Preface ...................................................... xvii
Notation ...................................................... xix
1 Introduction ................................................. 1
1.1 Generation of a Sea ..................................... 1
1.2 Wind Classification and Sea State ....................... 4
1.3 Ocean Engineering Literature ............................ 4
2 Review of Hydromechanics ..................................... 7
2.1 Hydrostatics ............................................ 7
Example 2.1: Pressure Hull Analysis .......................... 9
2.2 Conservation of Mass ................................... 11
Example 2.2: Flow Through a Manifold ........................ 13
2.3 Rotational and Irrotational Flows ...................... 14
A. Circulation ......................................... 15
B. The Velocity Potential .............................. 16
С. The Stream Function ................................. 17
D. Superposition of Irrotational Flow Patterns ......... 19
Example 2.3: Two-Dimensional Irrotational Flow about
a Circular Cylinder ........................... 19
2.4 Conservation of Momentum and Energy .................... 21
Example 2.4: Pressure Distribution on a Cylinder in
an Irrotational Flow ........................... 22
Example 2.5: Incipient Cavitation on a Vertical Circular
Cylinder ....................................... 23
2.5 Viscous Flows .......................................... 24
Example 2.6: Drag and Vortex Shedding for an OTEC
Cold-Water Pipe ................................ 27
2.6 Hydrodynamics of Submerged Bodies ...................... 30
Example 2.7: Flow about a Sphere ............................ 32
Example 2.8: Flow about a Body of Revolution ................ 35
2.7 Scaling ................................................ 37
Example 2.9: Wave Power Conversion .......................... 42
2.8 Closing Remarks ........................................ 43
3. Linear Surface Waves ........................................ 44
3.1 Wind-Wave Generation ................................... 45
3.2 Airy's Linear Wave Theory .............................. 47
Example 3.1: Linearization .................................. 49
3.3 Traveling or Progressive Waves ......................... 52
Example 3.2: Wavelength Variation with Water Depth .......... 53
Example 3.3: Wavelength Solution by Successive
Approximations ................................. 54
Example 3.4: Deep- and Shallow-Water Wavelength
Approximations ................................. 55
3.4 Standing Waves ......................................... 56
Example 3.5: Standing Waves at a Seawall .................... 57
3.5 Water Particle Motions ................................. 59
3.6 The Wave Group ......................................... 61
Example 3.6: Deep-Water Wave Group .......................... 63
3.7 Wave Energy and Power .................................. 64
Example 3.7: Deep- and Shallow-Water Wave Energy ............ 65
Example 3.8: Deep- and Shallow-Water Wave Power ............. 66
Example 3.9: Wave Power Conversion .......................... 67
3.8 Shoaling ............................................... 68
3.9 Closing Remarks ........................................ 72
4 Nonlinear Surface Waves ..................................... 73
4.1 Nonlinear Wave Properties .............................. 74
4.2 Stokes' Wave Theory .................................... 76
Example 4.1: Deep- and Shallow-Water Free-Surface
Profiles ....................................... 83
Example 4.2: Free-Surface Displacement in Deep Water ........ 85
4.3 Second-Order Particle Motions .......................... 86
4.4 Water Particle Convection .............................. 88
Example 4.3: Deep- and Shallow-Water Particle Convection
Velocities ..................................... 89
Example 4.4: Wave-Induced Spreading of a Surface Spill ...... 91
4.5 Long Waves in Shallow Water ............................ 92
A. Cnoidal Wave Theory ................................. 92
B. Application of the Cnoidal Theory ................... 98
Example 4.5: Application of the Cnoidal Theory ............. 100
С. The Solitary Wave .................................. 101
Example 4.6: Application of the Solitary Theory ............ 102
4.6 Breaking Waves ........................................ 104
A. Stokes' Deep-Water Analysis ........................ 104
B. Miche's Formula: Breaking Waves in Waters of
Finite Depth ....................................... 106
Example 4.7: Theoretical, Deep-Water Breaking Wave
Profiles ...................................... 107
С. Breaking Solitary Waves ............................ 108
Example 4.8: Breaking Height of a Shoaling Solitary
