Turbulence takes place in practically all flow situations that occur naturally or in modern technological systems. Therefore, considerable effort is being expended in an attempt to understand this very complex physical phenome­ non and to develop both empirical and mathematical models for its description. Such numerical and analytical computational schemes would allow the reliable prediction and design of turbulent flow processes to be carried out. The purpose of this book is to bring together, in a usable form, some of the fundamental concepts of turbulence along with turbulence models and experimental techniques. It is hoped that these have "general applicability" in current engineering design. The phrase "general applicabil­ ity" is highlighted because the theory of turbulence is still so much in a formative stage that completely general analyses are not available now, nor will they be available in the immediate future. The concepts and models described herein represent the state-of-the­ art methods that are now being used to give answers to turbulent flow problems. As in all turbulent flow analysis, the methods are a blend of analytical and empirical input, and the reader should be cognizant of the simplification and restrictions imposed upon the methods when applyingthem to physical situations different from those for which they have been developed.

1 The Complexity of Turbulent Fluid Motion.- 1.1. Introduction.- 1.2. On Continuum Fluid Motion.- 1.3. Further Remarks on Turbulence.- 1.4. Looking Onward.- References.- 2 An Introduction to Turbulence Phenomena.- 2.1. Introduction.- 2.2. On the Basic Equations of Motion.- 2.3. Reynolds' Decomposition.- 2.4. Correlations and the Closure Condition.- 2.5. The Turbulent Boundary Layer.- 2.6. Final Remarks.- References.- 3 Statistical Concepts of Turbulence.- 3.1. Basic Physical Model of Turbulence.- 3.2. Statistical Definitions.- 3.3. Statistical Moments.- References.- 4 Spectral Theory of Turbulence.- 4.1. Introduction.- 4.2. Harmonic Analysis.- 4.3. Frequency Spectra.- 4.4. Wave-Number Spectra.- 4.5. Characteristics of Energy Spectra.- References.- 5 Turbulence: Diffusion, Statistics, Spectral Dynamics.- 5.1. Introduction.- 5.2. Turbulent Diffusion.- 5.3. Fourier Transforms.- 5.4. Particle Diffusion.- 5.5. Another Look at Fourier Transforms.- 5.6. On the Interpretation of Frequency.- 5.7. Strong Interactions.- 5.8. Vorticity and Velocity.- 5.9. The "First Law" of Turbulence.- 5.10. The Energy Cascade.- 5.11. Some Enlightening Errors.- 5.12. Other Inertial Ranges.- 5.13. Turbulent Diffusion Revisited.- 5.14. Conclusions.- References.- 6 Transition.- 6.1. Introduction.- 6.2. Weak Oscillations of Simple Flow.- 6.3. Multiple Perturbations of Laminar Flow.- 6.4. Amplification of Initial Perturbations.- 6.5. Strong Disturbances of Simple Flows.- 6.6. Statistical Models.- 6.7. Comment.- References.- 7 Turbulence Processes and Simple Closure Schemes.- 7.1. Introduction.- 7.2. Theoretical Development.- 7.3. Final Remarks.- References.- 8 Kinetic Energy Methods.- 8.1. Introduction.- 8.2. Eddy Viscosity Transport Models.- 8.3. Turbulent Kinetic Energy Models.- 8.4. Summaryand Conclusions.- References.- 9 Use of Invariant Modeling.- 9.1. Introduction.- 9.2. Model Development.- 9.3. Evaluation of Model Coefficients.- 9.4. Model Verification.- 9.5. Local Equilibrium Approximations.- 9.6. Applications.- 9.7. Concluding Remarks.- References.- 10 Numerical Simulation of Turbulent Flows.- 10.1. Introduction.- 10.2. Methods.- 10.3. Problems.- 10.4. Survey of Applications.- 10.5. Comparison with Other Methods.- 10.6. Prospects.- References.- 11 Laboratory Instrumentation in Turbulence Measurements.- 11.1. Introduction.- 11.2. Measurement of Velocity Fluctuations.- 11.3. Measurement of Temperature Fluctuations.- 11.4. Measurement of Density and Pressure Fluctuations.- 11.5. Measurement of Concentration Fluctuations.- 11.6. Measurement of Surface Shear Fluctuations.- References.- 12 Techniques for Measuring Atmospheric Turbulence.- 12.1. Introduction.- 12.2. Measurements: Background, Instruments, Platforms, and Techniques.- 12.3. Measurements from Aircraft.- 12.4. Aircraft Measurement of Turbulent Airflow Downwind of a Mountain Range.- 12.5. Elk Mountain PBL Profiles.- 12.6. Suppression of Mixing Coefficient by Forced Boundary-Layer Upward Curvature.- 12.7. Turbulent Airflow across a Building.- 12.8. Concluding Remarks.- References.- 13 Optical and Acoustical Measuring Techniques.- 13.1. Introduction.- 13.2. Background and Basic Principles.- 13.3. Laser Doppler.- 13.4. Acoustic Doppler.- References.- 14 Monte Carlo Turbulence Simulation.- 14.1. Introduction.- 14.2. Control-System Simulation.- 14.3. Use of Standard System Function Elements.- 14.4. Digital Filter Simulation.- 14.5. Discrete Fourier Series.- 14.6. Non-Gaussian Simulation.- 14.7. Multidimensional Simulation.- 14.8. Nonhomogeneous Atmospheric Boundary-Layer Simulation.- 14.9. Self-Similar Simulation.- 114.10. Conclusions.- References.- 15 Wind, Turbulence, and Buildings.- Author Index.