Atmospheric Turbulence and Air Pollution Modelling: A Course held in The Hague, 21–25 September, 1981

374 Pages·1982·9.534 MB·English

by  J. A. Businger (auth.), F. T. M. Nieuwstadt, H. van Dop (eds.)

ATMOSPHERIC TURBULENCE AND AIR POLLUTION MODELLING
ATMOSPHERIC SCIENCES LIBRARY
Editorial Advisory Board
R. A. Anthes Nationsl Center for Atmospheric Research (U.S.A.)
A. Berger Universite Catholique Louvain (Belgium)
P. J. Crutzen Max-Planck-Institut fur Chemie (F.R.G.)
H.-W. Georgii Universitit Frankfurt (F.R.G.)
P. V. Hobbs University of Washington, Seattle (U.S.A.)
A. Hollingsworth European Centre for Medium Range Weather Forecasts, Reading (England)
G. E. Hunt University College London (England)
K. Ya. Kondratyev Main Geophysical Observatory, Moscow (U.S.S.R.)
T. N. Krishnamurti The Florida State University, Tallahassee (U.S.A.)
J. Latham University of Manchester Institute of Science and Technology (England)
D. K. Lilly National Center for Atmospheric Research (U.S.A.)
J.London University of Colorado, Boulder (U.S.A.)
A. H. Dort National Oceanic and Atmospheric Administration (U.S.A.)
I. Drlanski National Oceanic and A tmospheric Administration (U.S.A.)
H. R. Pruppacher Johannes Gutenberg Universitit, Mainz (F.R.G.)
N. J. Rosenberg University of Nebraska, Lincoln (U.S.A.)
C. J. E. Schuurmans Rijksuniversiteit Utrecht (The Netherlands)
H. Tennekes Koninklijk Nederlands Meteorologisch Instituut, de Bilt (The Netherlands)
S.A. Twomey The University of Arizona (U.S.A.)
T. M. L. Wigley University of East Anglia (England)
J. C. Wijngaard National Center for Atmospheric Research (U.S.A.)
V. E. Zuev Institute for Atmospheric Optics, Tomsk (U.S.S.R.)
Atmospheric Turbulence
and
Air Pollution Modelling
A Course held in The Hague,
21-25 September, 1981
edited by
F. T. M. NIEUWSTADT
and
H. VAN DOP
Royal Netherlands Meteorological Institute, de Bilt
D. Reidel Publishing Company
A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP "
Dordrecht I Boston I Lancaster
library of Congress Cataloging in Publication Data
Main entry under title:
Atmospheric turbulence and air pollution modelling.
(Atmospheric sciences library)
Bibliography: p.
Includes indexes.
1. Atmospheric turbulence-Mathematical models-Addresses, essays,
lectures. 2. Boundary layer (Meteorology)-Mathematical models-Addresses,
essays, lectures. 3. Atmospheric diffusion-Mathematical models-Addresses,
essays, lectures. 4. Air-Pollution-Meteorological aspects-Mathematical
models-Addresses, essays, lectures. I. Nieuwstadt, F. T. M. (Frans T. M.),
1946- . II. Dop, H. van (Han van), 1944- . III. Series.
QC880.4.T8A85 551.5'17 82-3758
ISBN-13: 978-90-277-1807-5 e-ISBN-13: 978-94-010-9112-1
DOl: 10.1007/978-94-010-9112-1 AACR2
Published by D. Reidel Publishing Company
P.O. Box 17, 3300 AA Dordrecht, Holland
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
190 Old Derby Street, Hingham, MA 02043, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, Holland
Reprinted with corrections.
All Rights Reserved
© 1982,1984 by D. Reidel Publishing Company, Dordrecht, Holland
No part of the material protected by this copyright notice may be reproduced or utilized
in any form or by any means, electronic or mechanical, including photocopying,
recording or by any information storage and retrieval system,
without written permission from the copyright owner
CONTENTS
PREFACE xi
SYMBOLS AND NOTATION xv
ACKNOWLEDGEMENTS xxi
1. EQUATIONS AND CONCEPTS - J.A. BUSINGER 1
1.1. INTRODUCTION 1
1.2. GOVERNING EQUATIONS 2
The Equations of Continuity 2
The Equation of State 3
Potential Temperature 4
The Equations of Motion 5
Conservation of Enthalpy 6
Conservation of Transferable Scalar Quantities 8
1.3. EQUATIONS OF THE MEAN FLOW 8
1.4. DISCUSSION OF THE BOUSSINESQ APPROXIMATIONS
AND THE CONSERVATION OF ENTHALPY EQUATION 13
1.5. SUMMARY OF THE BOUSSINESQ SET OF EQUATICNS 15
1.6. THE CLOSURE PROBLEM, FIRST-ORDER CLOSURE 16
1 .7. SECOND-ORDER VARIANCE AND COVARIANCE
EQUATIONS 19
1.8. THE TURBULENT KINETIC ENERGY BALANCE;
TEMPERATURE VARIANCE BALANCE 22
APPENDIX A. REQUIREMENTS FOR A DIVERGENCE-FREE
VELOCITY FIELD 26
vi CONTENTS
APPENDIX B. THE MAGNITUDE OF PRESSURE FLUCTUATIONS 30
APPENDIX C. THE ENTHALPY EQUATION FOR mIST AIR 30
APPENDIX D. THE EKMAN SPIRAL 33
2. SIMILARITY RELATIONS, SCALING LAWS AND SPECTRAL
DYNAMICS - H. TENNEKES 37
2.1. INTRODUCTION 37
