Fundamentals and applications
Walter O. Frost, Trevor H. Moulden · Medical Entomology and Zoology · 1977
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.- 2.2.1. General Considerations.- 2.2.2. Detailed Development.- 2.3. Reynolds' Decomposition.- 2.3.1. The Mean-Value Equations.- 2.3.2. Some Comments.- 2.3.3. On Pressure Fluctuations.- 2.3.4. Passage to Statistical Theory.- 2.4. Correlations and the Closure Condition.- 2.5. The Turbulent Boundary Layer.- 2.5.1. Preliminary Remarks.- 2.5.2. Comments.- 2.5.3. Further Developments.- 2.6. Final Remarks.- References.- 3 Statistical Concepts of Turbulence.- 3.1. Basic Physical Model of Turbulence.- 3.1.1. Vortex Stretching.- 3.1.2. Energy Cascade.- 3.2. Statistical Definitions.- 3.2.1. The Random Process.- 3.2.2. Stationarity and Ergodicity.- 3.2.3. Space-Dependent Random Variables.- 3.2.4. Homogeneous and Isotropic Turbulence.- 3.2.5. The Taylor Hypothesis.- 3.2.6. Random Field.- 3.2.7. Random Scalar and Vector Fields.- 3.3. Statistical Moments.- 3.3.1. Ordinary Moments.- 3.3.2. Central Moments.- 3.3.3. Joint Moments.- 3.3.4. Space-Time Moments.- 3.3.5. Other Terminology.- 3.3.6. Longitudinal and Lateral Correlations.- 3.3.7. Characteristics of Correlation Coefficients.- References.- 4 Spectral Theory of Turbulence.- 4.1. Introduction.- 4.2. Harmonic Analysis.- 4.2.1. Fourier Series.- 4.2.2. Fourier Integral.- 4.2.3. Stationary Random Process.- 4.2.4. Spectral Representation of a Stationary Random Process.- 4.2.5. Autocorrelation.- 4.3. Frequency Spectra.- 4.4. Wave-Number Spectra.- 4.4.1. From Taylor's Hypothesis.- 4.4.2. Three-Dimensional Wave-Number Spectra.- 4.5. Characteristics of Energy Spectra.- 4.5.1. Three-Dimensional Energy Spectra.- 4.5.2. One-Dimensional 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.- 8.3.1. ND Models I: Bradshaw etal.- 8.3.2. ND Models II: Morel etal.- 8.3.3. ND Models III: Lee and Harsha.- 8.3.4. PK Models I: Ng and Spalding Rodi and Spalding.- 8.3.5. PK Models II: Launder etal.- 8.3.6. Three-Equation Model: Hanjalic and Launder.- 8.3.7. Comparison of Turbulence-Model Predictions with Free Shear Layer Data.- 8.4. Summary and Conclusions.- References.- 9 Use of Invariant Modeling.- 9.1. Introduction.- 9.2. Model Development.- 9.2.1. Closure Requirements.- 9.2.2. Dissipation Terms.- 9.2.3. Pressure Correlations.- 9.2.4. Third-Order Velocity Correlations.- 9.2.5. Modeled Equations.- 9.2.6. Scale Determination.- 9.3. Evaluation of Model Coefficients.- 9.3.1. Dissipation Coefficient b.- 9.3.2. Diffusion Coefficient vc.- 9.3.3. Scale Determination.- 9.3.4. Low-Reynolds-Number Dependence.- 9.3.5. Additional Coefficients Required to Compute Temperature Fluctuations A, s, and s5.- 9.4. Model Verification.- 9.4.1. Axisymmetric Free Jet.- 9.4.2. Free Shear Layer.- 9.4.3. Two-Dimensional Wake.- 9.4.4. Axisymmetric Wake.- 9.4.5. Flat-Plate Boundary Layer.- 9.4.6. Flow over an Abrupt Change in Surface Roughness.- 9.4.7. Temperature Fluctuations in the Plane Turbulent Wake.- 9.4.8. Stability Influence in the Atmospheric Surface Layer.- 9.4.9. Shear Layer Entrainment in a Stratified Fluid.- 9.4.10. Free Convection.- 9.4.11. Planetary Boundary Layer for Neutral Steady State.- 9.5. Local Equilibrium Approximations.