Turbulence and Diffusion in the Atmosphere: Lectures in Environmental Sciences

ISBN-13: 9783642644252 / Angielski / Miękka / 2014 / 185 str.

Alfred K. Blackadar

Opis

This book grew out of an introductory course that I was invited to teach on a number of occasions to senior and graduate level students at the University of Kid. I have cherished these opportunities in part because I was never required to conduct examinations or give grades. For the students, however, my good fortune presented special problems that induced my sympathy: in addition to having to contend with a foreign language, they would eventually have to confront an examiner with his own ideas about what they should have learned. Although I always left a copy of my lecture notes with this person, they were too sketchy to be of much use. The present book is an attempt to solve some of these problems. The content is intended to be as broad as possible within the limitations of an introductory one-semester course. It aims at providing an insightful view of present understanding, emphasizing the methods and the history of their development. In particular I have tried to expose the power of intuitive reasoning - the nature of tensor invariants, the usefulness of dimensional analysis, and the relevance of scales of physical quantities in the inference of relationships.I know of no other subject that has benefited more from these important tools, which seem to be widely neglected in the teaching of more fundamental disciplines.

Spis treści

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.

Blurb

This book is written for students of meteorology and other specializations of atmospheric science and students of the environmental sciences who have had no previous experience in the subject. Basic knowledge of hydrodynamics is assumed. The author introduces turbulence theory and modeling related to the structure of the atmospheric boundary layer and includes methods for predicting the impact of industrial activities. The problems and examples have been selected with the intention of broadening the student's understanding of the atmosphere as well as his or her understanding of basic mathematics and the scientific method. In the appendices the author discusses two models that students can run on a PC using the supplementary computer programs on the disks accompanying the book.