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E-grāmata: Turbulence In Coastal And Civil Engineering

(Technical Univ Of Denmark, Denmark), (Bm Sumer Consultancy & Research, Turkey)
  • Formāts: 760 pages
  • Sērija : Advanced Series On Ocean Engineering 51
  • Izdošanas datums: 23-Mar-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813234321
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Turbulence In Coastal And Civil EngineeringPalielināt
  • Formāts: 760 pages
  • Sērija : Advanced Series On Ocean Engineering 51
  • Izdošanas datums: 23-Mar-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813234321
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This book discusses the subject of turbulence encountered in coastal and civil engineering.The primary aim of the book is to describe turbulence processes including transition to turbulence; mean and fluctuating flows in channels/pipes, and in currents; wave boundary layers (including boundary layers under solitary waves); streaming processes in wave boundary layers; turbulence processes in breaking waves including breaking solitary waves; turbulence processes such as bursting process and their implications for sediment transport; flow resistance in steady and wave boundary layers; and turbulent diffusion and dispersion processes in the coastal and river environment, including sediment transport due to diffusion/dispersion.Both phenomenological and statistical theories are described in great detail. Turbulence modelling is also described, and several examples for modelling of turbulence in steady flow and wave boundary layers are presented.The book ends with a chapter containing hands-on exercises on a wide variety of turbulent flows including experimental study of turbulence in an open-channel flow, using Laser Doppler Anemometry; Statistical, correlation and spectral analysis of turbulent air jet flow; Turbulence modelling of wave boundary layer flows; and numerical modelling of dispersion in a turbulent boundary layer, a set of exercises used by the authors in their Masters classes over many years.Although the book is essentially intended for professionals and researchers in the area of Coastal and Civil Engineering, and as a text book for graduate/post graduate students, the contents of the book will, however, additionally provide sufficient background in the study of turbulent flows relevant to many other disciplines, such as Wind Engineering, Mechanical Engineering, and Environmental Engineering.
Preface v
List of symbols and abbreviations
xxi
1 Introduction and the origin of turbulence
1(14)
1.1 Introduction
1(2)
1.2 Flow over a flat plate
3(2)
1.3 Flow in wave boundary layers
5(1)
1.4 Flow in wave boundary layers in solitary motion
6(1)
1.5 Steady flow in pipes
7(1)
1.6 Oscillatory flow in pipes
8(1)
1.7 Flow around a circular cylinder in a steady current
9(2)
1.8 Flow induced by breaking waves
11(1)
1.9 References
12(3)
Appendix to
Chapter 1 Transition to turbulence over a flat plate
15(38)
1.A Description of transition process
15(12)
1.A.1 Problem statement
15(1)
1.A.2 Emmons' (1951) observations
15(2)
1.A.3 Detailed description of a single turbulent spot
17(6)
1.A.4 Critical Reynolds number for transition
23(3)
1.A.5 Transition and turbulent spots over rough boundaries
26(1)
1.B Hydrodynamic stability theory for transition
27(8)
1.B.1 The Orr-Sommerfeld equation
27(4)
1.B.2 The eigenvalue problem
31(3)
1.B.3 Experimental verification of the hydrodynamic stability theory
34(1)
1.C Direct numerical simulation (DNS) of transition
35(4)
1.D References
39(4)
2 Basic equations for turbulent flows
43(10)
2.1 Method of averaging and Reynolds decomposition
43(2)
2.2 Continuity equation
45(1)
2.3 Equations of motion
45(2)
2.4 Energy equations
47(5)
2.4.1 Energy equation for laminar flows
47(1)
2.4.2 Energy equation for the mean flow
48(1)
2.4.3 Energy equation for the fluctuating flow
49(3)
2.5 Reference
52(1)
Appendix to
Chapter 2 Derivation of the continuity and Navier-Stokes equations
53(102)
2.A Continuity equation
53(2)
2.B Navier-Stokes equation
55(8)
2.C References
63(2)
