Turbulence and Diffusion in the Atmosphere

1 The Nature of Turbulence.- 1.1 Two-Dimensional Eddies in the Atmosphere.- 1.2 The Reynolds Number and Its Significance.- 1.3 The Reynolds Approach to the Equations of a Turbulent Fluid.- 1.4 Averaging the Equation of Continuity.- 1.5 Fluxes and the General Conservation Equation.- 1.6 The Closure Problem.- 1.7 First-Order Closure — Exchange Theory.- 1.8 Problems.- 2 The Navier—Stokes Equations.- 2.1 The Nature of Stress.- 2.2 Invariants of Fluid Motions.- 2.3 The Navier—Stokes Equations.- 2.4 Reynolds Number Similarity.- 2.5 Averaging the Navier—Stokes Equations.- 2.6 Problems.- 3 The Neutral Surface Boundary Layer.- 3.1 Overview of the Atmospheric Boundary Layer.- 3.2 Wind Distribution in the Neutral Surface Layer.- 3.3 Mean Flow in the Vicinity of the Surface.- 3.4 Miscellaneous Topics.- 3.5 Distribution of Passive Mean Properties.- 3.6 Problems.- 4 The Energy Equations of Turbulence.- 4.1 Energy of the Instantaneous State of a Fluid.- 4.2 Work Done on the Boundary.- 4.3 Heat.- 4.4 The Energy Equations and Energy Transformations.- 4.5 The Second Law of Thermodynamics.- 4.6 The Boussinesq Approximation.- 4.7 Open Systems.- 4.8 Energy Transformations in a Turbulent System.- 4.9 Problems.- 5 Diabatic Surface Boundary Layers.- 5.1 Heat Flux in the Surface Layer.- 5.2 The Richardson Number and the Criterion of Turbulence.- 5.3 Wind Profile Similarity.- 5.4 Profiles of Mean Temperature.- 5.5 Some Useful Relationships.- 5.6 Problems.- 6 Homogeneous Stationary Planetary Layers.- 6.1 The Ekman Spiral.- 6.2 A Two-Layer Model of the PBL.- 6.3 Universal Wind Hodograph and the Resistance Laws.- 6.4 The Mixed Layer of the Ocean.- 6.5 Problems.- 7 Unconstrained Boundary Layers.- 7.1 Flow downwind of a Change of Roughness.- 7.2 Non-stationary Boundary Layers.- 7.3 The Surface Heat Balance Equation.- 7.4 Daytime Conditions in the PBL.- 7.5 The Planetary Boundary Layer at Night.- 7.6 Model Simulation of the PBL.- 7.7 Problems.- 8 Statistical Representation of Turbulence I.- 8.1 Scaling Statistical Variables in the PBL.- 8.2 Vertical Distributions of the Variances.- 8.3 Problems.- 9 Statistical Representation of Turbulence II.- 9.1 Spectrum and Cross Spectrum of Turbulence.- 9.2 Spatial Representation of Turbulence.- 9.3 The Equilibrium Theory of Turbulence.- 9.4 The Inertial Subrange.- 9.5 Surface Layer Velocity Component Spectra.- 9.6 Mixed Layer Velocity Component Spectra.- 9.7 Spectra of Scalar Quantities Including Temperature.- 9.8 Cospectra and Quadrature Spectra.- 9.9 Problems.- 10 Turbulent Diffusion from Discrete Sources.- 10.1 Morphology of Smoke Plumes.- 10.2 Continuity Principles.- 10.3 Fickian Diffusion.- 10.4 The Gaussian Distribution Function.- 10.5 Taylor’s Diffusion Equation.- 10.6 Spectral Representation of Taylor’s Equation.- 10.7 Stability Parameters.- 10.8 Gaussian Plume Models.- 10.9 Estimations Based on Taylor’s Equation.- 10.10 Monte Carlo Models.- 10.11 Instantaneous Point Sources.- 10.12 Problems.- Appendix A. Derivation of the Tubulent Energy Equations.- A.1 Equations for the Instantaneous Energy.- A.2 The Equation of Mean Internal Energy.- A.3 The Mean Total Kinetic Energy Equation.- A.4 The Equation for the Energy of Mean Motion.- A.5 The Turbulent Kinetic Energy Equation.- Appendix B. Dimensional Analysis and Scaling Principles.- B.1 Checking Equations for Errors.- B.2 Inferring an Unknown Relationship.- B.3 Turkey Eggs, Anybody?.- B.4 Problems.- Appendix C. Matching Theory and the PBL Resistance Laws.- Appendix D. Description of the Planetary Boundary Layer Simulation Model.- D.1 Architecture of the Model.- D.2 Surface Boundary Condition.- D.3 The Free Convection Closure Scheme.- D.4 Treatment of Cloud Formation.- D.5 Treatment of Infrared Radiation.- Appendix E. A Monte Carlo Smoke Plume Simulation.- References.