Transition to Turbulence via Spatiotemporal Intermittency: Modeling and Critical Properties

  • Hugues Chaté
  • Paul Manneville
Part of the NATO ASI Series book series (NSSB, volume 237)


When studying the transition to turbulence in closed flow systems, it has become traditional to make a distinction between them according to confinement effects. These effects can be measured by aspect-ratios, i.e. ratios of the lateral dimensions of the physical system to some internal length linked to the basic instability mechanism. Small aspect-ratio systems are strongly confined so that the spatial structure of the modes involved can be considered as frozen. As such, they experience a transition to turbulence according to scenarios understood in the framework of low dimensional dynamical systems theory. The general procedure in this field involves the reduction to center manifold dynamics by elimination of stable modes, the Poincaré surface of section technique and the iteration of maps. Disorder is then interpreted rather as temporal chaos arising from the sensitivity of trajectories to initial conditions and small perturbations.


Cellular Automaton Space Dimension Critical Exponent Continuous Phase Transition Laminar State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bergé, P., 1987, From temporal chaos towards spatial effects, Nucl.Phys.B (Proc. suppl.) 2: 247.ADSCrossRefGoogle Scholar
  2. Bidaux, R., Boccara, N., and Chaté, H., 1988, Order of transition vs space dimension in a family of cellular automata, submitted to Phys. Rev. A.Google Scholar
  3. Bohr, T., Grinstein, G., Yu He, and Jayaprakash, C., 1987, Coherence chaos and broken symmetry in classical many-body dynamical systems, Phys. Rev. Lett. 58: 2155.ADSCrossRefGoogle Scholar
  4. Chaté, H. and Manneville, P., 1987, Transition to turbulence via spatiotemporal intermittency, Phys. Rev. Lett. 58: 112.ADSCrossRefGoogle Scholar
  5. Chaté, H. and Manneville, P., 1988a, Coupled map lattices as cellular automata, submitted to J. Stat. Phys..Google Scholar
  6. Chaté, H. and Manneville, P., 1988b, Spatiotemporal intermittency in coupled map lattices, to appear in Physica D.Google Scholar
  7. Chaté, H. and Manneville, P., 1988c, Continuous and discontinuous transition to spatiotemporal intermittency in two-dimensional coupled map lattices, Europhys. Lett. 6:591.ADSCrossRefGoogle Scholar
  8. Chaté, H. and Manneville, P., 1988d, Role of defects in the transition to turbulence via spatiotemporal intermittency, to appear in Physica D.Google Scholar
  9. Chaté, H., Manneville, P., Nicolaenko, B., and She, Z.S., 1988a, in preparation.Google Scholar
  10. Chaté, H., Manneville, P., and Rochwerger, D., 1988b, Mean-field approach of coupled map lattices, in preparation.Google Scholar
  11. Kaneko, K., 1985, Spatiotemporal intermittency in coupled map lattices, Prog. Theor. Phys. 74: 1033.ADSMATHCrossRefGoogle Scholar
  12. Kinzel, W., 1983, Directed percolation, in Percolation Structures and Processes, G. Deutscher et al. ed., Annals of the Israel Physical Society 5: 425.Google Scholar
  13. Kinzel, W., 1985, Phase transitions of cellular automata, Z. Phys. B 58: 229.MathSciNetMATHCrossRefGoogle Scholar
  14. Manneville, P., 1988, The Kurarnoto-Sivashinsky equation: a progress report, in Propagation in Systems Far from Equilibrium, J.E. Wesfreid et al. ed., Springer.Google Scholar
  15. Pomeau, Y., 1986, Front motion, metastability and subcritical bifurcations in hydrodynamics, Physica D 23: 3.ADSCrossRefGoogle Scholar
  16. Pomeau, Y., and Manneville, P., 1979, Stability and fluctuations of a spatially periodic convective flow, J. Phys. ( Paris) Lett. 40: 609.CrossRefGoogle Scholar
  17. Pomeau, Y., and Manneville, P., 1980, Wavelength Selection in Cellular Flows, Phys. Lett. A 75: 296.MathSciNetCrossRefGoogle Scholar
  18. Swift J., Hohenberg P.C., 1977, Hydrodynamic fluctuations at the convective instability, Phys. Rev. A 15: 319.ADSCrossRefGoogle Scholar
  19. Wolfram, S., 1986, Theory and Applications of Cellular Automata, World Scientific, Singapore.MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Hugues Chaté
    • 1
  • Paul Manneville
    • 1
  1. 1.Institut de Recherche FondamentaleDPh-G/PSRM, CEN-SaclayGif-sur-Yvette CedexFrance

Personalised recommendations