- 9.6. Applications.- 9.6.1. Diurnal Variations in the Planetary Boundary Layer.- 9.6.2. Stratified Wake.- 9.6.3. Pollutant Dispersal.- 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.- 11.2.1. Heat-Transfer Techniques.- 11.2.2. Tracer Techniques.- 11.2.3. Electrochemical Techniques.- 11.2.4. Sonic Anemometer.- 11.2.5. Lift and Drag Sensors.- 11.2.6. Corona-Discharge Anemometer.- 11.3. Measurement of Temperature Fluctuations.- 11.3.1. Resistance Thermometer.- 11.3.2. Measurement of Temperature-Velocity Correlations.- 11.4. Measurement of Density and Pressure Fluctuations.- 11.5. Measurement of Concentration Fluctuations.- 11.5.1. Heat-Transfer Techniques.- 11.5.2. Light Scattering.- 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.- 12.2.1. Instrument Response.- 12.2.2. Tower-Based Cup Anemometers.- 12.2.3. Wave Propagation Methods.- 12.2.4. Other Measurement Techniques.- 12.3. Measurements from Aircraft.- 12.3.1. Introduction.- 12.3.2. Simple Techniques of Lower Accuracy.- 12.3.3. Higher-Accuracy Methods.- 12.3.4. Data Processing and Analysis of Errors.- 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.- 13.3.1. General Types of Laser Doppler Systems.- 13.3.2. Typical Wavelengths and Common Uses of Lasers Presently in Use in LD V Systems.- 13.3.3. Conclusions and Recommendations Concerning Laser Doppler Systems.- 13.4. Acoustic Doppler.- 13.4.1. Types.- 13.4.2. Conclusions and Recommendations Concerning Acoustic Doppler Systems.- References.- 14 Monte Carlo Turbulence Simulation.- 14.1. Introduction.- 14.2. Control-System Simulation.- 14.3. Use of Standard System Function Elements.- 14.3.1. Fitting the Empirical Autocorrelation.- 14.3.2. The System Function.- 14.3.3. The State Space System.- 14.3.4. The Discrete State Space System.- 14.3.5. Effect of Digitizing on the Autocorrelation.- 14.3.6. Discrete Autocorrelations.- 14.3.7. Computer Signal Output.- 14.4. Digital Filter Simulation.- 14.4.1. Discretizing the Convolution Integral.- 14.4.2. Theoretical Correlation for the Control-System Simulation.- 14.5. Discrete Fourier Series.- 14.5.1. Discrete Fourier Transform.- 14.5.2. Discrete Fourier Series Using Randomly Chosen Coefficients.- 14.5.3. Relationship of the Fourier Spectrum to the Power Spectrum.- 14.5.4. Discrete Fourier Series Simulation.- 14.5.5. Theoretical Statistical Moments for Discrete Fourier Series Simulation.- 14.6. Non-Gaussian Simulation.- 14.7. Multidimensional Simulation.- 14.8. Nonhomogeneous Atmospheric Boundary-Layer Simulation.- 14.8.1. Definition of the Problem.- 14.8.2. Filter Synthesis.- 14.8.3. Coherence Matching.- 14.8.4. Autospectral Density Matching.- 14.8.5. Phase Angle Matching.- 14.8.6. Longitudinal Gust Statistics.- 14.8.7. Longitudinal Autospectra.- 14.8.8. Standard Deviation and Integral Scale of Turbulence.- 14.8.9. Coherence and Phase.- 14.8.10. Longitudinal Gust Simulation and Application...- 14.8.11. Coherence Determination.- 14.8.12. Autospectra Factorization.- 14.8.13. Phase Angle Determination.- 14.9. Self-Similar Simulation.- 14.9.1. Inverse Fourier Transformation.- 14.9.2 Transformation to Vehicle time Domain.- 114.10. Conclusions.- References.- 15 Wind, Turbulence, and Buildings.- Author Index.