Wave .......................................... 110
4.7 Summary ............................................... 111
4.8 Closing Remarks ....................................... 112
5. Random Seas ................................................ 113
5.1 Introduction .......................................... 113
5.2 Statistical Analysis of Measured Waves ................ 115
Example 5.1: Cumulative Probability of Occurrence .......... 117
Example 5.2: Probability Density and Most-Probable Wave
Height ........................................ 118
A. Average Wave Period and Wave Height ................ 119
B. Mean-Square and Root-Mean-Square Wave Heights ...... 120
С. Variance of the Wave Heights ....................... 120
Example 5.3: Average Wave Period and Statistical Wave
Heights ....................................... 120
D. Significant Wave Height and Period ................. 120
Example 5.4: Significant Wave Properties ................... 121
5.3 Continuous Probability Distributions .................. 122
A. Average Wave Period and Wave Height ................ 122
B. Mean-Square Wave Height ............................ 123
С. Variance of the Wave Heights ....................... 123
D. Significant Wave Height ............................ 123
5.4 Rayleigh Probability Distribution of Wave Heights ..... 124
Example 5.5: Rayleigh Probability Density and
Probability Functions ......................... 125
A. Average Wave Height ................................ 125
B. Probability of Exceedance .......................... 126
C. Significant Wave Height ............................ 126
D. Extreme Wave Height ................................ 127
Example 5.6: Significant and Extreme Wave Heights .......... 127
5.5 Weibull Probability Distribution of Wave Heights ...... 127
Example 5.7: Weibull Probability Density and
Probability Functions .................... 129
5.6 The Gaussian-Rayleigh Sea ............................. 129
Example 5.8: Root-Mean-Square Wave Properties ......... 132
5.7 Wave Spectral Density ................................. 133
A. Point Spectra from Discrete Wave Data .............. 134
Example 5.9: Wave Spectral Density from Discrete Wave
Data .......................................... 135
B. Empirical Expressions of the Point Spectral
Density ............................................ 136
5.8 Wind-Wave Spectra ..................................... 137
A. Statistical Wave Periods ........................... 138
Example 5.10: Statistical Wave Periods ..................... 139
B. The Bretschneider Spectrum ......................... 140
C. The Pierson-Moskowitz Wind-Wave Spectrum ........... 141
Example 5.11: Comparison of Open-Ocean Wind-Wave
Spectra ...................................... 143
D. The JONSWAP Spectra - the Fetch-Limited Sea ........ 144
E. Wave Property Relationships from Empirical
Wind-Wave Spectra .................................. 145
(1) Fully Developed, Open-Ocean Seas .............. 145
(2) Fetch-Limited Seas ............................ 147
(3) Duration-Limited Seas ......................... 148
Example 5.12: Fetch-Limited and Duration-Limited Seas ...... 148
F. Directional Properties of Wind-Generated Waves ..... 150
Example 5.13: Wave Power Resource Determination for
a Directional Sea ............................ 153
5.9 Long-Term Wave Statistics ............................. 156
5.10 Wave Spectra in Waters of Finite Depth ................ 158
Example 5.14: Bretschneider Spectra in Deep Water and
Waters of Finite Depth ....................... 159
5.11 Closing Remarks ....................................... 160
6. Wave Modification and Transformation ....................... 161
6.1 Wave Reflection from Vertical Barriers ................ 162
A. Perfect Reflection of Linear, Monochromatic
Waves .............................................. 164
Example 6.1: Perfect Oblique Reflection .................... 166
B. Imperfect Reflection of Direct, Monochromatic,
Linear Waves - Healy's Formula ..................... 167
Example 6.2: Direct Partial Reflection of Linear Waves ..... 168
C. Reflection from a Vertical Porous Barrier .......... 169
Example 6.3: Partial Reflection from a Porous
Breakwater .................................... 170
6.2 Reflection from Inclined Barriers - The Long-Wave
Equations ............................................. 171
A. The Long-Wave Equations ............................ 172
B. Perfect Reflection from an Inclined Barrier ........ 174
Example 6.4: Totally Reflected Waves on an Inclined
Barrier ....................................... 178
С. Nonreflecting Beaches .............................. 179
Example 6.5: Shoaling on a Nonreflecting Beach ............. 180
D. Reflection from a Bed of Intermediate Slope ........ 182
