Turbulence in Open Channels and River Flows

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Chapter 1: Introduction
Chapter 2: Statistical Methods
2.1 Introductory Remarks
2.2 Basic Features of Turbulence
2.2.1 What Is Turbulence?
2.2.1.1 Irregularity
2.2.1.2 Diffusibility
2.2.1.3 Three dimensionality
2.2.1.4 Dissipation of kinetic energy
2.2.1.5 Multi-scales
2.2.2 Generation of Turbulence
2.2.3 Diffusion in Turbulence
2.2.3.1 Molecular diffusion
2.2.3.2 Turbulent diffusion
2.2.4 Minimum Vortex in Multi-Scale Turbulence
2.3 Averaging Procedures
2.3.1 Time Average
2.3.2 Space Average
2.3.3 Ensemble Average
2.4 Differential Forms
2.4.1 Einstein Notation and Coordinate System
2.4.2 Continuity Equation
2.4.3 Euler Equations
2.4.3.1 Mathematical form of fluid acceleration
2.4.3.2 Derivation of Euler equations
2.5 Navier Stokes Equations
2.5.1 Momentum Equation of Viscous Fluid
2.5.2 Viscous Shear Stress
2.5.3 Viscous Normal Stress
2.5.4 Total Viscous Stress
2.5.5 Navier Stokes Equations
2.5.6 Viscosity and Kinetic Viscosity
2.6 Reynolds-Averaged Navier Stokes Equations
2.6.1 Momentum Equation of Viscous Fluid
Chapter 3: 2-D Open-Channel Turbulence
3.1 Introductory Remarks
3.2 Boundary Layer Theory
3.2.1 What Is Boundary Layer?
3.2.2 Rayleigh Problem
3.2.3 Definitions of Boundary Layer
3.2.3.1 99% thickness
3.2.3.2 Displacement thickness
3.2.3.3 Momentum thickness
3.2.4 Boundary Layer Equations
3.2.5 Blasius's Solution
3.2.6 Karman's Integral Equation of Momentum
3.3 Turbulence Generation
3.3.1 Transition of Laminar Boundary Layer to Turbulent Boundary Layer
3.3.2 Development of Turbulent Boundary Layer
3.3.3 Turbulence Generation
3.4 Governing Equation
3.4.1 Open-Channel and Boundary Layer
3.4.2 2-D Governing Equation in Open-Channel Flow
3.5 Modeling of Shear Stress
3.5.1 Reynolds Stress
3.5.2 Mixing Length Model
3.5.3 Eddy Viscosity Model
3.6 Time Mean Velocity Profile
3.6.1 Time Mean Velocity Profile
3.6.2 Law of the Wall
3.6.3 Inner Layer
3.6.4 Outer Layer
3.7 Turbulence Structure in Open-Channel
3.7.1 Profiles of Turbulence Statistics
3.7.2 Transport Equations of Mean Flow and Turbulent Kinetic Energy
3.7.3 Energy Equilibrium in the Depth Direction
3.8 Frequency Analysis and Cascade Process
3.8.1 Frequency and Wave Number Fields
3.8.2 Correlation Coefficient and Spectrum
3.8.2.1 Correlation coefficient
3.8.2.2 Spectrum
3.8.2.3 Wiener Khinchin theorem
3.8.2.4 Conversion between frequency spectrum and wave number spectrum
3.8.3 Kolmogorov's -5/3 Power Law
3.8.4 Inverse Cascade in Two-Dimensional Turbulence
3.9 Coherent Structures
3.9.1 Coherent Turbulence
3.9.2 Bursting Phenomenon
3.9.3 Streaks and Hairpin Vortex
3.9.4 Boil
3.10 Free-Surface Effects
3.10.1 Turbulence Damping in the Free Surface
3.10.2 Interaction of Bursting and Free Surface
3.10.3 Generation of Water Waves in Open-Channel Flow
3.11 Bottom Roughness Effects
3.11.1 Equivalent Sand Roughness
