9780521598866

Turbulent Flows

by
  • ISBN13:

    9780521598866

  • ISBN10:

    0521598869

  • Format: Paperback
  • Copyright: 10/16/2000
  • Publisher: Cambridge University Press
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Summary

This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.

Table of Contents

List of tables
xv
Preface xvii
Nomenclature xxi
PART ONE: FUNDAMENTALS 1(332)
Introduction
3(7)
The nature of turbulent flows
3(4)
The study of turbulent flows
7(3)
The equations of fluid motion
10(24)
Continuum fluid properties
10(2)
Eulerian and Lagrangian fields
12(2)
The continuity equation
14(2)
The momentum equation
16(2)
The role of pressure
18(3)
Conserved passive scalars
21(1)
The vorticity equation
22(1)
Rates of strain and rotation
23(1)
Transformation properties
24(10)
The statistical description of turbulent flows
34(49)
The random nature of turbulence
34(3)
Characterization of random variables
37(6)
Examples of probability distributions
43(11)
Joint random variables
54(7)
Normal and joint-normal distributions
61(4)
Random processes
65(9)
Random fields
74(5)
Probability and averaging
79(4)
Mean-flow equations
83(13)
Reynolds equations
83(3)
Reynolds stresses
86(5)
The mean scalar equation
91(1)
Gradient-diffusion and turbulent-viscosity hypotheses
92(4)
Free shear flows
96(86)
The round jet: experimental observations
96(15)
A description of the flow
96(1)
The mean velocity field
97(8)
Reynolds stresses
105(6)
The round jet: mean momentum
111(11)
Boundary-layer equations
111(4)
Flow rates of mass, momentum, and energy
115(1)
Self-similarity
116(2)
Uniform turbulent viscosity
118(4)
The round jet: kinetic energy
122(12)
Other self-similar flows
134(27)
The plane jet
134(5)
The plane mixing layer
139(8)
The plane wake
147(4)
The axisymmetric wake
151(3)
Homogeneous shear flow
154(4)
Grid turbulence
158(3)
Further observations
161(21)
A conserved scalar
161(6)
Intermittency
167(6)
PDFs and higher moments
173(5)
Large-scale turbulent motion
178(4)
The scales of turbulent motion
182(82)
The energy cascade and Kolmogorov hypotheses
182(9)
The energy cascade
183(1)
The Kolmogorov hypotheses
184(4)
The energy spectrum
188(1)
Restatement of the Kolmogorov hypotheses
189(2)
Structure functions
191(4)
Two-point correlation
195(12)
Fourier modes
207(12)
Fourier-series representation
207(4)
The evolution of Fourier modes
211(4)
The kinetic energy of Fourier modes
215(4)
Velocity spectra
219(30)
Definitions and properties
220(9)
Kolmogorov spectra
229(3)
A model spectrum
232(2)
Dissipation spectra
234(4)
The inertial subrange
238(2)
The energy-containing range
240(2)
Effects of the Reynolds number
242(4)
The shear-stress spectrum
246(3)
The spectral view of the energy cascade
249(5)
Limitations, shortcomings, and refinements
254(10)
The Reynolds number
254(1)
Higher-order statistics
255(3)
Internal intermittency
258(2)
Refined similarity hypotheses
260(3)
Closing remarks
263(1)
Wall flows
264(69)
Channel flow
264(26)
A description of the flow
264(2)
The balance of mean forces
266(2)
The near-wall shear stress
268(3)
Mean velocity profiles
271(7)
The friction law and the Reynolds number
278(3)
Reynolds stresses
281(7)
Lengthscales and the mixing length
288(2)
Pipe flow
290(8)
The friction law for smooth pipes
290(5)
Wall roughness
295(3)
Boundary layers
298(24)
A description of the flow
299(1)
Mean-momentum equations
300(2)
Mean velocity profiles
302(6)
The overlap region reconsidered
308(5)
Reynolds-stress balances
313(7)
Additional effects
320(2)
Turbulent structures
322(11)
PART TWO: MODELLING AND SIMULATION 333(308)
An introduction to modelling and simulation
335(9)
The challenge
335(1)
An overview of approaches
336(1)
Criteria for appraising models
336(8)
Direct numerical simulation
344(14)
Homogeneous turbulence
344(9)
Pseudo-spectral methods
344(2)
The computational cost
346(6)
Artificial modifications and incomplete resolution
352(1)
Inhomogeneous flows
353(3)
Channel flow
353(1)
Free shear flows
354(1)
Flow over a backward-facing step
355(1)
Discussion
356(2)
Turbulent-viscosity models
358(29)
The turbulent-viscosity hypothesis
359(6)
The intrinsic assumption
359(5)
The specific assumption
364(1)
Algebraic models
365(4)
Uniform turbulent viscosity
365(1)
The mixing-length model
366(3)
Turbulent-kinetic-energy models
369(4)
The k-ε model
373(10)
An overview
373(2)
The model equation for ε
375(7)
Discussion
382(1)
Further turbulent-viscosity models
383(4)
The k-ω model
383(2)
The Spalart-Allmaras model
