The Theory of Turbulence

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.

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.