As a first step toward the understanding of the nature of turbulence, the study of the emergence and destabilization of dissipative structures in out-of-equilibrium systems has attracted considerable attention. During this study, confinement effects have been shown to play a major role in controlling the nature of the nonlinear effective dynamics driving the unstable modes. In confined systems, the spatial structure of the modes remains frozen, so that we are left with a small number of degrees of freedom well accounted for by the theory of dissipative dynamical systems. Intrinsic stochas-ticity is then mainly synonymous of temporal chaos. In extended systems confinement effects are weak and spatial modulations are allowed, leading to the formation of patterns. A much larger number of degrees of freedom is then involved in the dynamics, which raises the problem of the transition to weak turbulence.
KeywordsPartial Differential Equation Directed Percolation Turbulent Spot Laminar State Plane Poiseuille Flow
Unable to display preview. Download preview PDF.
- 2.H. Chaté and P. Manneville, Transition to turbulence via spatiotemporal in-termittency: modeling and critical properties in Ref. 3 below.Google Scholar
- 3.P. Coullet and P. Huerre, eds., New trends in nonlinear dynamics and pattern forming phenomena, Proceedings Cargèse’88, (Plenum Press, to appear).Google Scholar
- 5.K. Kaneko, Prog. Theor. Phys. 74(1985)1033.Google Scholar
- 11.M. Rabaud, S. Michalland, and Y. Couder, preprint ENS Paris, 1989; Y. Couder, these proceedings.Google Scholar
- 14.see the review by D.J. Tritton, Physical fluid dynamics 2nd edition (Clarendon Press, Oxford, 1988).Google Scholar
- 15.S.E. Widnall, “Growth of turbulent spots in plane Poiseuille flow”, in Turbulence and Chaotic Phenomena in Fluids, T. Tatsumi, ed. (Elsevier, 1984)Google Scholar
- 15a.J.J. Riley and M. Gad-el-Hak, “The dynamics of turbulent spots”, in Frontiers in fluid dynamics, S.H. Davis and J.L. Lumley, eds (Springer, 1985).Google Scholar
- 16.H. Chaté and B. Nicolaenko, in the Cargèse’88 Proceedings, Ref. 3.Google Scholar