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Random functions and turbulence /
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Bulgarian |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1971]
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| Edición: | [1st ed.]. |
| Colección: | International series of monographs in natural philosophy ;
v. 32. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Random Functions and Turbulence; Copyright Page; Table of Contents; FOREWORD TO THE ENGLISH EDITION; INTRODUCTION; PART I: ELEMENTS OF THE THEORY OF RANDOM FUNCTIONS; Chapter 1. Certain Data on the Theory of Probability; 1. Random Variables and Distribution Functions; 2. Numerical Characteristics of Random Variables; 3. Multidimensional Random Variables with Spherical Symmetry; 4. Functional Transformations of Random Variables; 5. Certain Generalizations; 6. The Characteristic Function; 7. The Determination of Statistical Moments by Means of Characteristic Functions.
- Chapter 2. Random Processes 1. The Definition of the Random Function of One Variable. The Probability Distribution of a Random Function; 2. Statistical Moments. The Autocorrelation Function; 3. The Two-dimensional Random Process. The Cross Correlation Function; 4. The Stationarity and Ergodicity of Random Processes; 5. Fundamental Characteristics of the Autocorrelation and Cross Correlation Functions with Stationary Random Processes; 6. The Differentiation of Random Functions; 7. The Integration of Random Functions; 8. The Normally Distributed Random Processes.
- 9. The Harmonic Analysis of Random Processes 10. Generalized Harmonic Analysis. Spectral Expansions; 11. Random Processes with Stationary Increment. Structure Functions; 12. The Determination of the Correlation Function with Experimental Data; 13. The Influence of Finiteness of the Interval of Averaging; Chapter 3. Random Fields; 1. Supplementary Information; 2. Scalar and Vector Random Fields. The Random Functions of Several Variables; 3. Statistical Moments; 4. Homogeneous and Isotropie Random Fields; 5. Normal Random Fields.
- 6. The General Form of Tensor Statistical Moments 7. The Structure and Certain General Characteristics of Tensor Moments; 8. Spectral Expansions; 9. The Correlation of Random Solenoidal Vector Fields; 10. The Correlation of Random Potential Vector Fields; 11. The Joint Correlation of Solenoidal and Potential Random Vector Fields; 12. The Correlation of Certain Derived Fields; 13. Locally Homogeneous and Isotropie Random Fields. Structure Functions; 14. Some Additional Problems Concerning the Theory of Random Fields; PART II: HYDRODYNAMIC TURBULENCE.
- Chapter 4. The Statistical Theory of Turbulence- The Method of Similarity and Dimensionality 1. Some Data from the Theory of Dimensionality; 2. The Emergence of Turbulent Motion; 3. Turbulence with Very Large Reynolds Numbers; 4. Locally Isotropie Turbulence. The Theory of Kolmogorov; 5. The Microstructure of a Temperature Field in a Locally Isotropie Turbulent Flow. The Theory of Obukhov; Chapter 5. The Statistical Theory of Turbulence-The Correlation Method; 1. Isotropie Turbulence. The Equation of K�arm�an-Howarth; 2. The Invariant of Loitzianskii.