The Theory of Turbulence

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.