 | Battjes J. Unsteady flow in open channels / J.Battjes, R.J.Labeur. - Cambridge: Cambridge university press, 2017. - xix, 288 p.: ill. - Bibliogr.: p.279-282. - Auth., subject ind.: p.283-288.
- ISBN 978-1-107-15029-4
Шифр: (И/Ж12-В30) 02
|
List of Symbols ................................................ xi
Preface ........................................................ xv
1 Basic Equations for Long Waves ............................. 1
1.1 Approach ................................................... 1
1.2 Schematization of the Cross Section ........................ 2
1.3 Mass Balance ............................................... 3
1.4 Equations of Motion ........................................ 5
1.4.1 Euler Equations ..................................... 6
1.4.2 Flow Resistance ..................................... 8
1.4.3 Momentum Balance ................................... 10
1.5 Summary of the Long-Wave Equations ........................ 11
Problems .................................................. 12
2 Classification and Analysis of Long Waves ................. 13
2.1 Types of Long Waves ....................................... 13
2.1.1 Translatory Waves .................................. 13
2.1.2 Tsunamis ........................................... 14
2.1.3 Seiches ............................................ 16
2.1.4 Tides .............................................. 17
2.1.5 Flood Waves in Rivers .............................. 18
2.2 A Condition for the Long-Wave Approximation ............... 19
2.3 Estimation of Tenns ....................................... 21
2.3.1 Advective Acceleration Term ........................ 21
2.3.2 Resistance Term .................................... 23
2.4 Solution Methods .......................................... 24
2.4.1 Complete Equations ................................. 24
2.4.2 Simplified Equations ............................... 25
Problems .................................................. 26
3 Elementary Wave Equation .................................. 27
3.1 Simple Wave ............................................... 27
3.1.1 Propagation ........................................ 27
3.1.2 Balance Equations .................................. 28
3.2 Elementary Wave Equation .................................. 31
3.2.1 Derivation ......................................... 31
3.2.2 General Solution ................................... 32
3.2.3 Total Derivative ................................... 33
3.3 Relation between Discharge and Free-Surface Elevation in
a Progressive Wave ........................................ 34
3.4 Solution for Arbitrary Initial Conditions ................. 34
3.5 Boundary Conditions ....................................... 35
3.6 Periodic Progressive and Standing Waves ................... 37
3.6.1 Infinitely Long Canal .............................. 37
3.6.2 Semi-lnfinitely Long Canal with a Closed End ....... 39
3.6.3 Closed Basin ....................................... 39
3.6.4 Semi-Closed Basin Connected to a Reservoir or
Tideless Sea ....................................... 40
3.6.5 Semi-Closed Basin Connected to a Tidal Sea ......... 41
Problems .................................................. 42
4 Translatory Waves ......................................... 45
4.1 Introduction .............................................. 45
4.2 Low Translatory Waves in Uniform Channels ................. 46
4.3 Propagation in Non-Uniform Canals ......................... 48
4.3.1 Rapidly Varying Cross Section ...................... 48
4.3.2 Gradually Varying Cross Section .................... 51
4.4 Damping of Translatory Waves .............................. 53
4.5 High Translatory Waves .................................... 54
4.5.1 Wave Deformation ................................... 55
4.5.2 Tidal Bores ........................................ 57
4.5.3 Bore Propagation ................................... 58
4.6 Field Observations ........................................ 59
4.6.1 Observations in the Twenthekanaal .................. 59
4.6.2 Observations in the Approach Canal to the Lanaye
Lock ............................................... 63
Problems .................................................. 64
5 Method of Characteristics ................................. 67
5.1 Introduction .............................................. 67
5.2 Mathematical Formulation .................................. 68
5.3 Principle of Application .................................. 70
5.3.1 General Procedure .................................. 70
5.3.2 Characteristics .................................... 71
5.3.3 Boundary Conditions ................................ 72
5.3.4 External Forces .................................... 75
5.4 Graphical Solution Procedure .............................. 76
5.4.1 Initial Value Problem .............................. 77
5.4.2 Inclusion of the Boundary Conditions ............... 80
5.5 Simple Wave ............................................... 83
5.5.1 General Solution ................................... 83
5.5.2 Expansion Wave ..................................... 85
5.5.3 Compression Wave ................................... 86
Problems .................................................. 88
6 Tidal Basins .............................................. 91
6.1 Introduction .............................................. 91
6.2 Mathematical Formulation .................................. 92
6.2.1 Motion in the Basin ................................ 92
6.2.2 Motion in the Channel .............................. 93
6.2.3 Coupled System ..................................... 96
6.3 Linearization of the Quadratic Resistance ................. 98
6.4 System with Discrete Storage and Resistance .............. 101
6.4.1 Governing Equation ................................ 101
6.4.2 Nonhomogeneous Solution ........................... 101
6.4.3 Explicit Solution ................................. 102
6.5 System with Discrete Storage, Resistance and Inertia ..... 105
6.6 Solution through Complex Algebra ......................... 109
6.6.1 Complex Representation ............................ 109
6.6.2 Solution .......................................... 110
Problems ................................................. 111
7 Harmonic Wave Propagation ................................ 113
7.1 Introduction ............................................. 113
7.2 Complex Representation of Damped Progressive Harmonic
Waves .................................................... 114
7.3 Formulation and General Solution ......................... 116
7.3.1 Formulation ....................................... 116
7.3.2 General Solution .................................. 117
7.3.3 Solution of the Dispersion Equation ............... 118
7.3.4 Solution for the Discharge ........................ 119
7.4 Unidirectional Propagation ............................... 121
7.4.1 Physical lnteфretation ............................ 122
7.4.2 Propagation in Compound Channels .................. 124
