## Turbulence in FluidsTurbulence is a dangerous topic which is often at the origin of serious ?ghts in the scienti?c meetings devoted to it since it represents extremely di?erent points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even di?cult to agree on what exactly is the problem to be solved. Extremely schematically, two opposing points of view had been adv- ated during these last thirty years: the ?rst one was “statistical”, and tried to model the evolution of averaged quantities of the ?ow. This community, which had followed the glorious trail of Taylor and Kolmogorov, believed in the phenomenology of cascades, and strongly disputed the possibility of any coherence or order associated to turbulence. On the other bank of the river standed the “coherence among chaos” community, which considered turbulence from a purely deterministic point of view, by studying either the behaviour of dynamical systems, or the stability of ?ows in various situations. To this community were also associated the experimentalists and computer simulators who sought to identify coherent vortices in ?ows. Situation is more complex now, and the existence of these two camps is less clear. In fact a third point of view pushed by people from the physics community has emerged, with the concepts of renormalization group theory, multifractality, mixing, and Lagrangian approaches. |

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### Contents

II | 1 |

III | 4 |

IV | 13 |

V | 14 |

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VII | 20 |

VIII | 21 |

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LI | 221 |

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XC | 455 |

XCI | 467 |

XCII | 483 |

XCIII | 489 |

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### Common terms and phrases

anticyclonic atmospheric barotropic boundary layer calculation Chapter closure coherent vortices compressible convection corresponding courtesy cyclonic decay density developed diffusion direct-numerical dissipation downstream eddy viscosity Ekman layer energy spectrum enstrophy evolution experimental Figure Fluid Dynamics Fluid Mech Fourier space Gaussian geostrophic Grenoble hairpins homogeneous turbulence horizontal imensional incompressible initial instability inviscid isosurfaces isotropic turbulence Kelvin–Helmholtz kinetic energy kinetic-energy Kolmogorov Kraichnan Large-eddy simulation lence Lesieur longitudinal vortices Mach number Métais mixing layer mode motion Navier–Stokes equations nonlinear numerical simulations Orr-Sommerfeld equation p+q=k passive scalar perturbation Phys plane potential vorticity predictability pressure pseudo-spectral methods random Reynolds number Rossby number Rossby waves rotation scales shear flows sional small-scale spanwise spatial statistical stratified structure subgrid subgrid-scale t)dk temperature temporal mixing layer theory three-dimensional turbulent flow Turbulent Shear Flows two-dimensional turbulence upstream vector velocity field velocity profile vortex vortex rings wake wave number zero