## Turbulence: The Legacy of A. N. KolmogorovThis textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A.N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. First, a qualitative introduction is given to bring out the need for a probabilistic description of what is in essence a deterministic system. Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Considerable material is devoted to intermittency, the clumpiness of small-scale activity, which has led to the development of fractal and multifractal models. Such models, pioneered by B. Mandelbrot, have applications in numerous fields besides turbulence (diffusion limited aggregation, solid-earth geophysics, attractors of dynamical systems, etc). The final chapter contains an introduction to analytic theories of the sort pioneered by R. Kraichnan, to the modern theory of eddy transport and renormalization and to recent developments in the statistical theory of two-dimensional turbulence. The book concludes with a guide to further reading. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. |

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### Contents

CHAPTER 1 | 13 |

4 | 21 |

1 | 27 |

Two experimental laws of fully developed turbulence | 57 |

CHAPTER 6 | 73 |

Phenomenology of turbulence in the sense of Kolmogorov 1941 | 100 |

Intermittency | 120 |

97 | 167 |

CHAPTER 9 | 195 |

255 | |

283 | |

289 | |

### Other editions - View all

Turbulence: The Legacy of A. N. Kolmogorov Uriel Frisch,Andreĭ Nikolaevich Kolmogorov No preview available - 1995 |

### Common terms and phrases

Actually appear approximation argument assumed assumption average become called cascade consequence considered constant defined definition depend derivation developed dimension discussed dissipation dissipation scale distribution dynamical eddy energy dissipation energy spectrum equal equation example existence experimental exponent expression field finite flow fluid flux follows force Fourier Frisch Gagne Gaussian given gives Hence homogeneous inertial range initial integral intermittency invariant involves Kolmogorov Kraichnan leads limit mean measure methods moments multifractal Navier-Stokes equation needed negative nonlinear Note observed obtained positive possible predicted present probability problem properties quantity random random function range reference relation Reynolds number scale scaling exponent Section shown shows signal simulations singularities smaller solution space statistical structure functions symmetries theory transform turbulence turbulent flow two-dimensional unit universality variables velocity increments viscosity vorticity wavenumber zero

### Popular passages

Page 258 - Transition to chaos in a shell model of turbulence, Physica D 80, 105-119.

Page 258 - Brachet, ME, Meiron, DI, Orszag, SA, Nickel, BG, Morf, RH & Frisch, U. 1983. Small-scale structure of the Taylor-Green vortex, J. Fluid Mech. 130, 411-451 Brachet, ME, Meneguzzi, M., Politano, H.

Page 259 - Tabeling, P. 1994. Quantitative experimental study of the free decay of quasi-two-dimensional turbulence, Phys. Rev. E 49, 454^61.

Page 256 - Aurell, E., Frisch, U., Lutsko, J. & Vergassola, M. 1992. On the multifractal properties of the energy dissipation derived from turbulence data, /. Fluid Mech.

Page 259 - Mathematical examples illustrating relations occuring in the theory of turbulent fluid motion.