3.11.2 Virtual Zero Level
3.11.3 Mean Velocity Profile
3.11.4 Rough Flow Regime
3.11.5 Turbulence Structure
Chapter 4: Horizontal Open-Channel Turbulence
4.1 Horizontal Shear Instability
4.1.1 Horizontal Unstable Phenomena in Open-Channel
4.1.2 Theoretical Background
4.2 Horizontal Vortex
4.2.1 Kelvin Helmholtz Instability
4.2.2 Horizontal Turbulence in Rivers
4.2.2.1 Confluence zone
4.2.2.2 Compound channel
4.2.2.3 Bridge peer wake
4.2.2.4 Vegetation
4.2.2.5 Groynes
4.2.2.6 Side walls
4.3 Surface Velocity Divergence
4.3.1 Definition of Surface Velocity Divergence
4.3.2 Hydrodynamic Property
4.3.3 Scaling of Surface Velocity Divergence
4.4 2-D Depth-Averaged Governing Equations
4.4.1 Mathematical Preparations
4.4.2 Derivation of Depth-Averaged Governing Equations
4.4.2.1 Momentum equations
4.4.2.2 Continuity equation
Chapter 5: 3-D Turbulence Structure
5.1 Generation Mechanism of Secondary Currents
5.1.1 Introductory Remarks
5.1.2 First Kind of Secondary Currents
5.1.3 Second Kind of Secondary Currents
5.2 Three-Dimensional Turbulence in a Straight Channel
5.2.1 Secondary Cells
5.2.2 Three-Dimensional Large-Scale Motions
5.3 Three-Dimensional Turbulence in a Curved Channel
5.3.1 Hydrodynamics in a Curved Channel
5.3.2 Evolution of Streamwise Velocity
5.3.3 Evolution of Streamwise Velocity
5.3.4 Strength of Secondary Currents
5.4 Three-Dimensional Flow in a Flood
5.4.1 Meandering Flow in a Flood
5.4.2 Phenomenological Model of Compound Meandering Flow
Chapter 6: Turbulence Transport
6.1 Introductory Remarks
6.2 Turbulent Diffusion Equation
6.3 Particle Tracking Analysis
6.3.1 One-Particle Analysis
6.3.2 Two-Particle Analysis
6.3.3 Eddy-Dependent Trajectories
6.4 Dispersion
6.5 Peclet Number
Chapter 7: Applications to River Flow
7.1 Introductory Remarks
7.2 Vegetation Flow
7.2.1 Research Background
7.2.2 Emergent Vegetation
7.2.3 Submergent Vegetation
7.2.4 Flexible Vegetation
7.2.5 Summary of Vegetation Flow
7.3 Compound Open-Channel Flows
7.3.1 Characteristics in Compound Channels
7.3.2 Previous Works
7.3.3 Cross-Sectional Features
7.3.4 Spanwise Profiles of Streamwise Velocity and Bed Shear Stress
7.3.5 Interaction between Main Channel and Floodplain
7.3.6 Shiono and Knight Method (SKM)
7.3.7 Horizontal Vortex
7.4 Deadwater Zone
7.4.1 Research Background
7.4.2 Types of Local Deadwater Zones in Rivers
7.4.2.1 Isolated Groynes
7.4.2.2 Consecutive groynes
7.4.2.3 Embayment
7.4.3 Mean Currents in a Rectangular Embayment
7.4.4 Reynolds Stress Distribution in a Rectangular Embayment
7.4.5 Three-Dimensional Structure in a Rectangular Embayment
7.4.6 Free-Surface Oscillation
7.5 Sediment Transport
7.5.1 Introductory Remarks
7.5.2 Particle Movements by Fluid
7.5.2.1 Forces exerted on sediment particles
7.5.2.2 Particle movement
Rolling/Sliding
Saltation
Suspension
7.5.2.3 Unidirectional bed forms
7.5.2.4 Turbulent transport
Transport of bed load
