Statistical Theory and Modeling for Turbulent Flows, 2nd EditionISBN: 9780470689318
372 pages
October 2010

In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation.

Provides an excellent foundation to the fundamental theoretical concepts in turbulence.
 Features new and heavily revised material, including an entire new section on eddy resolving simulation.
 Includes new material on modeling laminar to turbulent transition.
 Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences.
 Accompanied by a website housing solutions to the problems within the book.
Preface to second edition.
Preface to first edition.
Motivation.
Epitome.
Acknowledgements.
Part I FUNDAMENTALS OF TURBULENCE.
1 Introduction.
1.1 The turbulence problem.
1.2 Closure modeling.
1.3 Categories of turbulent flow.
Exercises.
2 Mathematical and statistical background.
2.1 Dimensional analysis.
2.1.1 Scales of turbulence.
2.2 Statistical tools.
2.2.1 Averages and probability density functions.
2.2.2 Correlations.
2.3 Cartesian tensors.
2.3.1 Isotropic tensors.
2.3.2 Tensor functions of tensors; Cayley–Hamilton theorem.
Exercises.
3 Reynolds averaged Navier–Stokes equations.
3.1 Background to the equations.
3.2 Reynolds averaged equations.
3.3 Terms of kinetic energy and Reynolds stress budgets.
3.4 Passive contaminant transport.
Exercises.
4 Parallel and selfsimilar shear flows.
4.1 Plane channel flow.
4.1.1 Logarithmic layer.
4.1.2 Roughness.
4.2 Boundary layer.
4.2.1 Entrainment.
4.3 Freeshear layers.
4.3.1 Spreading rates.
4.3.2 Remarks on selfsimilar boundary layers.
4.4 Heat and mass transfer.
4.4.1 Parallel flow and boundary layers.
4.4.2 Dispersion from elevated sources.
Exercises.
5 Vorticity and vortical structures.
5.1 Structures.
5.1.1 Freeshear layers.
5.1.2 Boundary layers.
5.1.3 Nonrandom vortices.
5.2 Vorticity and dissipation.
5.2.1 Vortex stretching and relative dispersion.
5.2.2 Meansquared vorticity equation.
Exercises.
Part II SINGLEPOINT CLOSURE MODELING.
6 Models with scalar variables.
6.1 Boundarylayer methods.
6.1.1 Integral boundarylayer methods.
6.1.2 Mixing length model.
6.2 The k –ε model.
6.2.1 Analytical solutions to the k –ε model.
6.2.2 Boundary conditions and nearwall modifications.
6.2.3 Weak solution at edges of freeshear flow; freestream sensitivity.
6.3 The k –ω model.
6.4 Stagnationpoint anomaly.
6.5 The question of transition.
6.5.1 Reliance on the turbulence model.
6.5.2 Intermittency equation.
6.5.3 Laminar fluctuations.
6.6 Eddy viscosity transport models.
Exercises.
7 Models with tensor variables.
7.1 Secondmoment transport.
7.1.1 A simple illustration.
7.1.2 Closing the Reynolds stress transport equation.
7.1.3 Models for the slow part.
7.1.4 Models for the rapid part.
7.2 Analytic solutions to SMC models.
7.2.1 Homogeneous shear flow.
7.2.2 Curved shear flow.
7.2.3 Algebraic stress approximation and nonlinear eddy viscosity.
7.3 Nonhomogeneity.
7.3.1 Turbulent transport.
7.3.2 Nearwall modeling.
7.3.3 Noslip condition.
7.3.4 Nonlocal wall effects.
7.4 Reynolds averaged computation.
7.4.1 Numerical issues.
7.4.2 Examples of Reynolds averaged computation.
Exercises.
8 Advanced topics.
8.1 Further modeling principles.
8.1.1 Galilean invariance and frame rotation.
8.1.2 Realizability.
8.2 Secondmoment closure and Langevin equations.
8.3 Moving equilibrium solutions of SMC.
8.3.1 Criterion for steady mean flow.
8.3.2 Solution in twodimensional mean flow.
8.3.3 Bifurcations.
8.4 Passive scalar flux modeling.
8.4.1 Scalar diffusivity models.
8.4.2 Tensor diffusivity models.
8.4.3 Scalar flux transport.
8.4.4 Scalar variance.
8.5 Active scalar flux modeling: effects of buoyancy.
8.5.1 Secondmoment transport models.
8.5.2 Stratified shear flow.
Exercises.
Part III THEORY OF HOMOGENEOUS TURBULENCE.
9 Mathematical representations.
9.1 Fourier transforms.
9.2 Threedimensional energy spectrum of homogeneous turbulence.
9.2.1 Spectrum tensor and velocity covariances.
9.2.2 Modeling the energy spectrum.
Exercises.
10 Navier–Stokes equations in spectral space.
10.1 Convolution integrals as triad interaction.
10.2 Evolution of spectra.
10.2.1 Smallk behavior and energy decay.
10.2.2 Energy cascade.
10.2.3 Final period of decay.
Exercises.
11 Rapid distortion theory.
11.1 Irrotational mean flow.
11.1.1 Cauchy form of vorticity equation.
11.1.2 Distortion of a Fourier mode.
11.1.3 Calculation of covariances.
11.2 General homogeneous distortions.
11.2.1 Homogeneous shear.
11.2.2 Turbulence near a wall.
Exercises.
Part IV TURBULENCE SIMULATION.
12 Eddyresolving simulation.
12.1 Direct numerical simulation.
12.1.1 Grid requirements.
12.1.2 Numerical dissipation.
12.1.3 Energyconserving schemes.
12.2 Illustrations.
12.3 Pseudospectral method.
Exercises.
13 Simulation of large eddies.
13.1 Large eddy simulation.
13.1.1 Filtering.
13.1.2 Subgrid models.
13.2 Detached eddy simulation.
Exercises.
References.
Index.