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.

From the book reviews: "The book under review is part of the Lecture Notes in Physics series, and aims to 'quickly and informally' communicate knowledge in the subject. The book is structured in 25 chapters plus a prologue and epilogue. ... The book is addressed to both the novice and advanced reader, as it provides basic and advanced proofs, as well as different approaches and derivation of classical results." (Iuliana Stanculescu, Mathematical Reviews, May, 2014) "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)