Atmospheric Turbulence and Air Pollution Modelling

The study of turbulence in the atmosphere has seen considerable progress in the last decade. To put it briefly: boundary-layer meteorology, the branch of atmospheric science that concentrates on turbulence in the lower atmosphere, has moved from the surface layer into the boundary layer itself. The progress has been made on all fronts: theoretical, numerical and observational. On the other hand, air pollution modeling has not seen such a rapid evolution. It has not benefited as much as it should have from the increasing knowledge in the field of atmospheric turbulence. Air pollution modeling is still in many ways based on observations and theories of the surface layer only. This book aims to bring the reader up to date on recent advances in boundary-layer meteorology and to pave the path for applications in air pollution dispersion problems. The text originates from the material presented during a short course on Atmospheric Turbulence and Air Pollution Modeling held in The Hague during September 1981. This course was sponsored and organized by the Royal Netherlands Meteorological Institute, xi xii PREFACE to which both editors are affiliated. The Netherlands Government Ministry of Health and Environmental Protection and the Council of Europe also gave support.

Contenu

1. Equations and Concepts.- 1.1. Introduction.- 1.2. Governing Equations.- The Equations of Continuity.- The Equation of State.- Potential Temperature.- The Equations of Motion.- Conservation of Enthalpy.- Conservation of Transferable Scalar Quantities.- 1.3. Equations of the Mean Flow.- 1.4. Discussion of the Boussinesq Approximations and the Conservation of Enthalpy Equation.- 1.5. Summary of the Boussinesq Set of Equations.- 1.6. The Closure Problem, First-Order Closure.- 1.7. Second-Order Variance and Covariance Equations.- 1.8. The Turbulent Kinetic Energy Balance; Temperature Variance Balance.- Appendix A. Requirements for a Divergence-Free Velocity Field.- Appendix B. The magnitude of Pressure Fluctuations.- Appendix C. The Enthalpy Equation for Moist Air.- Appendix D. The Ekman Spiral.- 2. Similarity Relations, Scaling Laws and Spectral Dynamics.- 2.1. Introduction.- 2.2. Rossby-Number Similarity.- The Surface Layer.- The Process of Matching.- The Constant-Stress Layer.- The Von Karman Constant.- 2.3. Diabatic Extension of Rossby-Number Similarity.- 2.4. Monin-Obukhov Similarity in the Surface Layer.- 2.5. Scaling of Turbulence Quantities in the Surface Layer.- 2.6. Scaling of Turbulence Outside the Surface Layer.- 2.7. Correlation Functions and Spectra.- 2.8. Inertial Subranges.- 3. Boundary-Layer Modeling.- 3.1. The calculation of boundary-layer structure.- 3.2. Ensemble-average models.- First-Order or Eddy-Diffusivity (K) Closure.- Second-Order Closure.- 3.3. Volume-Average Models.- Large-Eddy Models.- Other Volume-Average Models.- 4. Observed Characteristics of the Atmospheric Boundary Layer.- 4.1. Introduction.- 4.2. Convective Boundary Layer.- Boundary-Layer Development.- Spectra of the Velocity Components.- Spectrum of Temperature.- Cospectra of Heat Flux and Stress.- Entrainment.- Variances, Dissipation Rates and Structure Parameters.- Turbulent Kinetic Energy Budget.- 4.3. Stable Boundary Layer.- General Characteristics of the SBL.- Waves and Turbulence.- Turbulence Spectra in the Stable Surface Layer.- Turbulence Behavior through the SBL Depth.- Depth of the SBL.- 4.4. Concluding Remarks.- 5. Diffusion in the Convective Boundary Layer.- 5.1. Introduction.- 5.2. Formulation of a Lagrangian Diffusion Model.- 5.3. Numerical Simulations of Non-Buoyant Material Diffusion and Comparisons With Observations.- Results.- Comparison of the Model Results with.- Observations.- 5.4. The Structure of Turbulence in the Convective Boundary Layer.- 5.5. Formulas for Application.- 5.6. Dispersion of Buoyant Emissions in a Convective Boundary Layer.- 6. Diffusion in the Stable Boundary Layer.- 6.1. Introduction.- 6.2. Basic Ideas about Molecular and Fluid Element Motion and Probability Distributions.- 6.3. Turbulent Diffusion in Idealized Flows.- Marked Fluid Elements in Unstratified Turbulence Away from Boundaries.- Unidirectional shear flow.- Straining flow.- Flux gradient relations - when are they likely to go wrong?.- Diffusion in Stably-Stratified Turbulence.- 6.4. Turbulence Diffusion in the Stably-Stratified Atmospheric Boundary Layer.- Some Properties of the Stably Stratified.- Atmospheric Boundary Layer.- Mean velocity profile.- Mean temperature profile.- Vertical turbulence and heat flux.- Horizontal components of turbulence.- Turbulence at heights of 50 to 300 m.- Diffusivities and temperature fluctuations.- Elevated Source above the Surface Layer.- Sources in the Surface Layer.- Elevated sources in the surface layer (t TL).- Comparison of vertical diffusion from ground-level and elevated sources.- 6.5. Concluding Remarks.- Concentration Distributions.- Complex Atmospheric Conditions.- Topography.- 7. Applications in Air Pollution Modeling.- 7.1. Introduction.- 7.2. Statistical Models of Diffusion.- Taylor's Statistical Theory.- Monte Carlo Diffusion Models.- Model description.- Turbulent energy and Lagrangian time scales in the unstable PBL.- Turbulent energy and Lagrangian time scales in the stable PBL.- Turbulent energy and Lagrangian time scales in the neutral PBL.- Results of application of the Monte Carlo model.- The Langevin Horizontal Diffusion Model.- 7.3. Improvements to the Gaussian Model.- Wind Speed in the Gaussian Plume Model.- Plume Rise Calculations.- Estimation of ?y and ?z using ?? and ?e.- Determination of Stability Class.- Revisions of Pasquill-Gifford (P-G) Sigma Curves.- 7.4. K-Diffusion Models.- Analytical Solutions to the Diffusion Equation.- Numerical Solutions to the Diffusion Equation.- 7.5. Progress in the Similarity Theory of Diffusion.- 7.6. Recent Special Applications.- Skewness of Vertical Turbulent Velocity.- Natural Variability of Pollutant Concentrations.- Representativeness of Wind-Speed Observations.- 8. Report from the Panel Discussion.- 9. References.- Authors Index.