Computational river dynamics

Computational River Dynamics

Computational River Dynamics

Weiming Wu

National Center for Computational Hydroscience and Engineering,

University of Mississippi, MS, USA

LONDON / LEIDEN / NEW YORK / PHILADELPHIA / SINGAPORE

Cover Illustration Credit:

Sediment laden drainage, Betsiboka River, Madagascar (2002)

Courtesy of NASA, National Aeronautics and Space Administration, Houston, TX 77058, USA

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Library of Congress Cataloging-in-Publication Data

Wu, Weiming.

Computational river dynamics / Weiming Wu.

p. cm.

Includes bibliographical references.

ISBN 978-0-415-44961-8 (hardcover : alk. paper) – ISBN 978-0-415-44960-1

(pbk. : alk. paper) 1. Sediment transport. I. Title.

TC175.2 .W82 2007

627’.042–dc22 2007040342

ISBN: 978-0-415-44961-8 (hardback)

ISBN: 978-0-415-44960-1 (paperback)

ISBN: 978-0-203-93848-5 (e-book)

This edition published in the Taylor & Francis e-Library, 2007.

“To purchase your own copy of this or any of Taylor & Francis or Routledge’s

collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.”

ISBN 0-203-93848-8 Master e-book ISBN

Contents

Preface ix

Notations xi

1 Introduction 1

1.1 Overview of river engineering 1

1.2 Role of computational simulation in river engineering

analysis 3

1.3 Scope, problems, and strategies of computational river

dynamics 4

1.4 Classification of flow and sediment transport models 7

1.5 Coverage and features of this book 9

2 Mathematical description of flow and sediment

transport 11

2.1 Properties of water and sediment 11

2.2 Governing equations of water and sediment two-phase flow 20

2.3 Time-averaged models of turbulent flow and sediment

transport 23

2.4 Derivation of 1-D and 2-D flow and sediment transport

equations 29

2.5 Net exchange flux of suspended load near bed 44

2.6 Equilibrium and non-equilibrium sediment transport models 49

2.7 Transport and sorting of non-uniform sediment mixtures 53

vi Contents

3 Fundamentals of sediment transport 59

3.1 Settling of sediment particles 59

3.2 Incipient motion of sediment 67

3.3 Movable bed roughness in alluvial rivers 75

3.4 Bed-load transport 81

3.5 Suspended-load transport 91

3.6 Bed-material load transport 99

3.7 Sediment transport over steep slopes 107

3.8 Temporal lags between flow and sediment transport 110

4 Numerical methods 113

4.1 Concepts of numerical solution 113

4.2 Finite difference method 118

4.3 Finite volume method 141

4.4 Numerical solution of Navier-Stokes equations 156

4.5 Solution of algebraic equations 168

5 1-D numerical models 175

5.1 Formulation of 1-D decoupled flow and sediment

transport model 175

5.2 1-D calculation of open-channel flow 188

5.3 1-D calculation of sediment transport 208

5.4 1-D coupled calculation of flow and sediment transport 225

5.5 Data requirements of 1-D model 232

5.6 Model sensitivity to input parameters 234

6 2-D numerical models 241

6.1 Depth-averaged 2-D simulation of flow in nearly

straight channels 241

6.2 Depth-averaged 2-D simulation of sediment transport

in nearly straight channels 257

Contents vii

6.3 Depth-averaged 2-D simulation of flow and sediment

transport in curved and meandering channels 269

6.4 Width-averaged 2-D model of flow and sediment transport 280

7 3-D numerical models 289

7.1 Full 3-D hydrodynamic model 289

7.2 3-D flow model with hydrostatic pressure assumption 296

7.3 3-D sediment transport model 302

7.4 3-D simulation of local scour around in-stream structures 312

8 Domain decomposition and model integration 323

8.1 Multiblock method 323

8.2 Coupling of 1-D, 2-D, and 3-D models 333

8.3 Integration of channel and watershed models 339

9 Simulation of dam-break fluvial processes 347

9.1 Simulation of dam-break flow over fixed beds 347

9.2 Simulation of dam-break flow over movable beds 363

9.3 Simulation of dam surface erosion due to overtopping flow 370

10 Simulation of flow and sediment transport

in vegetated channels 375

10.1 Effects of vegetation on flow and sediment transport 375

10.2 Simulation of flow in vegetated channels 389

10.3 Simulation of sediment transport in vegetated channels 397

11 Cohesive sediment transport modeling 403

11.1 Cohesive sediment transport processes 403

11.2 Multiple-floc-size model of cohesive sediment transport 417

11.3 Single-floc-size model of cohesive sediment transport 419

11.4 Simulation of transport of cohesive and non-cohesive

sediment mixtures 426

viii Contents

12 Contaminant transport modeling 429

12.1 Heat and salinity transport model 429

12.2 Water quality model 439

12.3 Simulation of sediment-borne contaminant transport 455

References 465

Index 489

Preface

Rivers, as part of the nature, have been a focus of human activities since the beginning

