Statistical Fluid Mechanics, Volume II Mechanics of Turbulence

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ISBN: 9780486458915 | 0486458911
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Copyright: 6/5/2007

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Written by two of Russia's, most eminent and productive scientists working in the fields of turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. Volume One begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulence, the behavior of thermally stratified media, and diffusion.

Authors' Preface to the English Edition	p. iii
Editor's Preface to the English Edition	p. v
Mathematical Description of Turbulence. Spectral Functions	p. 1
Spectral Representations of Stationary Processes and Homogeneous Fields	p. 1
Spectral Representation of Stationary Processes	p. 3
Spectral Representation of Homogeneous Fields	p. 16
Partial Derivatives of Homogeneous Fields. Divergence and Curl of a Vector Field	p. 23
Isotropic Random Fields	p. 29
Correlation Functions and Spectra of Scalar Isotropic Fields	p. 29
Correlation Functions and Spectra of Isotropic Fields	p. 35
Solenoidal and Potential Isotropic Vector Fields	p. 49
One-Point and Two-Point Higher-Order Moments of Isotropic Fields	p. 58
Three-Point Moments of Isotropic Fields	p. 75
Locally Homogeneous and Locally Isotropic Random Fields	p. 80
Processes with Stationary Increments	p. 80
Locally Homogeneous Fields	p. 93
Locally Isotropic Fields	p. 98
Isotropic Turbulence	p. 113
Equations for the Correlation and Spectral Functions of Isotropic Turbulence	p. 113
Definition of Isotropic Turbulence and the Possibilities of its Experimental Realization	p. 113
Equations for the Velocity Correlations	p. 117
Equations for the Velocity Spectra	p. 123
Correlations and Spectra Containing Pressure	p. 130
Correlations and Spectra Containing the Temperature	p. 136
The Simplest Consequences of the Correlation and Spectral Equations	p. 141
Balance Equations for Energy, Vorticity, and Temperature-Fluctuation Intensity	p. 141
The Loitsyanskii and Corrsin Integrals	p. 146
Final Period of Decay of Isotropic Turbulence	p. 152
Experimental Data on the Final Period of Decay. The Decay of Homogeneous Turbulence	p. 162
Asymptotic Behavior of the Correlations and Spectra of Homogeneous Turbulence in the Range of Large Length Scales (or Small Wave Numbers)	p. 169
The Influence of the Spectrum Singularity on the Final Period Decay	p. 174
Self-Preservation Hypotheses	p. 177
The von Karman Hypothesis on the Self-Preservation of the Velocity Correlation Functions	p. 177
Less Stringent Forms of the von Karman Hypothesis	p. 181
Spectral Formulation of the Self-Preservation Hypotheses	p. 185
Experimental Verification of the Self-Preservation Hypotheses	p. 189
The Kolmogorov Hypotheses on Small-Scale Self-Preservation at High Enough Reynolds Numbers	p. 197
Conditions for the Existence of Kolmogorov Self-Preservation in Grid Turbulence	p. 204
The Meso-Scale Quasi-Equilibrium Hypothesis. Self-Preservation of Temperature Fluctuations	p. 210
Spectral Energy-Transfer Hypotheses	p. 212
Approximate Formulas for the Spectral Energy Transfer	p. 212
Application of the Energy Transfer Hypotheses to the Study of the Shape of the Spectrum in the Quasi-Equilibrium Range	p. 225
Application of the Energy-Transfer Hypotheses to Decaying Turbulence behind a Grid	p. 235
Self-Preserving Solutions of the Approximate Equations for the Energy Spectrum	p. 237
The Miliionshchikov Zero-Fourth-Cumulant Hypothesis and its Application to the Investigation of Pressure and Acceleration Fluctuations	p. 241
The Zero-Fourth-Cumulant Hypothesis and the Data on Velocity Probability Distributions	p. 241
Calculation of the Pressure Correlation and Spectra	p. 250
Estimation of the Turbulent Acceleration Fluctuations	p. 256
Dynamic Equations for the Higher-Order Moments and the Closure Problem	p. 260
Equations for the Third-Order Moments of Flow Variables	p. 260
Closure of the Moment Equations by the Moment Discard Assumption	p. 267
Closure of the Second- and Third-Order Moment Equations Using the Millionshchikov Zero-Fourth-Cumulant Hypothesis	p. 271
Zero-Fourth-Cumulant Approximation for Temperature Fluctuations in Isotropic Turbulence	p. 286
Space-Time Correlation Functions. The Case of Stationary Isotropic Turbulence	p. 290
Application of Perturbation Theory and the Diagram Technique	p. 295
Equations for the Finite-Dimensional Probability Distributions of Velocities	p. 310