385(2)
Reynolds-stress and related models
387(76)
Introduction
387(1)
The pressure-rate-of-strain tensor
388(4)
Return-to-isotropy models
392(12)
Rotta's model
392(1)
The characterization of Reynolds-stress anisotropy
393(5)
Nonlinear return-to-isotropy models
398(6)
Rapid-distortion theory
404(18)
Rapid-distortion equations
405(1)
The evolution of a Fourier mode
406(5)
The evolution of the spectrum
411(4)
Rapid distortion of initially isotropic turbulence
415(6)
Final remarks
421(1)
Pressure-rate-of-strain models
422(6)
The basic model (LRR-IP)
423(2)
Other pressure-rate-of-strain-models
425(3)
Extension to inhomogeneous flows
428(5)
Redistribution
428(1)
Reynolds-stress transport
429(3)
The dissipation equation
432(1)
Near-wall treatments
433(12)
Near-wall effects
433(1)
Turbulent viscosity
434(1)
Model equations for k and ε
435(1)
The dissipation tensor
436(3)
Fluctuating pressure
439(3)
Wall functions
442(3)
Elliptic relaxation models
445(3)
Algebraic stress and nonlinear viscosity models
448(9)
Algebraic stress models
448(4)
Nonlinear turbulent viscosity
452(5)
Discussion
457(6)
PDF methods
463(95)
The Eulerian PDF of velocity
464(4)
Definitions and properties
464(1)
The PDF transport equation
465(2)
The PDF of the fluctuating velocity
467(1)
The model velocity PDF equation
468(15)
The generalized Langevin model
469(1)
The evolution of the PDF
470(5)
Corresponding Reynolds-stress models
475(4)
Eulerian and Lagrangian modelling approaches
479(1)
Relationships between Lagrangian and Eulerian PDFs
480(3)
Langevin equations
483(11)
Stationary isotropic turbulence
484(5)
The generalized Langevin model
489(5)
Turbulent dispersion
494(12)
The velocity-frequency joint PDF
506(10)
Complete PDF closure
506(1)
The log-normal model for the turbulence frequency
507(4)
The gamma-distribution model
511(3)
The model joint PDF equation
514(2)
The Lagrangian particle method
516(13)
Fluid and particle systems
516(3)
Corresponding equations
519(4)
Estimation of means
523(3)
Summary
526(3)
Extensions
529(26)
Wall functions
529(5)
The near-wall elliptic-relaxation model
534(6)
The wavevector model
540(5)
Mixing and reaction
545(10)
Discussion
555(3)
Large-eddy simulation
558(83)
Introduction
558(3)
Filtering
561(20)
The general definition
561(1)
Filtering in one dimension
562(3)
Spectral representation
565(3)
The filtered energy spectrum
568(3)
The resolution of filtered fields
571(4)
Filtering in three dimensions
575(3)
The filtered rate of strain
578(3)
Filtered conservation equations
581(6)
Conservation of momentum
581(1)
Decomposition of the residual stress
582(3)
Conservation of energy
585(2)
The Smagorinsky model
587(17)
The definition of the model
587(1)
Behavior in the inertial subrange
587(3)
The Smagorinsky filter
590(4)
Limiting behaviors
594(4)
Near-wall resolution
598(3)
Tests of model performance
601(3)
LES in wavenumber space
604(15)
Filtered equations
604(2)
Triad interactions
606(3)
The spectral energy balance
609(1)
The spectral eddy viscosity
610(1)
Backscatter
611(1)
A statistical view of LES
612(3)
Resolution and modelling
615(4)
Further residual-stress models
619(16)
The dynamic model
619(8)
Mixed models and variants
627(2)
Transport-equation models
629(2)
Implicit numerical filters
631(3)
Near-wall treatments
634(1)
Discussion
635(6)
An appraisal of LES
635(3)
Final perspectives
638(3)
PART THREE: APPENDICES 641(86)
Appendix A Cartesian tensors
643(18)
A.1 Cartesian coordinates and vectors
643(4)
A.2 The definition of Cartesian tensors
647(2)
A.3 Tensor operations
649(5)
A.4 The vector cross product
654(5)
A.5 A summary of Cartesian-tensor suffix notation
659(2)
Appendix B Properties of second-order tensors
661(9)
Appendix C Dirac delta functions
670(8)
C.1 The definition of δ(x)
670(2)
C.2 Properties of δ(x)
672(1)
C.3 Derivatives of δ(x)
673(2)
C.4 Taylor series
675(1)
C.5 The Heaviside function
675(2)
C.6 Multiple dimensions
677(1)
Appendix D Fourier transforms
678(5)
Appendix E Spectral representation of stationary random processes
683(9)
E.1 Fourier series
683(3)
E.2 Periodic random processes
686(3)
E.3 Non-periodic random processes
689(1)
E.4 Derivatives of the process
690(2)
Appendix F The discrete Fourier transform
692(4)
Appendix G Power-law spectra
696(6)
Appendix H Derivation of Eulerian PDF equations
702(5)
Appendix I Characteristic functions
707(6)
Appendix J Diffusion processes
713(14)
Bibliography 727(22)
Author index 749(5)
Subject index 754

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