Turbulence: The Legacy of A. N. Kolmogorov

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Cambridge University Press, Nov 30, 1995 - Science
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This 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. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.
 

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Contents

Introduction
1
12 Outline of the book
11
Symmetries and conservation laws
14
22 Symmetries
17
23 Conservation laws
18
24 Energy budget scalebyscale
21
Why a probabilistic description of turbulence?
27
32 A model for deterministic chaos
31
74 Reynolds numbers and degrees of freedom
106
75 Microscopic and macroscopic degrees of freedom
109
76 The distribution of velocity gradients
111
77 The law of decay of the energy
112
finitetime blowup of ideal flow
115
Intermittency
120
82 Selfsimilar and intermittent random functions
121
83 Experimental results on intermittency
127

33 Dynamical systems
36
34 The NavierStokes equation as a dynamical system
37
Probabilistic tools a survey
40
42 Random functions
45
43 Statistical symmetries
46
44 Ergodic results
49
45 The spectrum of stationary random functions
52
Two experimental laws of fully developed turbulence
57
52 The energy dissipation law
67
The Kolmogorov 1941 theory
72
62 Kolmogorovs fourfifths law
76
63 Main results of the Kolmogorov 1941 theory
89
the lack of universality
93
65 Historical remarks on the Kolmogorov 1941 theory
98
Phenomenology of turbulence in the sense of Kolmogorov 1941
100
72 Basic tools of phenomenology
101
73 The Richardson cascade and the localness of interactions
103
84 Exact results on intermittency
133
85 Intermittency models based on the velocity
135
86 Intermittency models based on the dissipation
159
87 Shell models
174
88 Historical remarks on fractal intermittency models
178
89 Trends in intermittency research
182
Further reading a guided tour
195
93 Mathematical aspects of fully developed turbulence
199
94 Dynamical systems fractals and turbulence
203
95 Closure functional and diagrammatic methods
206
96 Eddy viscosity multiscale methods and renormalization
222
97 Twodimensional turbulence
240
References
255
Author index
283
Subject index
289
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