Wave Mechanics for Ocean Engineering (eBook)

Front Cover 1
Wave Mechanics for Ocean Engineering 4
Copyright Page 5
List of Contents 20
Chapter 1. Periodic wave pattern: the approach of differential calculus 26
1.1 The irrotational flow, the continuity equation, the Bernoulli equation 26
1.2 The differential equations of an irrotational flow with a free surface 30
1.3 Introduction to wave mechanics 32
1.4 Stokes’ theory to the first order 34
1.5 Analysis of the linear dispersion rule 38
1.6 The flow field 41
1.7 Stokes’ theory to the second order 44
1.8 Non-linearity effects 46
1.9 Wave-current interaction. Part I: velocity potential and wavelength 48
1.10 Preliminary remarks on three dimensional waves 53
1.11 Wave reflection 54
1.12 Wave diffraction 59
Conclusive note 63
References 63
Chapter 2. Periodic wave pattern: the control volume approach 64
2.1 The linear momentum equation for a control volume 64
2.2 The energy equation for a control volume 67
2.3 Radiation stress, mean energy flux, mean wave energy per unit surface 71
2.4 Formulae for radiation stress and mean energy flux of progressive waves 73
2.5 The problem of the control volume extending from deep to shallow water 79
2.6 Practical consequences of the control volume problem 83
2.7 A current associated with the wave motion 86
2.8 Wave refraction for an arbitrary configuration of the seabed 90
2.9 The group celerity 95
2.10 Wave-current interaction. Part II: shoaling and set-down 99
Conclusive note 110
References 111
Chapter 3. Wave effects on coasts 112
3.1 The control volume from the breaker line to the beach 112
3.2 The run-up 113
3.3 The longshore transport 117
3.4 The analytical approach to the problem of beach planform evolution 119
3.5 Problem of beach planform evolution: the case of contour lines parallel up to deep water 120
3.6 Problem of beach planform evolution: the case of contour lines parallel only within a certain distance from the shoreline 125
3.7 Planform evolution of a natural shoreline 128
3.8 Stability of a nourished beach 129
3.9 Planform evolution of beach nourishment projects 132
3.10 A useful simplification 136
3.11 Beach planform evolution caused by structures 138
Conclusive note 141
References 143
Chapter 4. Wind generated waves: basic concepts 144
4.1 The sea state 144
4.2 The theory of the sea states 146
4.3 Some basic relations in the theory of the sea states 148
4.4 How to obtain the input data of the theory 151
4.5 A mathematical form of the wind wave spectrum 161
4.6 Possibility of testing small scale models in sea or lakes 165
4.7 Inferring the nature of waves from the bandwidth 170
Conclusive note 175
References 176
Chapter 5. Analysis of the sea states: the time domain 178
5.1 Why the surface displacement represents a stationary Gaussian process 178
5.2 Joint probability of surface displacements 182
5.3 Rice's problem 184
5.4 Rice's logic 186
5.5 Corollaries of Rice's problem 187
5.6 Solved and still unsolved problems 191
5.7 The period of a very high wave and the wave height probability under general bandwidth assumptions 192
5.8 Experimental verification 197
5.9 Characteristic wave heights 200
5.10 The maximum expected wave height in a sea state of given duration 202
Conclusive note 205
References 206
Chapter 6. The wave climate 208
6.1 The function Hs (t) 208
6.2 The probability of the significant wave height 211
6.3 The probability of the significant wave height for a given direction of wave advance 216
6.4 Probabilities of the significant wave height for a few areas of the globe 221
6.5 The maximum expected wave height in a storm with a given history 224
6.6 The concept of "equivalent triangular storm" 225
6.7 Storm durations 229
Conclusive note 231
References 231
Chapter 7. Design waves and risk analysis 232
7.1 The return period of a sea storm where the significant wave height exceeds a fixed threshold 232
7.2 The significant wave height and its persistence vs the return period 236
7.3 The encounter probability 238
7.4 The chain: lifetime, encounter probability – return period – significant wave height 246