Transport of suspended sediment
Rouse equation
7.5.3 Bursting and Sediment Entrainment
7.5.4 Particles and Fluid Interaction
7.6 Vertical 2-D Debris Flow
7.6.1 Introduction
7.6.2 Dependency on Bottom Slope
7.6.3 Velocity Profile in the Single-Layer Debris Flow
7.6.4 Velocity Profile in the Two-Layer Debris Flow
7.6.4.1 Velocity profile in sediment current layer
7.6.4.2 Velocity profile in water-current layer
7.6.4.3 Depth-averaged sediment concentration
7.6.5 End remarks
7.7 Unsteady Turbulent Open Channel
7.7.1 Introduction
7.7.2 Two-Dimensional Unsteady Open-Channel Flow
7.7.2.1 Velocity profiles in viscous sublayer
7.7.2.2 Time variations of velocity and flow depth
7.7.2.3 Bottom shear stress against time
7.7.2.4 Log law in the unsteady flow
7.7.2.5 Unsteadiness effect on turbulent energy
7.7.3 Unsteady Compound Open-Channel Flow
7.4.4 Inundation on a Floodplain
7.8 Accelerated Flow
7.8.1 Introduction
7.8.2 Distributions of Velocity and Reynolds Stress
7.8.3 Pressure Gradient Parameter
7.8.4 Mechanism of Relaminarization
7.8.5 Phenomenological Flow Model
7.9 Energy Dissipation
7.9.1 Introductory Remarks
7.9.2 Energy Dissipation in a Spillway
7.9.2.1 Still basin
7.9.2.2 Hydraulic jump
7.9.3 Energy Dissipation by Trees
7.9.3.1 Flood protection forest
7.9.3.2 Example of traditional flood protection forest
7.9.3.3 Laterally placed tree models
7.9.3.4 Potential core formed behind trees
7.9.3.5 Flood energy reduction
Chapter 8: Measurements in Open-Channel Turbulence
8.1 Introductory Remarks
8.2 Sampling of Turbulence
8.2.1 Sampling Theorem
8.2.2 Aliasing
8.3 Velocimetry
8.3.1 Laboratory Study
8.3.1.1 Pitot tube
8.3.1.2 Propeller current meter
8.3.1.3 Electromagnetic velocimetry (EMV)
8.3.1.4 Ultrasonic velocity profiler (UVP)
8.3.1.5 Acoustic Doppler velocimetry (ADV)
8.3.1.6 Hot film velocimetry
8.3.1.7 Laser Doppler anemometer (LDA)
8.3.1.8 Particle image velocimetry (PIV)
8.3.2 Field Study
8.3.2.1 Floating method
8.3.2.2 Price-type current meter
8.3.2.3 Acoustic Doppler current profiler (ADCP)
8.3.2.4 Microwave current meter
8.3.2.5 Large-scale PIV (LS-PIV)
8.3.2.6 Acoustic mapping velocimetry (AMV)
8.3.2.7 Unmanned surface vehicle (USV)
8.4 Detection Technique of Coherent Turbulence
8.4.1 Quadrant Analysis
8.4.2 Variable-Interval Time-Averaging (VITA)
8.4.3 Proper Orthogonal Decomposition (POD)
8.4.4 Vortex Detection
8.5 Example of Measurement Setup
8.5.1 Recirculation Flume
8.5.2 Measurement Instrumentation
8.5.3 Experimental Procedure
8.5.4 Examples of Experimental Flume
Appendix 1: Reynolds Decomposition
A.1.1 Reynolds Averaging
A.1.2 Reynolds Averaging of Continuity Equation
A.1.3 Reynolds Averaging of N-S Equations (Derivation of RANS)
A.1.4 Einstein Notation
Appendix 2: Calculation Procedure of Blasius Solution
A.2.1 Former Process
A.2.2 Latter Process
Appendix 3: Mathematical Derivation of Equation in the K-H Instability
References
Index