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| Additional Physical Format: | Online version: Durbin, P.A. Statistical theory and modeling for turbulent flows. Chichester ; New York : Wiley, c2001 (OCoLC)606526834 Online version: Durbin, P.A. Statistical theory and modeling for turbulent flows. Chichester ; New York : Wiley, c2001 (OCoLC)607094245 |
|---|---|
| Material Type: | Internet resource |
| Document Type: | Book, Internet Resource |
| All Authors / Contributors: |
Paul A Durbin; B A Pettersson Reif |
| ISBN: | 0471497363 9780471497363 0471497444 9780471497448 |
| OCLC Number: | 44841566 |
| Description: | xiii, 285 p. : ill. ; 25 cm. |
| Contents: | I Fundamentals of Turbulence xv -- 1.1 Turbulence Problem 1 -- 1.2 Closure Modeling 6 -- 1.3 Categories of Turbulent Flow 8 -- 2 Mathematical and Statistical Background 13 -- 2.1 Dimensional Analysis 13 -- 2.1.1 Scales of Turbulence 16 -- 2.2 Statistical Tools 17 -- 2.2.1 Averages and P.D.F.'s 17 -- 2.2.2 Correlations 23 -- 2.3 Cartesian Tensors 30 -- 2.3.1 Isotropic Tensors 32 -- 2.3.2 Tensor Functions of Tensors; Cayley-Hamilton Theorem 33 -- 2.4 Transformation to Curvilinear Coordinates 38 -- 2.4.1 Covariant and Contravariant Tensor Quantities 38 -- 2.4.2 Differentiation of Tensors 40 -- 2.4.3 Physical Components 42 -- 3 Reynolds Averaged Navier-Stokes Equations 47 -- 3.1 Reynolds Averaged Equations 49 -- 3.2 Terms of the Kinetic Energy and Reynolds Stress Budgets 51 -- 3.3 Passive Contaminant Transport 55 -- 4 Parallel and Self-Similar Shear Flows 59 -- 4.1 Plane Channel Flow 59 -- 4.1.1 Logarithmic Layer 62 -- 4.1.2 Roughness 65 -- 4.2 Boundary Layer 66 -- 4.2.1 Entrainment 70 -- 4.3 Free Shear Layers 71 -- 4.3.1 Spreading Rates 76 -- 4.3.2 Remarks on Self-Similar Boundary Layers 77 -- 4.4 Heat and Mass Transfer 78 -- 4.4.1 Parallel Flow and Boundary Layers 78 -- 4.4.2 Dispersion from Elevated Sources 82 -- 5 Vorticity and Vortical Structures 89 -- 5.1 Structure 90 -- 5.1.1 Free Shear Layers 91 -- 5.1.2 Boundary Layers 95 -- 5.1.3 Non-Random Vortices 99 -- 5.2 Vorticity and Dissipation 99 -- 5.2.1 Vortex Stretching and Relative Dispersion 102 -- 5.2.2 Mean-Squared Vorticity Equation 103 -- II Single Point Closure Modeling 107 -- 6 Models with Scalar Variables 109 -- 6.1 Boundary Layer Methods 110 -- 6.1.1 Integral Boundary Layer Methods 111 -- 6.1.2 Mixing Length Model 114 -- 6.2 [Kappa]--[varepsilon] Model 118 -- 6.2.1 Analytical Solutions to the [kappa]--[varepsilon] Model 120 -- 6.2.2 Boundary Conditions and Near-wall Modifications 124 -- 6.2.3 Weak Solution at Edges of Free-Shear Flow; Free-Stream Sensitivity 131 -- 6.3 [Kappa]--[omega] Model 132 -- 6.4 Stagnation Point Anomaly 136 -- 6.5 Question of Transition 138 -- 6.6 Eddy Viscosity Transport Models 140 -- 7 Models with Tensor Variables 147 -- 7.1 Second Moment Transport 147 -- 7.1.1 A Simple Illustration 148 -- 7.1.2 Closing the Reynolds Stress Transport Equation 148 -- 7.1.3 Models for the Slow Part 150 -- 7.1.4 Models for the Rapid Part 153 -- 7.2 Analytic Solutions to SMC Models 158 -- 7.2.1 Homogeneous Shear Flow 160 -- 7.2.2 Curved Shear Flow 162 -- 7.3 Non-homogeneity 166 -- 7.3.1 Turbulent Transport 167 -- 7.3.2 Near-Wall Modeling 168 -- 7.3.3 No-Slip 169 -- 7.3.4 Non-Local Wall Effects 170 -- 7.4 Reynolds Averaged Computation 181 -- 7.4.1 Numerical Issues 181 -- 7.4.2 Examples of Reynolds Averaged Computation 185 -- 8 Advanced Topics 201 -- 8.1 Further Modeling Principles 201 -- 8.1.1 Galilean Invariance and Frame Rotation 202 -- 8.1.2 Realizability 205 -- 8.2 Moving Equilibrium Solutions of SMC 207 -- 8.2.1 Criterion for Steady Mean Flow 208 -- 8.2.2 Solution in Two-Dimensional Mean Flow 209 -- 8.2.3 Bifurcations 212 -- 8.3 Passive Scalar Flux Modeling 215 -- 8.3.1 Scalar Diffusivity Models 215 -- 8.3.2 Tensor Diffusivity Models 216 -- 8.3.3 Scalar Flux Transport 218 -- 8.3.4 Scalar Variance 221 -- 8.4 Active Scalar Flux Modeling: Effects of Buoyancy 222 -- 8.4.1 Second Moment Transport Models 224 -- 8.4.2 Stratified Shear Flow 226 -- III Theory of Homogeneous Turbulence 229 -- 9 Mathematical Representations 231 -- 9.1 Fourier Transforms 232 -- 9.2 3-D Energy Spectrum of Homogeneous Turbulence 233 -- 9.2.1 Spectrum Tensor and Velocity Covariances 234 -- 9.2.2 Modeling the Energy Spectrum 236 -- 10 Navier-Stokes Equations in Spectral Space 247 -- 10.1 Convolution Integralss as Triad Interaction 247 -- 10.2 Evolution of Spectra 249 -- 10.2.1 Small [kappa]-Behavior and Energy Decay 249 -- 10.2.2 Energy Cascade 250 -- 10.2.3 Final Period of Decay 254 -- 11 Rapid Distortion Theory 257 -- 11.1 Irrotational Mean Flow 258 -- 11.1.1 Cauchy Form of the Vorticity Equation 258 -- 11.1.2 Distortion of a Fourier Mode 261 -- 11.1.3 Calculation of Covariances 262 -- 11.2 General Homogeneous Distortions 267 -- 11.2.1 Homogeneous Shear 268 -- 11.2.2 Turbulence Near a Wall 271. |
| Responsibility: | P.A. Durbin, B.A. Petterson [sic] Reif. |
| More information: |
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