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Cambridge2010Turbulence in the Atmosphere
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Contents Preface page ix Part I A grammar of turbulence 1 1 Introduction 3 1.1 Turbulence, its community, and our approach 3 1.2 The origins and nature of turbulence 4 1.3 Turbulence and surface fluxes 5 1.4 How do we study turbulence? 10 1.5 The equations of turbulence 11 1.6 Key properties of turbulence 14 1.7 Numerical modeling of turbulent flows 18 1.8 Physical modeling of turbulent flows 20 1.9 The impact of Kolmogorov 20 2 Getting to know turbulence 27 2.1 Average and instantaneous properties contrasted 27 2.2 Averaging 28 2.3 Ergodicity 34 2.4 The convergence of averages 35 2.5 The turbulence spectrum and the eddy velocity scale 38 2.6 Turbulent vorticity 43 2.7 Turbulent pressure 44 2.8 Eddy diffusivity 45 2.9 Reynolds-number similarity 49 2.10 Coherent structures 49 v vi Contents 3 Equations for averaged variables 55 3.1 Introduction 55 3.2 Ensemble-averaged equations 56 3.3 Interpreting the ensemble-averaged equations 59 3.4 Space-averaged equations 65 3.5 Summary 70 4 Turbulent fluxes 75 4.1 Introduction 75 4.2 Temperature flux in a boundary layer 76 4.3 Mass flux in scalar diffusion 78 4.4 Momentum flux in channel flow 83 4.5 The “mixture length” 84 4.6 Summary 85 5 Conservation equations for covariances 89 5.1 Introduction and background 89 5.2 The fluctuation equations 90 5.3 Example: The scalar variance equation 91 5.4 The scalar flux and Reynolds stress budgets 99 5.5 Applications 101 5.6 From the covariance equations to turbulence models 106 6 Large-eddy dynamics, the energy cascade, and large-eddy simulation 115 6.1 Introduction 115 6.2 More on space averaging 116 6.3 A “thought problem”: equilibrium homogeneous turbulence 120 6.4 Application to flows homogeneous in two dimensions 127 6.5 The physical mechanisms of interscale transfer 129 6.6 Large-eddy simulation 130 7 Kolmogorov scaling, its extensions, and two-dimensional turbulence 145 7.1 The inertial subrange 145 7.2 Applications of inertial-range scaling 151 7.3 The dissipative range 153 7.4 Revised Kolmogorov scaling 159 7.5 Two-dimensional turbulence 163 Contents vii Part II Turbulence in the atmospheric boundary layer 173 8 The equations of atmospheric turbulence 175 8.1 Introduction 175 8.2 The governing equations for a dry atmosphere 175 8.3 Accounting for water vapor, liquid water, and phase change 182 8.4 The averaged equations for moist air 185 9 The atmospheric boundary layer 193 9.1 Overview 193 9.2 The surface energy balance 197 9.3 Buoyancy effects 198 9.4 Average vs. instantaneous structure 204 9.5 Quasi-steadiness and local homogeneity 204 9.6 The mean-momentum equations 205 10 The atmospheric surface layer 215 10.1 The “constant-flux” layer 215 10.2 Monin–Obukhov similarity 217 10.3 Asymptotic behavior of M-O similarity 225 10.4 Deviations from M-O similarity 228 11 The convective boundary layer 241 11.1 Introduction 241 11.2 The mixed layer: velocity fields 241 11.3 The mixed layer: conserved-scalar fields 252 11.4 The interfacial layer 259 12 The stable boundary layer 267 12.1 Introduction 267 12.2 The late-afternoon ABL transition over land 273 12.3 The quasi-steady SBL 281 12.4 The evolving SBL 286 12.5 Modeling the equilibrium height of neutral and stable ABLs 288 Part III Statistical representation of turbulence 295 13 Probability densities and distributions 297 13.1 Introduction 297 13.2 Probability statistics of scalar functions of a single variable 298 viii Contents 13.3 Examples of probability densities 302 13.4 The evolution equation for the probability density 308 14 Isotropic tensors 313 14.1 Introduction 313 14.2 Cartesian tensors 313 14.3 Determining the form of isotropic tensors 314 14.4 Implications of isotropy 316 14.5 Local isotropy 319 15 Covariances, autocorrelations, and spectra 331 15.1 Introduction 331 15.2 Scalar functions of a single variable 331 15.3 Scalar functions of space and time 337 15.4 Vector functions of space and time 341 15.5 Joint vector and scalar functions of space and time 350 15.6 Spectra in the plane 351 16 Statistics in turbulence analysis 361 16.1 Evolution equations for spectra 361 16.2 The analysis and interpretation of turbulence signals 369 16.3 Probe-induced flow distortion 378 Index 387 |
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