Intermittency at onset of convection in a slowly rotating, self-gravitating spherical shell

  • Pascal Chossat
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 549)


I present a joint work with Guyard and Lauterbach [4] which shows the existence and stability of a robust heteroclinic cycle near onset of convection in a self-gravitating, slowly rotating spherical shell filled with a fluid. The consequence of this is the existence of a regime characterized by long periods of time spent near an axisymmetric steady-state followed by sudden bursts of “turbulent flow” which settles down to another axisymmetric state with fluid flow moving in the opposite direction to the previous one. The process repeats indefinitely but non-periodically.


Rayleigh Number Spherical Shell Unstable Manifold Center Manifold Heteroclinic Orbit 
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  1. 1.
    D. Armbruster, P. Chossat. Heteroclinic orbits in a spherically invariant system, Physica D 50 (1991) 155–176.zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    F. H. Busse and R.M. Clever. Nonstationary convection in a rotating system, in Recent Development in Theoretical and Experimental Fluid Mechanics, Eds U. Müller and K. G. Roesner and B. Schmidt, Springer Verlag, Berlin (1979), 376–385.Google Scholar
  3. 3.
    P. Chossat, F. Guyard. Heteroclinic cycles in bifurcation problems with O(3) symmetry, J. of Nonlin. Sci., 6, 201–238 (1996).zbMATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    P. Chossat, F. Guyard and R. Lauterbach. Generalized Heteroclinic Cycles in Spherically Invariant Systems and their Perturbations, J. Nonlinear Sci. 9, p. 479–524 (1999).zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. 5.
    P. Chossat, R. Lauterbach. Methods in equivariant Bifurcation and Dynamical Systems, to appear in Advanced Series in Nonlinear Dynamics, World Scientific Publishing, Singapur (1999).Google Scholar
  6. 6.
    R. Friedrich, H. Haken. Static, wavelike and chaotic thermal convection in spherical geometries, Phys. Rev. A 34 (1986), 2100–2120.CrossRefADSGoogle Scholar
  7. 7.
    J. Guckenheimer and P. Holmes. Structurally stable heteroclinic cycles, Math. proc. Cambridge Phil. Soc. 103 (1988), 189–192.zbMATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    M. Krupa, I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry, Ergod. Th. Dyn. Sys. 15, 1 (1995), 121–147.zbMATHMathSciNetGoogle Scholar
  9. 9.
    E. Stone, P. Holmes. Noise induced Intermittency in a Model of a Turbulent Boundary Layer, Physica D 37 (1989), 20–32.zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pascal Chossat
    • 1
  1. 1.I.N.L.N.CNRS and Université de NiceSophia-AntipolisFrance

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