2.2. SIMILARITY 39
ROSSBY~NUMBER
The Surface Layer 42
The Process of Matching 43
The Constant-Stress Layer 46
The Von Karman Constant 47
2.3. DIABATIC EXTENSION OF ROSSBY-NUMBER SIMILARITY 47
2.4. MONIN-OBUKHOV SIMILARITY IN THE SURFACE LAYER 50
2.5. SCALING OF TURBULENCE QUANTITIES IN THE
SURFACE LAYER 53
2.6. SCALING OF TURBULENCE OUTSIDE THE SURFACE LAYER 56
2.7. CORRELATION FUNCTIONS AND SPECTRA 60
2.8. INERTIAL SUBRANGES 64
3. BOUNDARY-LAYER MODELING - J.C. WYNGAARD 69
3.1. THE CALCULATION OF BOUNDARY-LAYER STRUCTURE 69
3.2. ENSEMBLE-AVERAGE MODELS 72
First-Order or Eddy-Diffusivity (K) Closure 72
Second-Order Closure 77
3.3. VOLUME-AVERAGE MODELS 97
Large-Eddy Models 98
Other Volume-Average Models 105
CONTENTS vii
4. OBSERVED CHARACTERISTICS OF THE ATMOSPHERIC
BOUNDARY LAYER - S.J. CAUGHEY 107
4.1. INTRODUCTION 107
4.2. CONVECTIVE BOUNDARY LAYER 110
Boundary-Layer Development 110
Spectra of the Velocity Components 114
SpectI'1B of Temperature 119
Cospectra of Heat Flux and Stress 121
Entrainment 127
Variances, Dissipation Rates and Structure
Parameters 131
Turbulent Kinetic Energy Budget 137
4.3. STABLE BOUNDARY LAYER 139
General Characteristics of the SBL 139
Waves and Turbulence 143
Turbulence Spectra in the Stable Surface Layer 148
Turbulence Behavior through the SBL Depth 150
Depth of the SBL 156
4.4. CONCLUDING REMARKS 156
5. DIFFUSION IN THE CONVECTIVE BOUNDARY LAYER - R.G. LAMB 159
5.1. INTRODUCTION 159
5.2. FORMULATION OF A LAGRANGIAN DIFFUSION HODEL 166
5.3. NUMERICAL SIMULATIONS OF NON-BUOYANT MATERIAL
DIFFUSION AND COMPARISONS WITH OBSERVATIONS 175
Results 176
Comparison of the Model Results with
Observations 183
5.4. THE STRUCTURE OF TURBULENCE IN THE CONVECTIVE
BOUNDARY LAYER 191
5.5. FORMULAS FOR APPLICATION 197
5.6. DISPERSION OF BUOYANT EMISSIONS IN A CONVECTIVE
BOUNDARY LAYER 206
viii CONTENTS
6. DIFFUSION IN THE STABLE BOUNDARY LAYER - J.C.R. HUNT 231
6.1. INTRODUCTION 231
6.2. BASIC IDEAS ABOUT MOLECULAR AND FLUID ELEMENT
MOTION AND PROBABILITY DISTRIBUTIONS 232
6.3. TURBULENT DIFFUSION IN IDEALIZED FLOWS 236
Marked Fluid Elements in Unstratified
Turbulence Away from Boundaries 236
Unidirectional shear flow 238
Straining flow 243
Flux gradient relations - when are they
likely to go wrong? 244
Diffusion in Stably-Stratified Turbulence 247
6.4. TURBULENCE DIFFUSION IN THE STABLY-STRATIFIED
ATMOSPHERIC BOUNDARY LAYER 253
Some Properties of the Stably Stratified
Atmospheric Boundary Layer 253
Mean velocity profile 254
Mean temperature profile 254
Vertical turbulence and heat flux 254
Horizontal components of turbulence 255
Turbulence at heights of 50 to 300 m 256
Diffusivities and temperature fluctuations 256
Elevated Source above the Surface Layer 258
Sources in the Surface Layer 260
<
Elevated sources in the surface layer (t TL) 260
>
Elevated sources in the surface layer (t TL) 262
Comparison of vertical diffusion from
ground-level and elevated sources 269
6.5. CONCLUDING REMARKS 271
Concentration Distributions 271
Complex Atmospheric Conditions 272
Topography 272
7. APPLICATIONS IN AIR POLLUTION MODELING - S.R. HANNA 275
7.1. INTRODUCTION 275
CONTENTS ix
7.2. STATISTICAL MODELS OF DIFFUSION 277
Taylor's Statistical Theory 277
Monte Carlo Diffusion Models 280
Model description 280
Turbulent energy and Lagrangian time
scales in the unstable PBL 282
Turbulent energy and Lagrangian time
scales in the stable PBL 283
Turbulent energy and Lagrangian time
scales in the neutral PBL 284
Results of application of the Monte Carlo
model 285
The Langevin Horizontal Diffusion Model 286
7.3. IMPROVEMENTS TO THE GAUSSIAN MODEL 288
Wind Speed in the Gaussian Plume Model 288
Plume Rise Calculations 289
Estimation of Gy and Gz using Ge and Ge 290
Determination of Stability Class 291
Revisions of Pasquill-Gifford (P-G) Sigma Curves 292
7.4. K-DIFFUSION MODELS 295
Analytical Solutions to the Diffusion Equation 295
Numerical Solutions to the Diffusion Equation 297
7.5. PROGRESS IN THE SIMILARITY THEORY OF DIFFUSION 300
7.6. RECENT SPECIAL APPLICATIONS 303
Skewness of'Vertical Turbulent Velocity 304
Natural Variability of Pollutant Concentrations 306
Representativeness of Wind-Speed Observations 307
8. REPORT FROM THE PANEL DISCUSSION - L. KRISTENSEN 311
9. REFERENCES 323
AUTHORS INDEX 343
SUBJECT INDEX 350
PREFACE
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