3 Steady turbulent boundary layer flows
65(90)
3.1 Flow close to a wall
65(27)
3.1.1 Idealized flow in the half space y < 0
65(6)
3.1.2 Mean and turbulence characteristics of flow close to a smooth wall
71(8)
3.1.3 Mean and turbulence characteristics of flow close to a rough wall
79(13)
3.2 Flow across the entire section
92(4)
3.3 Turbulence modelling approach
96(11)
3.3.1 Turbulence modelling of flow close to a wall
97(9)
3.3.2 Turbulence modelling of flow across the entire section
106(1)
3.4 Flow resistance
107(2)
3.4.1 Smooth circular pipe
107(1)
3.4.2 Rough circular pipe
108(1)
3.4.3 Transitional circular pipe
109(1)
3.4.4 Non-circular pipe and open channel
109(1)
3.5 Bursting process
109(17)
3.5.1 Description of the bursting process
112(2)
3.5.2 Flow visualization of the bursting process
114(4)
3.5.3 Contribution of ejection and sweep events to the Reynolds stress
118(2)
3.5.4 Bursting process over rough walls
120(3)
3.5.5 Important characteristics of the bursting process
123(3)
3.6 Implications of bursting process for sediment transport
126(24)
3.6.1 Particle motions near the bottom in an open channel: Mechanism of particle suspension
126(10)
3.6.2 Lift forces on moving particles near boundaries
136(4)
3.6.3 Initiation of suspension of particles from the bottom
140(6)
3.6.4 Suspension of particles released away from the bottom
146(4)
3.7 References
150(5)
Appendix to
Chapter 3 Dimensional analysis
155(68)
3.A Buckingham's Pi theorem
155(1)
3.B Example: Law of the wall
156(3)
4 Statistical, correlation and spectral analysis
159(64)
4.1 Statistical analysis
160(11)
4.1.1 Probability density function
160(1)
4.1.2 Statistical moments
161(4)
4.1.3 Matlab example: Basic statistics and creating a p.d.f
165(6)
4.2 Correlation analysis
171(13)
4.2.1 Space correlations
171(5)
4.2.2 Time correlations
176(2)
4.2.3 Taylor's frozen turbulence approximation
178(3)
4.2.4 Matlab example: Time correlation and scales
181(3)
4.3 Spectral analysis
184(35)
4.3.1 General considerations
184(3)
4.3.2 Energy balance in wave number space
187(4)
4.3.3 Kolmogorov's theory: Universal equilibrium range and inertial subrange
191(4)
4.3.4 Vortex stretching
195(5)
4.3.5 One-dimensional spectra
200(6)
4.3.6 Aliasing in one-dimensional spectra
206(3)
4.3.7 Matlab example: The discrete Fourier transform
209(5)
4.3.8 Matlab example: Creating a one-dimensional energy density spectrum
214(5)
4.4 References
219(4)
Appendix to
Chapter 4 Proofs of some common isotropic turbulence relationships
223(178)
4.A Proof of the isotropic relationship between the correlation functions f(r) and g(r), Eq. 4.24
223(2)
4.B Proof of Eqs. 4.30 and 4.31, relating λf and λgs to the variance of fluctuating velocity gradients
225(1)
4.C Proof of isotropic relation Eq. 4.66, the governing equation for the correlation function Qij(r)
226(4)
4.D Proof that the integral of T(k) over all wave numbers is zero, Eq. 4.77
230(1)
4.E Proof of the isotropic relationship between the one-dimensional spectra F(k) and G(k), Eq. 4.118
230(1)
4.F Proof of the isotropic relationship between E(k) and F(k), Eq. 4.119
231(1)
4.G Proof of the isotropic dissipation rate e, Eq. 4.83
232(3)
4.H References
235(2)
5 Wave boundary layers
237(164)
5.1 Laminar wave boundary layers
239(6)
5.1.1 Velocity distribution across the boundary layer depth
239(5)
5.1.2 Bed shear stress
244(1)
5.2 Laminar-to-turbulent transition
245(19)
5.2.1 General description: Turbulent spots
245(9)
5.2.2 Critical Reynolds number for transition
254(1)
5.2.3 Imprint of turbulent spot in bed shear stress signal
255(2)
5.2.4 Laminar-to-turbulent transition in terms of friction coefficient
257(2)
5.2.5 Turbulent spots over a rough bed
259(2)
5.2.6 Transition in terms of flow resistance and phase
261(3)
5.3 Turbulent wave boundary layers: Smooth bed
264(18)
5.3.1 Oscillating tunnel in Jensen et al. (1989) study
265(2)
5.3.2 Ensemble averaging
267(1)
5.3.3 General description of turbulent wave boundary layer
268(1)
5.3.4 Mean flow velocity
269(4)
5.3.5 Turbulence quantities
273(2)
5.3.6 Effect of Reynolds number
275(1)
5.3.7 Wall-normal pressure gradient
276(5)
5.3.8 Boundary-layer thickness