of civilization. Through engineering practices, such as flood control, water supply,

irrigation, drainage, channel design, river regulation, navigation improvement, power

generation, environment enhancement, and aquatic habitat protection, humans have

come to understand more about rivers and established basic principles and analytical

methodologies for river engineering. With the help of computation and information

techniques, numerical modeling of flow and sediment transport in rivers has improved

greatly in recent decades and been applied widely as a major research tool in solving

river engineering problems. These advances motivated me to write this book on the

physical principles, numerical methods, and engineering applications of computational

river dynamics.

Most of the topics included in this book have been the central theme of my research

work. I developed a simple 1-D quasi-steady sediment transport model for my bach￾elor’s degree in 1986, a width-averaged 2-D unsteady open-channel flow model in

my master’s thesis in 1988, and an integrated 1-D and depth-averaged 2-D sediment

transport model under quasi-steady flow conditions in my Ph.D. dissertation in 1991

at the Department of River Engineering, Wuhan University of Hydraulic and Electric

Engineering, China. In 1995–1997, I established a 3-D sediment transport model at

the Institute for Hydromechanics, University of Karlsruhe, supported by the Alexander

von Humboldt Foundation, Germany. Since 1997, I have revisited 1-D and 2-D mod￾els and developed a 1-D channel network model and a depth-averaged 2-D model for

unsteady flow and non-uniform sediment transport at the National Center for Com￾putational Hydroscience and Engineering, University of Mississippi, USA, through a

Specific Research Agreement between the USDA Agricultural Research Service and the

University of Mississippi. I have also reviewed sediment transport theories, established

several sediment transport formulas, and developed models for dam-break fluvial pro￾cesses, vegetation effects, cohesive sediment transport, and contaminant transport. All

these model developments and studies contributed to this book.

This book is intended primarily as a reference book for river scientists and engineers.

It is also useful for professionals in hydraulic, environmental, agricultural, and geo￾logical engineering. It can be used as a textbook for civil engineering students at the

graduate level.

My fascination with river engineering and computational river dynamics began

with my first supervisor, Prof. Jianheng Xie. Later I learned a great deal about tur￾bulence models and computational techniques in CFD from Prof. Wolfgang Rodi.

x Preface

I also would like to acknowledge Prof. Sam S.Y. Wang for his long-term support and

encouragement. I am greatly indebted to these three scientists.

I sincerely thank Drs. Mustafa S. Altinakar, Xiaobo Chao, George S. Con￾stantinescu, Blair Greimann, Eddy J. Langendoen, Wolfgang Rodi, Steve H. Scott,

F. Douglas Shields, Jr., Pravi Shrestha, Dalmo A. Vieira, Thomas Wenka, Keh-Chia

Yeh, Xinya Ying, and Tingting Zhu for reviewing this book. I also thank my colleagues

in Wuhan, Karlsruhe, and Ole Miss and my friends all over the world for their care

and encouragement.

I would like to thank Taylor & Francis for publishing this book. In particular, many

thanks are due to Dr. Germaine Seijger and Mr. Lukas Goosen for their professional

handling of this project, Ms. Maartje Kuipers for designing the cover, Mrs. Shyamala

Ravishankar and her team for carefully typesetting the manuscript, and the Anthony

Rowe Ltd for printing it. I also thank my assistants Dr. Zhiguo He and Miss Podjanee

Inthasaro for their help in proofreading of this book.

Special thanks go to my wife Ling and daughter Siyuan who gave me tremendous

support during this endeavor.

