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E-grāmata: Turbulence and Dispersion in the Planetary Boundary Layer

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This book offers a comprehensive review of our current understanding of the planetary boundary layer, particularly the turbulent exchanges of momentum, heat and passive scalars between the surface of the Earth and the atmosphere. It presents and discusses the observations and the theory of the turbulent boundary layer, both for homogeneous and more realistic heterogeneous surface conditions, as well as the dispersion of tracers. Lastly it addresses the main problems arising due to turbulence in weather, climate and atmospheric composition numerical models. Written for postgraduate and advanced undergraduate-level students and atmospheric researchers, it is also of interest to anyone wanting to understand the findings and obtain an update on problems that have yet to be solved.
1 Introduction
1(16)
1.1 The Basic Definition of the Planetary Boundary Layer
1(1)
1.2 A Few Words About Turbulence
2(1)
1.3 The Structure and Evolution of the PBL
3(6)
1.3.1 Local Equilibrium
4(2)
1.3.2 Heterogeneities and Unsteadiness
6(2)
1.3.3 The Boundary Layer Depth
8(1)
1.4 The Transport Problem and the Turbulent Dispersion
9(1)
1.5 Observations
10(1)
1.6 Numerical Experiments and Simulations
11(6)
Appendix
11(3)
References
14(3)
2 A Summary of Mathematics and Physics for PBL
17(34)
2.1 Eulerian and Lagrangian Description
17(1)
2.2 The Equations for Velocity and Passive Scalars
18(7)
2.2.1 The Navier-Stokes Equations (NSE) in a Rotating Reference Frame
18(1)
2.2.2 The Hydrostatic Pressure and the PBL Form of NSE
19(1)
2.2.3 The Continuity Equation
20(1)
2.2.4 The Equation for a Passive Scalar
20(1)
2.2.5 A Little Thermodynamics
21(2)
2.2.6 The Equations for the Temperature and for the Potential Temperature
23(1)
2.2.7 The Nondimensional Form of the Equations
24(1)
2.3 Stochastic Variables
25(9)
2.3.1 Probability Density Function and Moments
25(1)
2.3.2 Averaging
26(2)
2.3.3 Covariances and Spectra
28(6)
2.4 Reynolds Averaged Equations
34(7)
2.4.1 The Equations for the First-Order Moments
34(2)
2.4.2 The Equations for the Fluctuations
36(1)
2.4.3 The Equations for the Second-Order Moments of Velocity
36(1)
2.4.4 The Equation for the Temperature Variance
37(1)
2.4.5 The Equations for the Heat Fluxes
38(1)
2.4.6 The Interpretation of the Fluctuation Covariances and the Eddy Diffusion Model
39(2)
2.5 Universal Features of Shear-Dominated Turbulence
41(10)
2.5.1 Velocity Covariances and Spectra
42(4)
2.5.2 The Spectra of the Passive Tracer Variances
46(1)
2.5.3 Some Consequences of Isotropy
46(1)
2.5.4 Final Remarks
47(1)
Exercises
48(1)
References
48(3)
3 The Basic Paradigm: Horizontal Homogeneity Over Flat Terrain
51(66)
3.1 The Governing Equations
51(2)
3.2 Inner and Outer Scaling from the Wind Profile
53(1)
3.3 Similarity, Obukhov Length and Beyond
54(2)
3.4 The Surface Layer in Neutral and Unstable Conditions
56(21)
3.4.1 The Quasi-Neutral Conditions and the Mean Wind Profile
56(4)
3.4.2 Unstable Conditions
60(9)
3.4.3 The Higher-Order Moments of the Velocity Components and of the Temperature Fluctuations
69(8)
3.5 The Outer Region in Neutral Conditions
77(3)
3.5.1 The Mean Velocity in the Ekman Layer
77(1)
3.5.2 Truly-Neutral and Conventionally-Neutral Boundary Layers
78(1)
3.5.3 Resistance Laws
79(1)
3.6 Some Features of the Convective Boundary Layer
80(8)
3.6.1 Second- and Third-Order Moments of Fluctuations
82(1)
3.6.2 The Morning Growth of the CBL
83(4)
3.6.3 The Day-Night Transition and the Residual Layer (RL)
87(1)
3.7 Stable Boundary Layers
88(18)
3.7.1 Local Similarity
93(5)
3.7.2 The Second-Order Moments
98(3)
3.7.3 The Nieuwstadt (1984) Model
101(4)
3.7.4 The Neutral and Stable Boundary Layer Depth
105(1)
3.8 Some Remarks About the Spectra
106(11)
Exercises
111(1)
References
112(5)
4 Horizontal Heterogeneities
117(38)
4.1 Explicit Treatment vs. Parameterization
