The Theory of Turbulence: Subrahmanyan Chandrasekhar's 1954 Lectures (Lecture Notes in Physics, 810)

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. Front Matter....Pages I-XVII The Turbulence Problem....Pages 1-2 The Net Energy Balance....Pages 3-6 Interchange of Energy Between States of Motion....Pages 7-9 Some Remarks....Pages 11-12 The Spectrum of Turbulent Energy....Pages 13-17 Some Preliminaries to the Development of a Theory of Turbulence....Pages 19-20 Heisenberg’s Theory of Turbulence....Pages 21-27 Other Derivations of the k −5/3 Law....Pages 29-33 An Alternate Approach: Correlations....Pages 35-36 The Equations of Isotropic Turbulence....Pages 37-48 The Karman-Howarth Equations....Pages 49-50 The Meanings of the Defining Scalars....Pages 51-53 Some Results from the Karman–Howarth Equation....Pages 55-59 The Relation Between the Fourth and Second Order Correlations When the Velocity Follows a Gaussian Distribution....Pages 61-70 Chandrasekhar’s Theory of Turbulence....Pages 71-79 A More Subjective Approach to the Derivation of Chandrasekhar’s Equation....Pages 81-82 The Dimensionless Form of Chandrasekhar’s Equation....Pages 83-83 Some Aspects and Advantages of the New Theory....Pages 85-87 The Problem of Introducing the Boundary Conditions....Pages 89-89 Discussion of the Case of Negligible Inertial Term....Pages 91-94 The Case in Which Viscosity Is Neglected....Pages 95-97 Solution of the Non-Viscous Case Near r =0....Pages 99-100 Solution of the Heat Equation....Pages 101-101 Solution of the Quasi-Wave Equation....Pages 103-109 The Introduction of Boundary Conditions....Pages 111-113 Back Matter....Pages 115-117