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The Theory of Turbulence

by Spiegel, Edward A.
Authors: SpringerLink (Online service) Series: Lecture Notes in Physics, 0075-8450 ; . 810 Physical details: XVII, 117p. online resource. ISBN: 9400701179 Subject(s): Physics. | Physics. | Classical Continuum Physics. | Statistical Physics, Dynamical Systems and Complexity. | Fluid- and Aerodynamics. | History and Philosophical Foundations of Physics. | Astrophysics and Astroparticles.
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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.

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.

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