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# The Theory of Turbulence: Subrahmanyan Chandrasekhar's 1954 lectures

## EditorEdward A. Spiegel

### Paperback | October 28, 2010

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In January 1937, Nobel laureate in Physics Subrahmanyan Chandrasekhar was recruited to the University of Chicago. He was to remain there for his entire career, becoming Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics in 1952 and attaining emeritus status in 1985. This is where his then student Ed Spiegel met him during the summer of 1954, attended his lectures on turbulence and jotted down the notes in hand. His lectures had a twofold purpose: they not only provided a very elementary introduction to some aspects of the subject for novices, they also allowed Chandra to organize his thoughts in preparation to formulating his attack on the statistical problem of homogeneous turbulence. After each lecture Ed Spiegel transcribed the notes and filled in the details of the derivations that Chandrasekhar had not included, trying to preserve the spirit of his presentation and even adding some of his side remarks. The lectures were rather impromptu and the notes as presented here are as they were set down originally in 1954. Now they are being made generally available for Chandrasekhar's centennial.

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Title:The Theory of Turbulence: Subrahmanyan Chandrasekhar's 1954 lecturesFormat:PaperbackDimensions:134 pagesPublished:October 28, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9400701160

ISBN - 13:9789400701168

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Table of Contents

1: The Turbulence Problem. 1.1 The Meaning of 'Turbulence' 1.2 Two Fundamental Aspects of Turbulence 2: The Net Energy Balance. 3: The Interchange of Energy Between States of Motion. 4. Some Remarks. 4.1. On the Harmonic Analysis. 4.2. On the Concept of Isotropy. 4.3. On the Possibility of a Universal Theory. 5: The Spectrum of Turbulent Energy. 5.1 The Spectrum 5.2. An Equation for the Spectrum 6: Some Preliminaries to the Development of a Theory of Turbulence. 7: Heisenberg's Theory of Turbulence. 7.1 The Fundamental Equation of the Theory 7.2 Chandrasekhar's Solution of (7.17) for the Case of Stationary Turbulence 8: Other Derivatives of K-2/3 Law. 8.1 Fermi's Approach 8.2 Kolmogoroff's Theory 8.3 The Method of von Neumann 8.4 Conclusion 9: An Alternate Approach - Correlations. 10: The Equations of Isotropic Turbulence. 10.1 The Concept of Isotropy 10.2 Qij as an Isotropic Tensor 10.3 Solenoidal Isotropic Tensors 11: The Karman-Howarth Equations. 12: The Meanings of the Defining Scalars. 13: Some Results from the Karman-Howarth Equation. 13.1 The Taylor Microscale 13.2 The Study of the Decay of Turbulence 13.3 The Connection between the Karman-Howarth Equation and the Kolmogoroff Theory 14: The Relation Between Fourth Order and Second Order Correlations when the Velocity Follows a Gaussian Distribution. 14.1 Some Properties of the Gaussian Distribution 14.2 Addition Theorem for Gaussian Distributions 14.3 Proof of Equation (14.2) 15: Chandrasekhar's Theory of Turbulence. 16: A More Subjective Approach to the Derivation of Chandrasekhar's Equation. 17: The Dimensionless Form of Chandrasekhar's Equation. 18: Some Aspects and Advantages of the New Theory. 18.1 A Mathematical Justification of the Assumptions of the Heisenberg Theory 18.2 Compatibility with the Kolmogoroff Theory 19: The Problem of Introducing the Boundary Conditions. 20: Discussion of the Case of Negligible Inertial Term. 21: The Case in which Viscosity is Neglected. 22: Solution of the Non-Viscous Case near r = 0. 23: Solution of the Heat Equation. 24: Solution of the Quasi-Wave Equation. 25. The Introduction of Boundary Conditions. 26. Epilogue.

Editorial Reviews

From the reviews:"The lecture notes on Turbulence by S. Chandrasekhar are transcribed and filled in with details by Edward Spiegel in the year 1954. . it is interesting to have a book on these lecture notes for three reasons: 1. The scientific historian will enjoy this compilation. 2. The didactically interested lecturer can learn much about presentations in theoretical physics. 3. Students will find many explicitly calculated details in the presentation of the mathematical formalism." (Johannes Viktor Feitzinger, Zentralblatt MATH, Vol. 1207, 2011)