Example 6.6: Convergence of the Reflection Coefficient
and Phase Angle ............................... 184
Example 6.7: Reflection from a Bed Transition .............. 185
6.3 Refraction without Reflection - Snell's Law ........... 185
Example 6.8: Shoaling and Refraction on a Straight,
Parallel Contoured Beach ...................... 187
6.4 Diffraction ........................................... 188
A. Huygens' Principle ................................. 189
B. Basic Equations and Boundary Conditions in
the Analysis of Diffraction ........................ 190
С. Modified Huygens-Fresnel Principle ................. 192
D. Diffraction Analyses of Water Waves ................ 198
(1) Diffraction of Waves Directly Incident
upon a Semi-Infinite Breakwater ............... 198
Example 6.9: Diffraction Coefficients along the Leeward
Sides of Rigid and Compliant Breakwaters ...... 203
(2) Diffraction of Waves Obliquely Incident
upon a Semi-Infinite Breakwater ............... 204
Example 6.10: Diffraction Coefficients along the Leeward
Sides of a Rigid Breakwater ................... 205
(3) Diffraction of Waves by a System of
Detached Breakwaters .......................... 207
Example 6.11:Waves Directly Incident on a Gap between
Semi-Infinite Breakwaters ..................... 211
6.5 The Mild-Slope Equation ............................... 212
A. Derivation of the Mild-Slope Equation .............. 213
B. Application to a Straight and Parallel Contoured
Bed ................................................ 216
Example 6.12:Application of the Mild Slope to Pure
Shoaling ...................................... 221
6.6 Closing Remarks ....................................... 223
7. Waves in the Coastal Zone .................................. 224
7.1 Coastal Zone Phenomena ................................ 225
7.2 Empirical Analyses of Breaking Waves on Beaches ....... 226
Example 7.1: Breaking Wave Properties over a Flat,
Horizontal Bed ................................ 229
Example 7.2: Breaking Wave Properties on a Beach of
Uniform Slope - Empirical Equations ........... 230
7.3 Surf Similarity ....................................... 231
A. Breaking Waves ..................................... 232
B. Wave Reflection .................................... 233
C. Runup .............................................. 233
Example 7.3: Breaking Wave Properties on a Beach of
Uniform Slope - Surf Similarity ............... 234
7.4 Surf Zone Hydromechanics - Radiation Stress ........... 234
A. Radiation Stress ................................... 235
(1) Radiation Stress in the Direction of Wave
Travel ........................................ 235
(2) Radiation Stress Transverse to the Wave
Travel ........................................ 237
(3) Radiation Stress Matrix ....................... 237
Example 7.4: Comparison of Radiation Stress in Deep and
Shallow Waters ................................ 238
(4) Transformation of the Radiation Stress
Matrix ........................................ 238
Example 7.5: Normal and Diagonal Radiation Stress
Components for a Breaking Wave ................ 240
B. Wave Set-Up and Set-Down ........................... 240
Example 7.6: Comparison of Theoretical and Experimental
Wave Height, Water Depth, and Set-Down at
a Break and Runup ............................. 245
Example 7.7: Set-Up in the Surf Zone ....................... 246
C. Longshore Velocity ................................. 246
(1) Negligible Lateral Mixing ..................... 251
(2) Negligible Bed Friction ....................... 251
(3) Combined Bed Friction and Lateral Mixing
Effects ....................................... 251
Example 7.8: Maximum Longshore Velocity .................... 254
D. Average Longshore Volume Flow Rate ................. 255
Example 7.9: Longshore Volume Transport Rate ............... 256
Example 7.10:Longshore Sediment Transport Rate ............. 257
7.5 Closing Remarks ....................................... 257
8. Coastal Engineering Considerations ......................... 258
8.1 Shore Protection Methods .............................. 258
Example 8.1: Planning a Groin Field ........................ 261
8.2 Decision Process in Coastal Protection ................ 262
Example 8.2: Decision Tree for Shoreline Erosion
Abatement ..................................... 262
8.3 Rubble-Mound Structures ............................... 263
A. Stone Selection for Rubble-Mound Breakwaters ....... 265
(1) Armor Stone ................................... 265
(2) Shield Stone .................................. 265
(3) Foundation Stone .............................. 265
(4) Toe-Berm Stone ................................ 266
Example 8.3: Preliminary Design of a Rubble-Mound
