| Foreword Preface 1 Introduction 1.1 Historical Background 1.2 Outline of the Book 2 H-Functional 2.1 Hydrodynamic Random Fields 2.2 H-Functional 3 H-Functional Equation 3.1 Derivation of H-Functional Equation 3.2 H-Functional Equation 3.3 Balance Equations 3.4 Reformulation 4 K-Functional 4.1 Definition of K-Functional 5 Some Useful Formulas 5.1 Some Useful Formulas 5.2 A Remark on H-Functional Equation 6 Turbulent Gibbs Distributions 6.1 Asymptotic Analysis for Liouville Equation 6.2 Turbulent Gibbs Distributions 6.3 Gibbs Mean 7 Euler K-Functional Equation 7.1 Expressions of B2 and B3 7.2 Euler K-Functional Equation 7.3 Reformulation 7.4 Special Cases 7.5 Case of Deterministic Flows 8 Functionals and Distributions 8.1 K-Functionals and Turbulent Gibbs Distributions 8.2 Turbulent Gibbs Measures 8.3 Asymptotic Analysis 9 Local Stationary Liouville Equation 9.1 Gross Determinism 9.2 Temporal Part of Material Derivative of TN 9.3 Spatial Part of Material Derivative of TN 9.4 Stationary Local Liouville equation 10 Second Order Approximate Solutions 10.1 Case of Reynolds-Gibbs Distributions 10.2 A Poly-spherical Coordinate System 10.3 A Solution to the Equation (10.24)1 …… 11 A Finer K-Functional Equation 12 Conclusions A Some Facts About Spherical Harmonics Bibliography Index |
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