281(1)
5.4 Turbulent wave boundary layers: Rough bed
282(6)
5.4.1 Experimental setup in Jensen et al. (1989) rough-bed experiments
283(1)
5.4.2 Comparison of rough-bed and smooth-bed results
284(3)
5.4.3 Boundary-layer thickness
287(1)
5.5 Flow resistance in wave boundary layers
288(8)
5.5.1 Wave friction coefficient for smooth-bed wave boundary layer
289(1)
5.5.2 Wave friction coefficient for rough-bed wave boundary layer
290(5)
5.5.3 Wave friction coefficient for transitional-bed wave boundary layer
295(1)
5.6 Combined wave and current boundary layers
296(23)
5.6.1 Experimental setup in Lodahl et al. (1998) study
298(2)
5.6.2 Laminar-to-turbulent transition in combined scillatory flow and current
300(7)
5.6.3 Mean wall shear stress
307(5)
5.6.4 Friction coefficient for combined flow
312(2)
5.6.5 Wave-induced apparent roughness
314(1)
5.6.6 Oscillating component of the wall shear stress in combined flow
315(1)
5.6.7 Flow resistance in combined wave and current boundary layers
316(3)
5.7 Boundary layers in wave flumes
319(6)
5.7.1 Waves alone
320(2)
5.7.2 Combined waves and current
322(3)
5.8 Bursting process in wave boundary layers
325(3)
5.9 Miscellaneous wave boundary layer examples
328(3)
5.10 Solitary wave boundary layers
331(25)
5.10.1 Laminar solitary wave boundary layers
331(3)
5.10.2 Transitional and turbulent solitary wave boundary layers
334(1)
5.10.3 Experimental facility in Sumer et al. (2010) study
335(1)
5.10.4 Flow regimes in solitary wave boundary layers
336(11)
5.10.5 Flow resistance in solitary wave boundary layers
347(4)
5.10.6 Velocity profiles in solitary wave boundary layers
351(3)
5.10.7 Remarks on practical applications
354(2)
5.11 Tsunami wave boundary layers
356(17)
5.11.1 Idealized tsunami signals
357(5)
5.11.2 Signals based on tsunami observations
362(5)
5.11.3 Time variation of the boundary layer thickness and bed shear stress
367(3)
5.11.4 Comparison with tsunami field observations in the presence of energetic wind waves
370(3)
5.12 Mathematical modelling of turbulent wave boundary layers
373(15)
5.12.1 One-dimensional vertical (1DV) RANS equations
373(2)
5.12.2 Treatment of convective acceleration terms
375(2)
5.12.3 Pressure gradient
377(1)
5.12.4 Two-equation k-ω turbulence closure
378(1)
5.12.5 Boundary conditions
379(1)
5.12.6 Numerical solution
379(1)
5.12.7 Standard Wilcox (2006) k-ω closure model results
380(3)
5.12.8 Low Reynolds number Wilcox (2006) k-ω closure model results
383(5)
5.13 References
388(13)
Appendix to
Chapter 5 Some essentials of linear potential flow wave theory
401(72)
5.A Governing equations
401(2)
5.B Surface elevation and velocity kinematics beneath a progressive regular wave
403(1)
5.C Linear dispersion relation
404(1)
5.D Wave drift
404(2)
5.E Energy flux
406(1)
5.F Radiation stress
406(1)
5.G Shallow water approximations
407(1)
5.H Deep water approximations
408(1)
5.I Shoaling
409(1)
5.J Link to wave boundary layer quantities
410(1)
5.K References
410(3)
6 Streaming in wave boundary layers
413(60)
6.1 Streaming beneath sinusoidal progressive waves
414(10)
6.1.1 Laminar theory
414(6)
6.1.2 Turbulent streaming beneath progressive waves
420(4)
6.2 Streaming in converging-diverging oscillatory flow
424(10)
6.2.1 Laminar theory
424(4)
6.2.2 Turbulent streaming in oscillatory converging-diverging flow
428(6)
6.3 Streaming due to changing bottom roughness
434(11)
6.3.1 Anisotropic turbulence model of Fuhrman et al. (2011)
435(3)
6.3.2 Normally-directed oscillatory flow
438(5)
6.3.3 Obliquely-directed oscillatory flow
443(2)
6.4 Streaming beneath non-sinusoidal waves
445(15)
6.4.1 Streaming due to free-stream velocity skewness
446(8)
6.4.2 Streaming due to free-stream acceleration skewness
454(6)
6.5 Examples of streaming beneath real waves
460(3)
6.6 Importance of streaming and wave shape in coastal sediment transport
463(2)
6.7 References
465(8)
Appendix to
Chapter 6 The vorticity equation
473(114)
6 A Derivation of the vorticity equation
473(4)
6.B Vorticity generation due to anisotropic normal Reynolds stresses
474(3)
7 Flow and turbulence in breaking waves
477(110)
7.1 Wave breaking and breaker types
479(2)
