Séminaire Bourbaki 25 (1982-1983): 179-197. <http://eudml.org/doc/110006>.
@article{Iooss1982-1983,
author = {Iooss, Gérard},
journal = {Séminaire Bourbaki},
keywords = {transition to turbulence; incompressible fluids; bifurcation theory; models of Lorenz; Rayleigh-Bénard convection; period doubling; population dynamics; motion of a pendulum; intermittency effects},
language = {fre},
pages = {179-197},
publisher = {Société Mathématique de France},
title = {Modélisation de la transition vers la turbulence},
url = {http://eudml.org/doc/110006},
volume = {25},
year = {1982-1983},
}
TY - JOUR
AU - Iooss, Gérard
TI - Modélisation de la transition vers la turbulence
JO - Séminaire Bourbaki
PY - 1982-1983
PB - Société Mathématique de France
VL - 25
SP - 179
EP - 197
LA - fre
KW - transition to turbulence; incompressible fluids; bifurcation theory; models of Lorenz; Rayleigh-Bénard convection; period doubling; population dynamics; motion of a pendulum; intermittency effects
UR - http://eudml.org/doc/110006
ER -
References
top- [1] A. Arnéodo, P. Coullet, C. Tresser, Occurence of strange attractors in three-dimensional Volterra equations, Phys.Lett.79A, 4, 259, (1980) Zbl0432.58014MR590579
- [2] A. Arnéodo, P. Coullet, C. Tresser, Oscillators with chaotic behavior, J.Stat.Phys., 27,1, 171, (1982) Zbl0522.58033MR656874
- [3] V. Arnold, Chapitres supplémentaires de la Théorie des Equations Différentielles ordinaires, MIR, Moscou, (1980) Zbl0455.34001MR626685
- [4] D.G. Aronson, M.A. Chory, G.R. Hall, R.P. Mc Gehee, Bifurcations from an invariant circle for two-parameter families of maps of the plane, Comm.Math.Phys.83, 303, (1982) Zbl0499.70034MR649808
- [5] P. Bergé, M. Dubois, P. Manneville, Y. Pomeau, Intermittency in Rayleigh-Bénard convection, J. de Phys. Lettres41, L341, (1980)
- [6] M. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf, U. Frisch, J.Fluid.Mech.,(1982), (à paraître)
- [7] A. Chenciner, Bifurcations de difféomorphismes de IR2, au voisinage d'un point fixe elliptique. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) Zbl0582.58025MR806175
- [8] P. Collet, J.P. Eckmann,Iterated maps on the interval as dynamical systems, P. Ph 1, Birkhaüser, Boston, 1980 Zbl0458.58002MR613981
- [9] M. Dubois, P. Bergé, V. Croquette, Study of non steady convective regimes using Poincaré sections, J.de Phys.Lettres43, L295, (1982)
- [10] J.P. Eckmann, Route to chaos with special emphasis on period doubling. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) Zbl0616.58032
- [11] C. Foias, G. Prodi, Rend. Sem. Math., Univ. Padova39, 1, (1967) Zbl0176.54103MR223716
- [12] C. Foias, O.P. Manley, R. Témam, I.M. Trèves, Number of modes governing two-dimensional viscous incompressible flows, Phys. Rev. Lett., 50, 14, p. 1031-1034, 1983. MR700069
- [13] H. Fujita, T. Kato, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal.16, 4 , 269, (1964) Zbl0126.42301MR166499
- [14] M. Giglio, S. Musazzi, U. Perini, Transition to chaos via a well ordered sequence of period doubling bifurcations, Phys.Rev.Lett.47, 243, (1981)
- [15] J.P. Gollub, S.V. Benson, Many routes to turbulent convection, J.Fluid Mech.,100, 3, 449, (1980)
- [16] J. Guckenheimer, On a codimension two bifurcation, Dynamical Systems and Turbulence, p.99, Lecture Notes in Math., 898, Springer Verlag, 1981 Zbl0482.58006MR654886
- [17] M. Hénon, Y. Pomeau, Two strange attractors with a simple structure, Turbulence and Navier Stokes equations, Orsay1975, Lecture Notes in Math565, (1976) Zbl0379.76049MR448436
- [18] J.H. Curry, J.R. Herring, J. Loncaric, S.A. Orszag, Order and disorder in two and three dimensional Bénard convection, (preprint). Zbl0547.76093
- [19] E. Hopf, A mathematical example displaying features of turbulence, Comm. Pure & Appl. Math.1, 303, (1948) Zbl0031.32901MR30113
- [20] G. Iooss, Sur la deuxième bifurcation d'une solution stationnaire de systèmes du type Navier-Stokes, partie II, Arch.Rat.Mech.Anal.64, 339, (1977) Zbl0356.35068MR650472
- [21] G. Iooss, Bifurcation of maps and applications, North Holland Math.Studies36, Amsterdam, 1979 Zbl0408.58019MR531030
- [21]2 G. Iooss, Persistance d'un cercle invariant par une application voisinede "l'application temps T "d'un champ de vecteurs intégrable(I&II), CR.Ac.Sci.ParisA, 1982 (à paraître) Zbl0526.34033
- [22] A. Chenciner, G. Iooss, Bifurcations de tores invariants, Arch.Rat.Mech.Anal, 69, 2, 109-198 et 71, 301-306, (1979) Zbl0405.58033MR521266
- [23] V.I. Iudovich, On the stability of steady flows of a viscous incompressible fluid, D.A.N. SSSR, 161, 5, 1037, (1965) Zbl0139.21901
- [24] L. Landau, E. Lifchitz, Mécanique des fluides, p.131-132, MIR, Moscou1971
- [25] O.E. Lanford III, Smooth transformations of intervals, Séminaire Bourbaki,n°563, 1980 Zbl0514.58028
- [26] O.E. Lanford III, Introduction to the mathematical theory of dynamical systems, Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland (à paraître) Zbl0565.58027
- [27] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach (2nd ed.), New York1969 Zbl0184.52603MR254401
- [28] O.A. Ladyzhenskaya, Mathematical analysis of Navier-Stokes equations for incompressible liquids, Annual Rev. Fluid Mech.7, 249, (1975) Zbl0344.76014
- [29] E.N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sci.20, 130,(1963)
- [30] J. Maurer, A. Libchaber, Rayleigh-Bénard experiment in liquid helium; frequency locking and the onset of turbulence, J. de Phys.Lettres40, L419,(1979)
- [31] M. Misiurewicz, Maps of an internal. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) Zbl0565.58025
- [32] S.E. Newhouse, The creation of non-trivial recurrence in the dynamics of diffeomorphisms. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland (à paraître) Zbl0556.58017
- [33] Y. Pomeau, P. Manneville, Intermittency and the Lorenz model, Physics Lett.75A,1, (1979) Zbl0985.37503MR594556
- [34] D. Ruelle, F. Takens, On the nature of turbulence, Comm. Math. Phys.,20, 167-192, (1971) Zbl0223.76041MR284067
- [35] L.P. Shil'nikov, Sov.Math.Dokl.,6, 163,(1965), et Mat.USSR, Sb.10, 91,(1970) MR193352
- [36] R. Témam, Navier-Stokes equations, North Holland, Amsterdam, 1977 Zbl0383.35057MR769654
- [37] C. Vidal, A. Pacault (éd.), Nonlinear phenomena in chemical dynamics, Springer Series in Synergetics12, Springer Verlag, (1981) MR689902
- [38] R.F. Williams, The structure of Lorenz attractors, Turbulence seminar, Berkeley1976-77, Lecture Notes in Math.615, p.94,(1977). Zbl0363.58005MR461581
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