Breakwater .................................... 267
8.4 Reliability of a Rubble-Mound Structure ............... 268
Example 8.4: Reliability of a Rubble-Mound Breakwater ...... 269
Example 8.5: Weibull Reliability of a Rubble-Mound
Breakwater .................................... 271
8.5 Closing Remarks ....................................... 272
9 Wave-Induced Forces and Moments on Fixed Bodies ............ 273
9.1 Wave-Induced Forces and Moments on a Seawall .......... 274
A. Pressure, Force, and Moment Resulting from Direct
Reflection of Linear Waves ......................... 274
Example 9.1: Wave Force and Moment on a Seawall Due to
Standing Linear Waves ......................... 276
B. Pressure and Force Resulting from Direct
Reflection of a Solitary Wave ...................... 276
Example 9.2: Pressure Distribution on a Seawall beneath
a Solitary Wave ............................... 279
9.2 Wave-Induced Forces on Submerged and Surface-
Piercing Bodies ....................................... 280
A. The Concept of Added Mass .......................... 280
(1) Cylinders with Circular Cross-Sections ........ 282
(2) Cylinders with Noncircular Cross-Sections -
Lewis Forms ................................... 283
Example 9.3: Two Lewis Forms ............................... 286
Example 9.4: Added Mass of a Noncircular Cylinder .......... 288
B. Natures of Wave-Induced Forces on Circular
Cylinders .......................................... 289
C. Wave-Induced Drag Forces ........................... 290
D. The Morison Equation ............................... 292
Example 9.5: Force and Moment on a Vertical Circular Pile
in Shallow Water .............................. 294
E. Circular Cylinders of Large Diameter - The
MacCamy-Fuchs Analysis ............................. 297
Example 9.6: Force and Moment on a Cofferdam in Shallow-
Water Linear Waves ............................ 303
F. Mass Coefficient for a Circular Cylinder ........... 304
G. Diffraction Force and Moment on a Rectangular
Cylinder ........................................... 305
Example 9.7: Force and Moment on a Square Cylinder in
Shallow-Water Linear Waves .................... 307
H. Truncated Circular Cylinder of Large Diameter ...... 307
(1) Approximations of the Horizontal Force and
Resulting Moment .............................. 308
(2) Approximations of the Vertical Force and
Resulting Moment .............................. 309
Example 9.8: Wave-Induced Forces on a Spar Work Platform ... 311
(3) Garrett's Analysis ............................ 312
(4) Results of the Approximate and Garrett
Forces ........................................ 322
I. Scattering Effects of Large-Diameter Leg Arrays .... 324
Example 9.9: Wave-Induced Forces on an In-Line, Two-Leg
Platform ...................................... 332
9.3 Wave-Induced Forces and Moments on Bodies in Random
Seas .................................................. 334
A. Spectral Nature of Wave-Induced Viscous-Pressure
and Inertia Forces ................................. 336
Example 9.10:Predicted and Measured Wave and Force
Spectra on a Circular Pile .................... 338
B. Probabilistic Nature of the Viscous-Pressure and
Inertia Wave Forces ................................ 338
Example 9.11:Probabilities of Occurrence for the Maximum
Drag Force on a Circular Pile ................. 342
Example 9.12:Most-Probable Maximum Force for the 100-Year
Storm ......................................... 343
C. Random Nature of Diffraction Forces on a Fixed,
Vertical Circular Cylinder ......................... 345
Example 9.13:Diffraction Forces on a Monolithic Gravity
Structure ..................................... 346
Example 9.14:Extreme Diffraction Forces on a Monolithic
Gravity Structure ............................. 348
9.4 Closing Remarks ...................................... 349
10 Introduction to Wave-Structure Interaction ................. 350
10.1 Basic Concepts ........................................ 350
A. Equations of Motion ................................ 351
B. Added Mass and Radiation Damping ................... 352
C. Equivalent Viscous Damping Coefficient ............. 354
D. Steady-State Solution of the Heaving Equation ...... 356
Example 10.1:Heaving Motion of a Can Buoy .................. 356
E. Determination of Added Mass and Resonant Damping
Coefficients in Calm Water ......................... 358
Example 10.2:Experimental Determination of Heaving Added
Mass and Damping Logarithmic Decrement
Method ........................................ 360
F. Bandwidth Determination of Damping in Wave-
Induced Heaving Motions ............................ 361
Example 10.3:Experimental Determination of Damping in