7.2 Flow induced by spilling waves
481(14)
7.2.1 The surface roller model
482(3)
7.2.2 A simple model of undertow
485(8)
7.2.3 Comparison with measured undertow profile of Ting and Kirby (1994)
493(2)
7.3 Flow induced by plunging waves
495(29)
7.3.1 Experimental setup in Sumer et al. (2013) study
498(2)
7.3.2 Description of plunging breaking waves in Sumer et al. (2013) study
500(8)
7.3.3 Bed shear stress in Sumer et al. (2013) study
508(10)
7.3.4 Mechanism of sediment suspension by plunging waves
518(6)
7.4 Flow induced by surging waves
524(6)
7.4.1 Experiments of Jensen et al. (2014)
524(2)
7.4.2 Description of plunging and surging breaking waves in Jensen et al. (2014) study
526(4)
7.5 Flow induced by plunging solitary waves
530(18)
7.5.1 Experimental setup in Sumer et al. (2011) study
532(2)
7.5.2 Description of plunging solitary wave in Sumer et. al. (2011) study
534(5)
7.5.3 Bed shear stress in Sumer et al. (2011) study
539(8)
7.5.4 Sediment-bed experiments of Sumer et al. (2011) study
547(1)
7.6 Numerical simulation of breaking waves
548(25)
7.6.1 Background
548(2)
7.6.2 Stability analysis of two-equation closure models
550(8)
7.6.3 Model description for breaking wave simulations
558(1)
7.6.4 Simulation of spilling breaking waves of Ting and Kirby (1994)
559(8)
7.6.5 Simulation of plunging breaking waves of Ting and Kirby (1994)
567(6)
7.6.6 Summary and concluding remarks
573(1)
7.7 References
573(14)
Appendix to
Chapter 7 The depth-integrated momentum equation
587(54)
8 Diffusion and dispersion
591(50)
8.1 One-particle analysis
592(10)
8.1.1 Diffusion for small times
595(1)
8.1.2 Diffusion for large times
596(6)
8.2 Conservation of mass: Eulerian analysis
602(2)
8.3 Longitudinal dispersion
604(5)
8.3.1 Mechanism of longitudinal dispersion
604(2)
8.3.2 Application of one-particle analysis
606(3)
8.4 Longitudinal dispersion in an open channel
609(14)
8.4.1 Formulation
610(2)
8.4.2 Zeroth moment of concentration
612(1)
8.4.3 Mean particle velocity
613(2)
8.4.4 Longitudinal dispersion coefficient
615(8)
8.5 Longitudinal dispersion in rivers
623(2)
8.6 Longitudinal dispersion in an oscillating tunnel
625(11)
8.7 Dispersion in the surf zone
636(1)
8.8 References
637(4)
Appendix to
Chapter 8 Calculation of the settling velocity
641(52)
8.A General formulation
641(1)
8.B Small Reynolds number: Stokes law
642(1)
8.C Larger Reynolds numbers
642(1)
8.D References
643(2)
9 Mathematical modelling of turbulence
645(48)
9.1 The closure problem
646(1)
9.2 Types of turbulence models
647(1)
9.3 Mixing length model of Prandtl (1925)
648(7)
9.3.1 The eddy viscosity
648(2)
9.3.2 Prandtl's mixing length hypothesis
650(1)
9.3.3 Prandtl's second hypothesis
650(1)
9.3.4 The mixing length and solution for flow above a smooth wall
651(3)
9.3.5 The mixing length and solution for flow above transitional and rough walls
654(1)
9.3.6 Turbulence quantities
655(1)
9.4 The k-w model of Wilcox (2006)
655(20)
9.4.1 Model equations
656(6)
9.4.2 Wall boundary conditions
662(6)
9.4.3 Numerical computation
668(2)
9.4.4 An application example
670(5)
9.5 Large eddy simulation (LES)
675(8)
9.5.1 Model equations
675(2)
9.5.2 An application example
677(6)
9.6 Scaling of computational costs in the modelling of turbulent flows
683(4)
9.6.1 Direct numerical simulation (DNS)
683(1)
9.6.2 Large eddy simulation (LES)
684(1)
9.6.3 Turbulence energy equation models
685(2)
9.7 References
687(6)
Appendix to
Chapter 9 The exact k equation
693(22)
9.A Derivation of the exact k equation
693(1)
9.B Reference
694(1)
10 Hands-on exercises
695(20)
10.1 Introduction
695(1)
10.2 Data sets
696(1)
10.3 MatRANS fc-w turbulence model in Matlab
696(2)
10.4 Exercise 1: Analysis of a turbulent boundary layer in an open channel
698(3)
10.5 Exercise 2: A simple numerical model of dispersion in a turbulent boundary layer flow
701(5)
10.6 Exercise 3: Statistical, correlation, and spectral analysis of turbulent air jet flow
706(2)
10.7 Exercise 4: Turbulence modelling of oscillatory wave boundary layer flows
708(6)
10.8 References
714(1)
Author index 715(10)
Subject index 725
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