7.5 Bi-directional Wave Propagation .......................... 126
7.5.1 Relation between the Complex Amplitudes at the
Ends of a Prismatic Section ....................... 126
7.5.2 Response Function of a Semi-Closed Prismatic
Basin ............................................. 129
7.6 Propagation in Non-Uniform Channels ...................... 131
7.6.1 Abrupt Channel Transition ......................... 131
7.6.2 Exponentially Varying Cross Section ............... 132
7.7 Propagation in Networks .................................. 137
7.8 Nonlinear Effects ........................................ 139
7.8.1 Tidal Wave Deformation ............................ 139
7.8.2 Mean Slope of the Free Surface .................... 139
Problems ................................................. 141
8 Flood Waves in Rivers .................................... 143
8.1 Introduction ............................................. 143
8.2 Quasi-Steady Approximation ............................... 144
8.3 Quasi-Uniform Approximation .............................. 145
8.3.1 Formulation and General Solution .................. 146
8.3.2 The High-Water Wave Speed ......................... 146
8.3.3 Kinematic Wave Behaviour .......................... 147
8.4 Influence of Variable Free-Surface Slope ................. 148
8.4.1 Diffusion Model for Flood Waves ................... 149
8.4.2 Elementary Solution ............................... 151
8.4.3 Observations ...................................... 152
8.5 Discussion ............................................... 153
Problems ................................................. 154
9 Steady Flow .............................................. 157
9.1 Rapidly Varying Flow ..................................... 157
9.1.1 Scaling Analysis .................................. 157
9.1.2 Flow Patterns ..................................... 158
9.1.3 Bernoulli Equation ................................ 161
9.1.4 Relations between Water Level and Discharge ....... 161
9.1.5 Hydraulic Jump .................................... 167
9.2 Gradually Varying Flow ................................... 168
9.2.1 Governing Differential Equation ................... 168
9.2.2 Integral Curves ................................... 169
9.2.3 Classification of Backwater Curves ................ 171
9.2.4 Boundary Conditions ............................... 172
9.2.5 Explicit Representation ........................... 172
9.3 Uniform Flow ............................................. 176
9.3.1 Equilibrium Relations ............................. 176
9.3.2 Resistance Relations .............................. 177
9.3.3 The Overall Resistance of a Channel ............... 181
9.3.4 Applicability to Unsteady Flow .................... 182
Problems ................................................. 182
10 Transport Processes ...................................... 185
10.1 Introduction ............................................. 185
10.2 Generic Balance Equation ................................. 186
10.3 Molecular Diffusion ...................................... 187
10.3.1 Pick's Law of Diffusion ........................... 188
10.3.2 One-Dimensional Diffusion ......................... 188
10.3.3 The Random Walk Model ............................. 192
10.3.4 Two-Dimensional Diffusion ......................... 194
10.4 Advection and Molecular Diffusion ........................ 194
10.5 Turbulent Diffusion ...................................... 196
10.5.1 Reynolds Averaging ................................ 196
10.5.2 Closure Hypothesis ................................ 197
10.6 Vertical Diffusion in Free-Surface Flows ................. 198
10.6.1 Turbulence Diffusivity ............................ 198
10.6.2 Vertical Distribution of Horizontal Velocity ...... 199
10.7 Horizontal Transport in Free-Surface Flows ............... 200
10.7.1 Introduction ...................................... 200
10.7.2 Two-Dimensional Horizontal Transport .............. 201
10.7.3 One-Dimensional Horizontal Transport .............. 207
Problems ................................................. 210
11 Numerical Computation of Solutions ....................... 211
11.1 Introduction ............................................. 211
11.2 Canal-Basin System ....................................... 212
11.2.1 Model Equations ................................... 212
11.2.2 Discretization .................................... 213
11.2.3 Semi-implicit Method .............................. 213
11.2.4 Some Other Solution Methods ....................... 215
11.2.5 Properties of the Semi-implicit Method ............ 216
11.2.6 Python Implementation ............................. 218
11.2.7 Verification ...................................... 220
11.3 Semi-Implicit Method for Long Waves ...................... 223
11.3.1 Model Equations ................................... 223
11.3.2 Discretization .................................... 224
11.3.3 Semi-Implicit Method .............................. 225
11.3.4 Some Other Solution Methods ....................... 229
11.3.5 Properties of the Semi-Implicit Method ............ 232
11.3.6 Python Implementation ............................. 235
11.3.7 Verification ...................................... 238
11.4 Characteristics-Based Methods ............................ 241
11.4.1 Characteristic Equations .......................... 241
11.4.2 Space-Time Discretization ......................... 242
11.4.3 Forward Time Backward Space Method ................ 243
11.4.4 Some Other Characteristics-Based Methods .......... 247
11.4.5 Properties ........................................ 250
11.4.6 Python Implementation ............................. 252
11.4.7 Verification ...................................... 254
Problems ................................................. 256
Appendix A Pressurized Flow in Closed Conduits ................ 259
A.1 Introduction ............................................. 259
A.2 Governing Equations ...................................... 260
A.2.1 Constitutive Equations ............................ 260
A.2.2 Conservation of Mass ............................... 262
A.2.3 Conservation of Momentum ........................... 263
A.3 Pressure Waves in Pipelines .............................. 263
A.3.1 Characteristic Equations .......................... 263
A.3.2 Physical Behaviour ................................. 264
A.4 Closure Procedures ....................................... 265
A.4.1 Abrupt Closure ..................................... 265
A.4.2 Gradual Closure .................................... 266
A.4.3 Influence of Exit Losses and/or Wall Friction ...... 269
A.4.4 Influence of Time Scales ........................... 269
Problems ................................................. 270
Appendix В Summary of Formulas ................................ 271
References .................................................... 279
Author Index .................................................. 283
Subject Index ................................................. 285
|
|
