From Chaos to Turbulence in Fluid Dynamics

  • P. Manneville
Part of the International Centre for Mechanical Sciences book series (CISM, volume 319)


The transition to turbulence is a wide subject impossible to set out in few lectures. Here we review some selected topics and, in each case, present a small set of experiments chosen to bring into light a new facet of the problem [1]. Chapter 1 is mainly devoted to setting the general frame, introducing indispensable prerequisites about instability mechanisms, discussing briefly the roles of confinement in closed flows and advection in open flows, and outlining specific difficulties involved in case of “direct” transition to turbulence. In Chapter 2 we consider “plain convection” best illustrating the connection between chaos and turbulence. Both the instability mechanism and confinement effects are appealingly intuitive. We first examine the case of confined systems with frozen spatial structure, which makes the theory of dissipative dynamical systems relevant. Then we turn to extended systems where key-words are modulations and patterns. This presentation is further completed by a brief introduction to convection in binary mixtures (Chapter 3) and centrifugal instabilities (Chapter 4). The first topic adds the possibility of propagating waves and related new features of the nonlinear processes leading to weak turbulence. The second topic is illustrated by the case of a Couette flow between coaxial cylinders rotating at different angular speeds, which introduce the effects of shear in a seemingly simple context. At last we examine plane parallel shear flows (Chapter 5). We first discuss the instability mechanisms and introduce the basic distinction between “absolute” and “convective” instabilities dealing with the specificities of downstream advection. Then we review the phenomenology of the transition to turbulence from the early nonlinear stages to the late stages, including the dynamics of turbulent spots in flows of engineering interest. The importance of the recent advances reviewed is assessed in the conclusion.


Rayleigh Number Couette Flow Unstable Mode Instability Mechanism Small Scale Turbulence 
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© Springer-Verlag Wien 1991

Authors and Affiliations

  • P. Manneville
    • 1
  1. 1.CEN SACLAYGif-sur-YvetteFrance

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