Turbulence in Compressible Fluids	p. 317
Invariants of Isotropic Compressible Turbulence	p. 317
Linear Theory; Final Period of Decay of Compressible Turbulence	p. 321
Quadratic Effects; Generation of Sound by Turbulence	p. 328
Locally Isotropic Turbulence	p. 337
General Description of the Small-Scale Structure of Turbulence at Large Reynolds Numbers	p. 337
A Qualitative Scheme for Developed Turbulence	p. 337
Definition of Locally Isotropic Turbulence	p. 341
The Kolmogorov Similarity Hypotheses	p. 345
Local Structure of the Velocity Fluctuations	p. 351
Statistical Characteristics of Acceleration, Vorticity, and Pressure Fields	p. 368
Local Structure of the Temperature Field for High Reynolds and Peclet Numbers	p. 377
Local Characteristics of Turbulence in the Presence of Buoyancy Forces and Chemical Reactions. Effect of Thermal Stratification	p. 387
Dynamic Theory of the Local Structure of Developed Turbulence	p. 395
Equations for the Structure and Spectral Functions of Velocity and Temperature	p. 395
Closure of the Dynamic Equations	p. 403
Behavior of the Turbulent Energy Spectrum in the Far Dissipation Range	p. 421
Behavior of the Temperature Spectrum at Very Large Wave Numbers	p. 433
Experimental Data on the Fine Scale Structure of Developed Turbulence	p. 449
Methods of Measurement; Application of Taylor's Frozen-Turbulence Hypothesis	p. 449
Verification of the Local Isotropy Assumption	p. 453
Verification of the Second Kolmogorov Similarity Hypothesis for the Velocity Fluctuations	p. 461
Verification of the First Kolmogorov Similarity Hypothesis for the Velocity Field	p. 486
Data on the Local Structure of the Temperature and other Scalar Fields Mixed by Turbulence	p. 494
Data on Turbulence Spectra in the Atmosphere beyond the Low-Frequency Limit of the Inertial Subrange	p. 517
Diffusion in an Isotropic Turbulence	p. 527
Diffusion in an Isotropic Turbulence. Statistical Characteristics of the Motion of a Fluid Particle	p. 527
Statistical Characteristics of the Motion of a Pair of Fluid Particles	p. 536
Relative Diffusion and Richardson's Four-Thirds Law	p. 551
Hypotheses on the Probability Distributions of Local Diffusion Characteristics	p. 567
Material Line and Surface Stretching in Turbulent Flows	p. 578
Refined Treatment of the Local Structure of Turbulence, Taking into Account Fluctuations in Dissipation Rate	p. 584
General Considerations and Model Examples	p. 584
Refined Similarity Hypothesis	p. 590
Statistical Characteristics of the Dissipation	p. 594
Refined Expressions for the Statistical Characteristics of Small-Scale Turbulence	p. 640
More General Form of the Refined Similarity Hypothesis	p. 650
Wave Propagation Through Turbulence	p. 653
Propagation of Electromagnetic and Sound Waves in a Turbulent Medium	p. 653
Foundations of the Theory of Electromagnetic Wave Propagation in a Turbulent Medium	p. 653
Sound Propagation in a Turbulent Atmosphere	p. 668
Turbulent Scattering of Electromagnetic and Sound Waves	p. 674
Fluctuations in the Amplitude and Phase of Electromagnetic and Sound Waves in a Turbulent Atmosphere	p. 685
Strong Fluctuations of Wave Amplitude	p. 704
Stellar Scintillation	p. 721
Fluctuations in the Amplitude and Phase of Star Light Observed on the Earth's Surface	p. 721
The Effect of Telescope Averaging and Scintillation of Stellar and Planetary Images	p. 729
Time Spectra of Fluctuations in the Intensity of Stellar Images in Telescopes	p. 733
Chromatic Stellar Scintillation	p. 737
Functional Formulation of the Turbulence Problem	p. 743
Equations for the Characteristic Functional	p. 743
Equations for the Spatial Characteristic Functional of the Velocity Field	p. 743
Spectral Form of the Equations for the Spatial Characteristic Functional	p. 751
Equations for the Space-Time Characteristic Functional	p. 760
Equations for the Characteristic Functional in the Presence of External Forces	p. 763
Methods of Solving the Equations for the Characteristic Functional	p. 773
Use of a Functional Power Series	p. 773
Zero-Order Approximation in the Reynolds Number	p. 783
Expansion in Powers of the Reynolds Number	p. 791
Other Expansion Schemes	p. 798
Use of Functional Integrals	p. 802
Bibliography	p. 813
Supplementary Remarks to Volume 1	p. 853
References	p. 854
Errata to Volume 1	p. 855
Author Index	p. 863
Subject Index	p. 871
Table of Contents provided by Ingram. All Rights Reserved.

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