The Theory of Turbulence Subrahmanyan Chandrasekhar's 1954 Lectures

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.

1: The Turbulence Problem.- 2: The Net Energy Balance.- 3: The Interchange of Energy between States of Motion.- 4.- Some Remarks.- 5: The Spectrum of Turbulent Energy.- 6: Some Preliminaries to the Development of a Theory of Turbulence.- 7: Heisenberg's Theory of Turbulence.- 8: Other Derivatives of K-2/3 Law.- 9: An Alternate Approach – Correlations.- 10: The Equations of Isotropic Turbulence.- 11: The Karman-Howarth Equations.- 12: The Meanings of the Defining Scalars.- 13: Some Results from the Karman-Howarth Equation.- 14: The Relation Between Fourth Order and Second Order Correlations when the Velocity Follows a Gaussian Distribution.- 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.- 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.

Nobel Laureate Chandrasekhar derived a novel theory of Turbulence in the 1950's. These notes give a first hand account from Chandrasekhar of the development of this theory. Transcribed by his then student Ed Spiegel, these notes provide a unique insight into the development of this theory. Ed Spiegel is a renowned and highly respected expert in the field of astrophysics, and astrophysical fluid dynamics (he coined the term Blazar), and he provides a wonderful introduction describing the course given by Chandrasekhar with some interesting anecdotes from the lectures as well as a short account of how the theory has evolved since Chandrasekhar's unique contributions over half a century ago.