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1 | (16) |
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1.1 The Basic Definition of the Planetary Boundary Layer |
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1 | (1) |
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1.2 A Few Words About Turbulence |
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2 | (1) |
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1.3 The Structure and Evolution of the PBL |
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3 | (6) |
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4 | (2) |
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1.3.2 Heterogeneities and Unsteadiness |
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6 | (2) |
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1.3.3 The Boundary Layer Depth |
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8 | (1) |
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1.4 The Transport Problem and the Turbulent Dispersion |
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9 | (1) |
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10 | (1) |
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1.6 Numerical Experiments and Simulations |
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11 | (6) |
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11 | (3) |
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14 | (3) |
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2 A Summary of Mathematics and Physics for PBL |
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17 | (34) |
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2.1 Eulerian and Lagrangian Description |
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17 | (1) |
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2.2 The Equations for Velocity and Passive Scalars |
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18 | (7) |
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2.2.1 The Navier-Stokes Equations (NSE) in a Rotating Reference Frame |
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18 | (1) |
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2.2.2 The Hydrostatic Pressure and the PBL Form of NSE |
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19 | (1) |
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2.2.3 The Continuity Equation |
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20 | (1) |
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2.2.4 The Equation for a Passive Scalar |
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20 | (1) |
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2.2.5 A Little Thermodynamics |
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21 | (2) |
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2.2.6 The Equations for the Temperature and for the Potential Temperature |
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23 | (1) |
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2.2.7 The Nondimensional Form of the Equations |
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24 | (1) |
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25 | (9) |
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2.3.1 Probability Density Function and Moments |
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25 | (1) |
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26 | (2) |
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2.3.3 Covariances and Spectra |
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28 | (6) |
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2.4 Reynolds Averaged Equations |
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34 | (7) |
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2.4.1 The Equations for the First-Order Moments |
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34 | (2) |
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2.4.2 The Equations for the Fluctuations |
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36 | (1) |
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2.4.3 The Equations for the Second-Order Moments of Velocity |
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36 | (1) |
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2.4.4 The Equation for the Temperature Variance |
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37 | (1) |
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2.4.5 The Equations for the Heat Fluxes |
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38 | (1) |
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2.4.6 The Interpretation of the Fluctuation Covariances and the Eddy Diffusion Model |
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39 | (2) |
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2.5 Universal Features of Shear-Dominated Turbulence |
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41 | (10) |
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2.5.1 Velocity Covariances and Spectra |
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42 | (4) |
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2.5.2 The Spectra of the Passive Tracer Variances |
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46 | (1) |
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2.5.3 Some Consequences of Isotropy |
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46 | (1) |
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47 | (1) |
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48 | (1) |
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48 | (3) |
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3 The Basic Paradigm: Horizontal Homogeneity Over Flat Terrain |
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51 | (66) |
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3.1 The Governing Equations |
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51 | (2) |
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3.2 Inner and Outer Scaling from the Wind Profile |
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53 | (1) |
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3.3 Similarity, Obukhov Length and Beyond |
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54 | (2) |
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3.4 The Surface Layer in Neutral and Unstable Conditions |
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56 | (21) |
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3.4.1 The Quasi-Neutral Conditions and the Mean Wind Profile |
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56 | (4) |
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3.4.2 Unstable Conditions |
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60 | (9) |
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3.4.3 The Higher-Order Moments of the Velocity Components and of the Temperature Fluctuations |
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69 | (8) |
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3.5 The Outer Region in Neutral Conditions |
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77 | (3) |
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3.5.1 The Mean Velocity in the Ekman Layer |
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77 | (1) |
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3.5.2 Truly-Neutral and Conventionally-Neutral Boundary Layers |
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78 | (1) |
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79 | (1) |
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3.6 Some Features of the Convective Boundary Layer |
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80 | (8) |
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3.6.1 Second- and Third-Order Moments of Fluctuations |
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82 | (1) |
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3.6.2 The Morning Growth of the CBL |
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83 | (4) |
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3.6.3 The Day-Night Transition and the Residual Layer (RL) |
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87 | (1) |
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3.7 Stable Boundary Layers |
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88 | (18) |
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93 | (5) |
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3.7.2 The Second-Order Moments |
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98 | (3) |
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3.7.3 The Nieuwstadt (1984) Model |
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101 | (4) |
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3.7.4 The Neutral and Stable Boundary Layer Depth |
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105 | (1) |
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3.8 Some Remarks About the Spectra |
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106 | (11) |
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111 | (1) |