Weiming Wu

Ole Miss, October 2007

Notations

Symbol Meaning

A Cross-sectional area of flow in 1-D model

Ab Bed area at the cross-section

B Channel width at the water surface

b Flow width at height z in width-averaged 2-D model

C Depth-, width- or section-averaged suspended-load concentration

Contaminant concentration

Cd Drag coefficient of sediment particle or vegetation

Cd, Cs, Ct Concentrations of dissolved, sorbed, and total contaminants

Ch Chezy coefficient

Ct Depth- or cross-section-averaged concentration of total load

C∗ Depth- or cross-section-averaged equilibrium suspended-load concentration

c Local sediment concentration

cb, cb∗ Actual and equilibrium near-bed suspended-load concentrations

cv0, cv local and depth-averaged concentrations of vegetation

D Diameter of vegetation stem

Db, Eb Near-bed deposition and entrainment fluxes of sediment

Dsx , Dsy Dispersion fluxes of suspended load

Dxx , Dxy, Dyx , Dyy Dispersion transports of momentum

d Sediment diameter

d50 Median diameter of sediment mixture

dk Sediment diameter of size class k

dm Arithmetic mean diameter of sediment

F

d, f

d Drag forces on vegetation

Fw, Fs, Fb, ... Fluxes across cell faces

Fi External force per unit volume

fc Coriolis coefficient

g Gravitational acceleration

h Flow depth

hv Vegetation height

J Jacobian determinant

K Conveyance of channel

k Turbulent kinetic energy

xii Notations

Symbol Meaning

ks Equivalent (effective) roughness height

Subscript k Sediment size class index

Associated with turbulent kinetic energy

L, Lt Adaptation length of sediment

lm Mixing length

Na Vegetation density

n Manning roughness coefficient

Pk Production of turbulence by shear

p Pressure

p Pressure correction

pbk Bed-material gradation in mixing layer

p

m Porosity of sediment deposit

Q Flow discharge

Qb, Qb∗ Actual and equilibrium bed-load transport rates

Qt, Qt∗ Actual and equilibrium total-load transport rates

q Unit flow discharge

qb, qb∗ Actual and equilibrium unit bed-load transport rates

q1, qblk, qslk, qtlk Side discharges of flow and sediment

R Hydraulic radius of channel

Rb Hydraulic radius of channel bed

Rs Hydraulic radius of vegetated bed

S Source term

Sf Energy slope, friction slope

T Temperature or transport stage number

Txx , Txy, Tyx , Tyy Depth-averaged stresses

t Time

U(Uˆ) Depth- or section-averaged flow velocity

Ux , Uy Depth-averaged flow velocities in x- and y-directions

Ux , Uz (U

x , U

z) Width-averaged flow velocities in x- and z-directions

Uc Critical average velocity for incipient motion

U∗ bed shear velocity

ub, Ub Bed-load velocities

ui(ux , uy, uz) Flow velocities in xi(x,y, z) directions

uˆm(uˆξ , uˆη, uˆζ ) Flow velocities in ξm(ξ , η, ζ ) directions

x, y Horizontal Cartesian coordinates

xi i-coordinate in the Cartesian coordinate system

z Vertical coordinate above a datum (or bed)

zb Bed surface elevation

zs Water surface elevation

α Adaptation coefficient of sediment

αbx , αby Direction cosines of bed-load movement

β Correction factor for momentum

βs, βt Correction factors for suspended and total loads

χ Wetted perimeter at the cross-section

 Sand dune height

AP Area of the control volume centered at P

t Time step

x, y Grid spacings

zb, Ab Changes in bed elevation and area

δ Thickness of bed-load layer

δij Kronecker delta

Notations xiii

Symbol Meaning

δm Mixing layer thickness

δh, δQ Increments of water stage and flow discharge

ε Dissipation rate of turbulent energy

εs Turbulent diffusivity of sediment

φr Repose angle of sediment

γ Specific weight of water and sediment mixture

γf , γs Specific weights of water and sediment

κ Von Karman constant

λ Darcy-Weisbach friction factor

µ, ν Dynamic and kinematic viscosities of water

νt Turbulent or eddy viscosity

π Circumference-diameter ratio ≈ 3.14159

 Shields number

c Critical Shields number

θ, ψ Temporal, spatial weighting factors

ρ Density of water and sediment mixture

ρ0 Density of flow density at water surface

ρb Density of water and sediment mixture at bed surface layer

ρd Dry density of sediment deposit

ρf , ρs Densities of water and sediment

σs Schmidt number

τ , τij Shear stresses

τb, τ

b Bed shear stress, grain shear stress

τc Critical shear tress for incipient motion

τce Critical shear stress for erosion

τs Wind driving force at the water surface

ωs Sediment settling velocity

ωsf Floc settling velocity

ξ , η, ζ Logical or curvilinear coordinates