Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Armbruster, P. Chossat. Heteroclinic orbits in a spherically invariant system, Physica D 50 (1991) 155–176.
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.
P. Chossat, F. Guyard. Heteroclinic cycles in bifurcation problems with O(3) symmetry, J. of Nonlin. Sci., 6, 201–238 (1996).
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).
P. Chossat, R. Lauterbach. Methods in equivariant Bifurcation and Dynamical Systems, to appear in Advanced Series in Nonlinear Dynamics, World Scientific Publishing, Singapur (1999).
R. Friedrich, H. Haken. Static, wavelike and chaotic thermal convection in spherical geometries, Phys. Rev. A 34 (1986), 2100–2120.
J. Guckenheimer and P. Holmes. Structurally stable heteroclinic cycles, Math. proc. Cambridge Phil. Soc. 103 (1988), 189–192.
M. Krupa, I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry, Ergod. Th. Dyn. Sys. 15, 1 (1995), 121–147.
E. Stone, P. Holmes. Noise induced Intermittency in a Model of a Turbulent Boundary Layer, Physica D 37 (1989), 20–32.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chossat, P. (2000). Intermittency at onset of convection in a slowly rotating, self-gravitating spherical shell. In: Egbers, C., Pfister, G. (eds) Physics of Rotating Fluids. Lecture Notes in Physics, vol 549. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45549-3_18
Download citation
DOI: https://doi.org/10.1007/3-540-45549-3_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67514-3
Online ISBN: 978-3-540-45549-3
eBook Packages: Springer Book Archive