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The Theory of Homogeneous Turbulence : Cambridge Science Classics - G. K. Batchelor

The Theory of Homogeneous Turbulence

Cambridge Science Classics


Published: 26th July 1982
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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.

Prefacep. ix
The study of homogeneous turbulencep. 1
Mathematical formulation of the problemp. 3
Brief history of the subjectp. 7
Mathematical Representation of the Field of Turbulence
Method of taking averagesp. 14
The complete statistical specification of the field of turbulencep. 17
Mean values of velocity productsp. 19
General properties of the velocity correlation and spectrum tensorsp. 23
Fourier analysis of the velocity fieldp. 28
The Kinematics of Homogeneous Turbulence
The velocity correlation and spectrum tensorsp. 34
The vorticity correlation and spectrum tensorsp. 38
Symmetry conditionsp. 40
Isotropic turbulencep. 45
Some Linear Problems
Simple harmonic oscillator subject to a random forcep. 55
Passage of a turbulent stream through wire gauzep. 58
Effect of sudden distortion of a turbulent streamp. 68
The General Dynamics of Decay
Methods of using the Navier-Stokes equationp. 76
The flow of energyp. 82
The permanence of big eddiesp. 88
The final period of decayp. 92
Dynamical equations for isotropic turbulencep. 99
The Universal Equilibrium Theory
The hypothesis of statistical equilibriump. 103
Turbulent motion at large Reynolds numberp. 106
The hypothesis of independence of Fourier components for distant wave-numbersp. 109
The universal equilibriump. 114
The inertial subrangep. 121
The energy spectrum in the equilibrium rangep. 125
Decay of the Energy-containing Eddies
The decay of total energyp. 133
Evidence for the existence of a unique statistical state of the energy-containing eddiesp. 139
The quasi-equilibrium hypothesisp. 148
The equilibrium at large wave-numbers for moderate Reynolds numbersp. 155
Heisenberg's form of the energy spectrum in the quasiequilibrium rangep. 161
The Probability Distribution of u(x)
The experimental evidencep. 169
The hypothesis of a normal distribution of the velocity field associated with the energy-containing eddiesp. 174
Determination of the pressure convariancep. 177
The small-scale properties of the motionp. 183
Bibliography of Research on Homogeneous Turbulencep. 188
Indexp. 196
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521041171
ISBN-10: 0521041171
Series: Cambridge Science Classics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 212
Published: 26th July 1982
Country of Publication: GB
Dimensions (cm): 21.69 x 14.05  x 1.35
Weight (kg): 0.27