The Theory of Turbulence

1: The Turbulence Problem. 1.1 The Meaning of 'Turbulence' 1.2 Two Fundamental Aspects of Turbulence 2: The Net Energy Balance. 3: The Interchange of Energy Between States of Motion. 4. Some Remarks. 4.1. On the Harmonic Analysis. 4.2. On the Concept of Isotropy. 4.3. On the Possibility of a Universal Theory. 5: The Spectrum of Turbulent Energy. 5.1 The Spectrum 5.2. An Equation for the Spectrum 6: Some Preliminaries to the Development of a Theory of Turbulence. 7: Heisenberg's Theory of Turbulence. 7.1 The Fundamental Equation of the Theory 7.2 Chandrasekhar's Solution of (7.17) for the Case of Stationary Turbulence 8: Other Derivatives of K-2/3 Law. 8.1 Fermi's Approach 8.2 Kolmogoroff's Theory 8.3 The Method of von Neumann 8.4 Conclusion 9: An Alternate Approach - Correlations. 10: The Equations of Isotropic Turbulence. 10.1 The Concept of Isotropy 10.2 Qij as an Isotropic Tensor 10.3 Solenoidal Isotropic Tensors 11: The Karman-Howarth Equations. 12: The Meanings of the Defining Scalars. 13: Some Results from the Karman-Howarth Equation. 13.1 The Taylor Microscale 13.2 The Study of the Decay of Turbulence 13.3 The Connection between the Karman-Howarth Equation and the Kolmogoroff Theory 14: The Relation Between Fourth Order and Second Order Correlations when the Velocity Follows a Gaussian Distribution. 14.1 Some Properties of the Gaussian Distribution 14.2 Addition Theorem for Gaussian Distributions 14.3 Proof of Equation (14.2) 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. 18.1 A Mathematical Justification of the Assumptions of the Heisenberg Theory 18.2 Compatibility with the Kolmogoroff 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.