Wave-Induced Heaving-Half-Power Bandwidth
Method ........................................ 363
Example 10.4:Experimental Determination of Component
Damping Coefficients .......................... 364
10.2 Power Take-Off ....................................... 365
Example 10.5:Power Take-Off of a Heaving Circular
Cylinder at Resonance ......................... 366
10.3 Random Motions ....................................... 368
Example 10.6:Root-Mean-Square Heaving Response of Under
damped Motions of a Can Buoy in a Random
Sea ........................................... 371
Example 10.7:Root-Mean-Square and Extreme Heaving
Amplitudes of Highly Damped Motions of
a Can Buoy in a Random Sea .................... 372
10.4 Closing Remarks ...................................... 375
11 Wave-Induced Motions of Floating Bodies .................... 376
11.1 Hydrostatic Considerations - Initial Stability ....... 377
Example 11.1:Roll Stability of a Can Buoy .................. 380
11.2 Floating Body Motions ................................ 380
A. Boundary Condition on the Body ..................... 381
Example 11.2:Body Condition for a Semi-Submerged,
Heaving Sphere ................................ 382
B. Heaving and Pitching Equations of Motion ........... 383
C. Introduction to Strip Theory ....................... 384
(1) Hydrostatic Restoring Force and Moment ........ 386
(2) Viscous Damping Force and Moment .............. 386
(3) Hydrodynamic Forces and Moments ............... 387
D. Coupled Heaving and Pitching Equations of Motion ... 390
11.3 Two-Dimensional Hydrodynamics - Vertical Body
Motions ............................................... 392
A. Strip Geometries - Lewis Forms ..................... 393
Example 11.3:Lewis Ship-Shape Section (Strip) .............. 396
B. Velocity Potentials ................................ 398
(1) Incident Wave Potential ....................... 398
(2) Vertical Motions of Lewis Forms - Velocity
Potential and Stream Function ................. 399
Example 11.4:Velocity Potential and Stream Function for
a Heaving Circular Strip ...................... 401
(3) Velocity Potential for the Wave-Body
Interaction ................................... 402
(4) Total Velocity Potential ...................... 402
C. Hydrodynamic Pressures and Forces on the Strip
in Deep Water ...................................... 402
(1) Wave-Induced Pressure and Force ............... 403
Example 11.5:Wave-Induced Vertical Forces on Two Strip
Geometries .................................... 405
(2) Motion-Induced Pressure and Force ............. 407
Example 11.6:Spatial Variation of a Semicircular
Sectional Area ................................ 408
Example 11.7:Motion-Induced Vertical Forces on Two Strip
Geometries .................................... 410
(3) Wave-Body Interaction Pressure and Force on
a Strip ....................................... 411
Example 11.8:Wave-Body Interaction Forces on Two Strip
Geometries .................................... 413
D. Radiation Damping .................................. 415
Example 11.9:Radiation Damping Coefficients Using the
YFF Formula ................................... 416
Example 11.10:Radiation Damping Coefficient Using the
Tasai Formula ................................. 417
11.4 Coupled Heaving and Pitching Motions Based on Strip
Theory ................................................ 419
Example 11.11:Transverse Stability and Planar Motions
of a Barge in Linear Waves .................... 422
11.5 Experimental and Theoretical Hydrodynamic
Coefficient Data ...................................... 431
A. Modification of the Lewis Added-Mass Coefficients
to Include Frequency Dependence .................... 431
B. Vertical Motions of a Rectangular Section .......... 432
C. Vertical Motions of a Semicircular Section ......... 433
11.6 Singularity Method of Determining the Hydrodynamic
Coefficients .......................................... 434
A. The Source Pair .................................... 436
B. Distributed Sources - Rectangular Strip ............ 438
(1) Alternative Infinite-Frequency Added Mass
of a Heaving Rectangular Strip ................ 440
Example 11.12:Alternative Expression for the Added Mass
for a Heaving Rectangular Strip ............... 442
(2) Radiation Damping of a Heaving Rectangular
Strip ......................................... 444
Example 11.13:Radiation Damping Coefficient for a Heaving
Rectangular Strip ............................. 445
11.7 Two-Dimensional Haskind Force Relationships ........... 446
A. Newman's Formulation ............................... 446
B. Wave-Induced Vertical Force on Rectangular
Section ............................................ 451
Example 11.14:Wave-Induced Forces on a Heaving
