The Theory of Homogeneous Turbulence

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Cambridge University Press, 1953 - Mathematics - 197 pages
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This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
 

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Contents

INTRODUCTION
1
12 Mathematical formulation of the problem
3
13 Brief history of the subject
7
MATHEMATICAL REPRESENTATION OF THE FIELD OK TURBULENCE
14
22 The complete statistical specification of the field of turbulence
17
23 Mean values of velocity products
19
24 General properties of the velocity correlation and spectrum tensors
23
25 Fourier analysis of the velocity field
28
55 Dynamical equations for isotropic turbulence
99
THE UNIVERSAL EQUILIBRIUM THEORY
103
62 Turbulent motion at large Reynolds number
106
63 The hypothesis of independence of Fourier components for distant wavenumbers
109
64 The universal equilibrium
114
65 The inertial subrange
121
66 The energy spectrum in the equilibrium range
125
DECAY OF THE ENERGYCONTAINING EDDIES
133

THE KINEMATICS OF HOMOGENEOUS TURBULENCE
34
32 The vorticity correlation and spectrum tensors
38
33 Symmetry conditions
40
34 Isotropic turbulence
45
SOME LINEAR PROBLEMS
55
42 Passage of a turbulent stream through wire gauze
58
43 Effect of sudden distortion of a turbulent stream
68
THE GENERAL DYNAMICS OF DECAY
76
52 The flow of energy
82
53 The permanence of big eddies
88
54 The final period of decay
92
72 Evidence for the existence of a unique statistical state of the energycontaining eddies
139
73 The quasiequilibrium hypothesis
148
74 The equilibrium at large wavenumbers for moderate Reynolds numbers
155
75 Heisenbergs form of the energy spectrum in the quasi equilibrium range
161
THE PROBABILITY DISTRIBUTION OF ux
169
82 The hypothesis of a normal distribution of the velocity field associated with the energycontaining eddies
174
83 Determination of the pressure covariance
177
84 The smallscale properties of the motion
183
BIBLIOGRAPHY OF RESEARCH ON HOMOGENEOUS TURBULENCE
188
INDEX
196
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