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112 | (5) |
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4 Horizontal Heterogeneities |
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117 | (38) |
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4.1 Explicit Treatment vs. Parameterization |
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117 | (1) |
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4.1.1 A Criterion for Horizontal Homogeneity |
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117 | (1) |
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4.2 Internal Boundary Layers |
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118 | (5) |
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4.2.1 Roughness Length Changes |
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119 | (2) |
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4.2.2 The Thermal IBL at the Sea-Land Transition |
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121 | (2) |
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4.3 The Boundary Layer Over Hills and Valleys |
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123 | (11) |
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4.3.1 The Linearized Equations |
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123 | (1) |
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4.3.2 The Inner and Outer Layer Concept in the Neutral Flow |
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124 | (3) |
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4.3.3 The Outer Layer and the Stratification Effects |
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127 | (3) |
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4.3.4 A Discussion About the Inner Layer |
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130 | (2) |
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4.3.5 The Turbulent Wake and the Separation |
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132 | (2) |
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4.3.6 Spectra Modifications |
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134 | (1) |
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4.4 Subgrid Effects of the Heterogeneous Surface Features |
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134 | (3) |
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4.4.1 Distributions of Roughness Elements on a Flat Surface |
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134 | (1) |
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4.4.2 The Effective Roughness of Topography |
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135 | (2) |
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4.5 Low Wind, Small Vertical Fluxes |
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137 | (3) |
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4.6 Canopy Flow and the Urban PBL |
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140 | (15) |
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4.6.1 Some Scales and the Drag Due to the Buildings |
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141 | (3) |
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4.6.2 The Flow Above the Canopy |
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144 | (1) |
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4.6.3 The Average Flow in a Volume with an Array of Solid Obstacles: The Urban Canopy Layer |
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145 | (3) |
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4.6.4 Heterogeneous Urban Canopy |
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148 | (2) |
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150 | (1) |
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150 | (5) |
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155 | (36) |
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5.1 The Transport Problem for Fluid Parcels |
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155 | (2) |
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5.1.1 Probability Density Functions, Concentration and Well Mixed Condition (WMC) |
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156 | (1) |
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5.2 Absolute Dispersion of Tracer Parcels |
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157 | (5) |
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5.2.1 Steady Homogeneous Conditions: Taylor (1921) |
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157 | (3) |
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5.2.2 Extension to Inhomogeneous Conditions |
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160 | (2) |
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5.3 Two-Parcel Dispersion |
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162 | (3) |
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5.3.1 The Dispersion in the Inertial Subrange |
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163 | (1) |
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5.3.2 The Diffusive Phase |
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164 | (1) |
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165 | (2) |
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5.5 Observations of Dispersion |
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167 | (2) |
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5.5.1 Mikkelsen et al. (1987): Horizontal Meandering and Relative Dispersion in the Surface Layer |
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167 | (1) |
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5.5.2 Vertical and Lateral Dispersion in a Laboratory CBL |
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167 | (2) |
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5.6 The Stochastic Approach to the Absolute Dispersion of Tracer Parcels |
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169 | (12) |
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5.6.1 The Link Between the Eulerian and Lagrangian Descriptions |
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169 | (1) |
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5.6.2 The Model with Uncorrected Velocities: N = 3 |
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170 | (3) |
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5.6.3 The Model with Uncorrelated Accelerations: N = 6 |
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173 | (8) |
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5.7 Dispersion of Inertial Particles |
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181 | (10) |
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5.7.1 The Parameterization of the Integral Time Scales for Particles |
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184 | (3) |
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187 | (1) |
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187 | (4) |
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6 Numerical Modeling of Turbulence for PBL Flows |
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191 | (22) |
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191 | (1) |
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6.2 Closures for the Reynolds-Averaged Equations |
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192 | (9) |
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6.2.1 The Eddy Diffusion Model for the RANS Equations |
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192 | (3) |
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6.2.2 The Closure for the Second-Order Moment Equations |
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195 | (4) |
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6.2.3 TKE and TPE Based Models |
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199 | (1) |
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6.2.4 The CBL and the Problem of Non-diffusive Behaviour (Counter-Gradient Fluxes) |
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199 | (2) |
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6.3 Large Eddy Simulations |
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201 | (6) |
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202 | (3) |
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6.3.2 Closure of the Filtered Equations |
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205 | (1) |
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6.3.3 The Transition from RANS to LES |
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206 | (1) |
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6.4 Numerical Simulations of PBL Problems |
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207 | (6) |
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209 | (1) |
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209 | (4) |
Solutions |
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213 | (24) |
References |
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237 | (2) |
Index |
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239 | |