Rectangular Strip ............................. 451
11.8 Closing Remarks ....................................... 452
12 Wave-Induced Motions of Compliant Structures ............... 453
12.1 Compliant Structures .................................. 453
12.2 Basic Mooring Configurations .......................... 455
A. Taut Moorings ...................................... 455
Example 12.1: Tension in a SeaStar Tether .................. 457
B. Slack Moorings ..................................... 458
Example 12.2:Effective Spring Constant for Slack Line ...... 461
Example 12.3:Effective Spring Constant for a Barge
Moored with Four Slack Lines .................. 464
12.3 Soil-Structure Interactions ........................... 465
A. Embedded Structures ................................ 468
(1) Bending Deflection in the Plastic Zone ......... 470
(2) Bending Deflection in the Elastic Zone ......... 471
(3) Complete Bending Solution ...................... 471
(4) Comparison of Analysis and Data ............... 473
B. Spread Footings - Gravity Structures ............... 474
12.4 Motions of a Tension-Leg Platform (TLP) .............. 476
A. Tethers ............................................ 478
Example 12.4:Effective Spring Constants for a TLP .......... 479
B. Soil Reactions ..................................... 479
С. Wave-Induced Forces ................................ 480
(1) Drag Force .................................... 481
(2) Diffraction Force ............................. 482
D. Hydrodynamic Coefficients for a Spar ............... 483
(1) Heaving Added Mass and Radiation Damping ...... 484
Example 12.5:Added-Mass and Radiation-Damping
Coefficients for a Heaving Vertical
Cylindrical Hull in Water of Finite Depth ..... 486
(2) Surging Added Mass and Radiation Damping ...... 486
E. Surging Motions in Regular Seas .................... 489
Example 12.6:Surging Motions of a TLP ...................... 491
F. Surging Motions in Random Seas ..................... 495
Example 12.7:Root-Mean-Square Surge Response of Motions
of a TLP ...................................... 496
Example 12.8:Spectral Density of the Surge Response of
Motions of a TLP .............................. 497
12.5 Motions of an Articulated-Leg Platform (ALP) ......... 498
Example 12.9:Wave-Induced Motions of an ALP .......... 506
12.6 Motions of Flexible Towers ........................... 509
A. Effective Spring Constants ......................... 511
B. Analysis of the Motions of a Flexible Offshore
Tower (FOT) ........................................ 514
(1) Swaying Motions of a FOT ...................... 515
Example 12.10:First Modal Swaying Frequency of a FOT ....... 517
Example 12.11:First Modal Swaying Frequency of a Three-
Panel FOT .................................... 518
(2) Bending Motions of a TRAP .................... 519
Example 12.12:Deflection of a TRAP in a Design Sea ......... 525
12.7 Closing Remarks ....................................... 528
Appendices ................................................. 529
A. Bessel Functions ................................... 529
B. Runga-Kutta Solution of Differential Equations ..... 530
C. Green's Theorem .................................... 532
C1. Three-Dimensional Green's Theorem .............. 532
C2. Two-Dimensional Green's Theorem ................ 533
C3. Green's Theorem Applied to an Irrotational
Flow ........................................... 533
D. Green's Function ................................... 534
D1. Three-Dimensional Green's Function ............. 534
(1) Three-Dimensional Flow Source ............. 534
(2) Three-Dimensional Wave Source ............. 536
D2. Two-Dimensional Green's Function ............... 536
E. Solutions of Laplace's Equation .................... 537
El. Cartesian Coordinates .......................... 538
E2. Cylindrical Coordinates ........................ 539
F. Fourier Transforms ................................. 540
G. Lewis Sharp-Bilge Analysis ......................... 541
H. Infinite-Frequency Added-Mass Expressions .......... 544
HI. Two-Dimensional Added Mass ..................... 544
(1) Motions in an Infinite Liquid ............. 544
(2) Motions of a Rectangular Section in
Liquid with a Free Surface ................ 546
H2. Three-Dimensional Added Mass ................... 547
(1) Flat Plate Motions in an Infinite
Liquid .................................... 547
(2) Motions of a Sphere in an Infinite
Liquid and beneath a Free Surface ......... 547
H3. Frequency-Dependent Added Mass ................. 548
References .................................................... 549
Index ......................................................... 575
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