117(1)
4.1.1 A Criterion for Horizontal Homogeneity
117(1)
4.2 Internal Boundary Layers
118(5)
4.2.1 Roughness Length Changes
119(2)
4.2.2 The Thermal IBL at the Sea-Land Transition
121(2)
4.3 The Boundary Layer Over Hills and Valleys
123(11)
4.3.1 The Linearized Equations
123(1)
4.3.2 The Inner and Outer Layer Concept in the Neutral Flow
124(3)
4.3.3 The Outer Layer and the Stratification Effects
127(3)
4.3.4 A Discussion About the Inner Layer
130(2)
4.3.5 The Turbulent Wake and the Separation
132(2)
4.3.6 Spectra Modifications
134(1)
4.4 Subgrid Effects of the Heterogeneous Surface Features
134(3)
4.4.1 Distributions of Roughness Elements on a Flat Surface
134(1)
4.4.2 The Effective Roughness of Topography
135(2)
4.5 Low Wind, Small Vertical Fluxes
137(3)
4.6 Canopy Flow and the Urban PBL
140(15)
4.6.1 Some Scales and the Drag Due to the Buildings
141(3)
4.6.2 The Flow Above the Canopy
144(1)
4.6.3 The Average Flow in a Volume with an Array of Solid Obstacles: The Urban Canopy Layer
145(3)
4.6.4 Heterogeneous Urban Canopy
148(2)
Exercises
150(1)
References
150(5)
5 Turbulent Dispersion
155(36)
5.1 The Transport Problem for Fluid Parcels
155(2)
5.1.1 Probability Density Functions, Concentration and Well Mixed Condition (WMC)
156(1)
5.2 Absolute Dispersion of Tracer Parcels
157(5)
5.2.1 Steady Homogeneous Conditions: Taylor (1921)
157(3)
5.2.2 Extension to Inhomogeneous Conditions
160(2)
5.3 Two-Parcel Dispersion
162(3)
5.3.1 The Dispersion in the Inertial Subrange
163(1)
5.3.2 The Diffusive Phase
164(1)
5.4 Meandering
165(2)
5.5 Observations of Dispersion
167(2)
5.5.1 Mikkelsen et al. (1987): Horizontal Meandering and Relative Dispersion in the Surface Layer
167(1)
5.5.2 Vertical and Lateral Dispersion in a Laboratory CBL
167(2)
5.6 The Stochastic Approach to the Absolute Dispersion of Tracer Parcels
169(12)
5.6.1 The Link Between the Eulerian and Lagrangian Descriptions
169(1)
5.6.2 The Model with Uncorrected Velocities: N = 3
170(3)
5.6.3 The Model with Uncorrelated Accelerations: N = 6
173(8)
5.7 Dispersion of Inertial Particles
181(10)
5.7.1 The Parameterization of the Integral Time Scales for Particles
184(3)
Exercises
187(1)
References
187(4)
6 Numerical Modeling of Turbulence for PBL Flows
191(22)
6.1 Introduction
191(1)
6.2 Closures for the Reynolds-Averaged Equations
192(9)
6.2.1 The Eddy Diffusion Model for the RANS Equations
192(3)
6.2.2 The Closure for the Second-Order Moment Equations
195(4)
6.2.3 TKE and TPE Based Models
199(1)
6.2.4 The CBL and the Problem of Non-diffusive Behaviour (Counter-Gradient Fluxes)
199(2)
6.3 Large Eddy Simulations
201(6)
6.3.1 Filtered Equations
202(3)
6.3.2 Closure of the Filtered Equations
205(1)
6.3.3 The Transition from RANS to LES
206(1)
6.4 Numerical Simulations of PBL Problems
207(6)
Exercises
209(1)
References
209(4)
Solutions 213(24)
References 237(2)
Index 239
Francesco Tampieri is director of research of CNR in Italy. His main research interest is in environmental science, with special attention to fluid dynamics and atmospheric physics. In particular his activity concerns theoretical, modelling and experimental studies on the atmospheric boundary layer, on turbulence and on transport and dispersion. He published more than 60 papers on international referred journals and is member of the Editorial Board of the ERCOFTAC Bulletin and of Boundary Layer Meteorology. During his career he was visiting researcher at the Dept. of Applied Mathematics and Theoretical Physics, Cambridge (UK) and at the ECMWF (European Centre for Medium Range Weather Forecasts), Reading (UK). He has also been director of the Istituto per lo studio delle Metodologie Geofisiche Ambientali of CNR and of the Istituto di Scienze dell'Atmosfera e dell'Oceano of CNR. He gave courses and lectures in Italian Universities and in International Schools, in particular since 2001 hegives a course on "Planetary boundary layer and dispersion processes' at the Science Faculty, Bologna University.