7.5 Coastal structures: the design sea state 248
7.6 The return period of a wave with a height exceeding a fixed threshold 251
7.7 The return period of a sea storm containing at least one wave higher than a fixed threshold 253
7.8 Offshore structures: the design wave 260
7.9 Calculations for different wave directions 264
7.10 Corollary of risk analysis: a general relation between the confidence interval and the sampling rate 267
Conclusive note 271
References 272
Chapter 8. Analysis of the sea states in the space-time 274
8.1 The concept of homogeneous wave field 274
8.2 The wave field in the open sea 276
8.3 The directional spectrum 279
8.4 Shoaling and refraction of the wind-generated waves 282
8.5 Reflection of the wind-generated waves 288
8.6 Diffraction of the wind-generated waves 292
8.7 Long-crested random waves: the link between periodic waves and wind- generated waves 295
8.8 Direct proportion between the maximum expected wave height and the diffraction coefficient 299
8.9 Space-time covariances 301
Conclusive note 304
References 304
Chapter 9. The theory of quasi-determinism 306
9.1 A sufficient condition for occurrence of a wave of given height very large 306
9.2 A necessary condition for occurrence of a wave of given height very large 311
9.3 The water surface on space-time, if a wave of given height very large occurs at a fixed point 313
9.4 The velocity potential if a wave of given height very large occurs at a fixed point 316
9.5 Theory's generality and consistency with Stokes' theory 318
9.6 Formal proof of the necessary condition. Part I: symbols and assumptions 319
9.7 Formal proof of the necessary condition. Part II: core of the proof 321
9.8 Formal proof of the necessary condition. Part III: the central inequality 325
9.9 Formal proof of the necessary condition. Part IV: conclusion 328
9.10 Corollary: the closed solution for the wave height distribution 331
Chapter 10. Uses and consequences of the quasi-determinism theory 336
10.1 The first way to employ the theory 336
10.2 A three dimensional wave group 342
10.3 The waves are higher on the time domain than on the space domain! 343
10.4 Effects of water depth and of spectrum shape on the wave group 345
10.5 Shoaling and refraction of the wave group 349
10.6 Explanation of the first big difference between sea waves and periodic waves 351
10.7 Explanation of the second big difference between sea waves and periodic waves 360
10.8 The second way to employ the theory 364
10.9 The "genetic code" of the sea waves 371
10.10 The determinism arises from within the random waves 375
Conclusive note 383
References 384
Chapter 11. Analysis of the wave forces on offshore structures 386
11.1 Wave forces on gravity offshore platforms 386
11.2 Local perturbation of the flow field at an offshore structure 389
11.3 Wave forces on submerged tunnels 392
11.4 The diffraction coefficients of the forces 398
11.5 Wave forces on space frame structures 408
11.6 The long-structure problem 412
Conclusive note 417
References 417
Chapter 12. Calculation of the wave forces on offshore structures 418
12.1 Calculation of the wave forces on a gravity offshore platform 418
12.2 Calculation of the wave forces on a space frame structure 422
12.3 Design of a submerged tunnel. I: calculation of the wave forces 427
12.4 Design of a submerged tunnel. II: the effect of currents 437
12.5 Design of a submerged tunnel. III: the risk of resonance 438
Chapter 13. Stability analysis of coastal structures 444
13.1 Wave pressure on a wall 444
13.2 Forces on a vertical breakwater 452
13.3 Design of vertical breakwaters 455
13.4 Further verifications of the vertical breakwaters 461
13.5 The Japanese practice 463
13.6 The problem of the rubble mound breakwaters 466
Conclusive note 470
References 470
Chapter 14. Topics calling for an overall overview of offshore and coastal engineering 472
14.1 A comparison between tsunami and wind waves from the open sea to the coast 472
14.2 Small scale models 475
14.3 Wave measurements 480
Conclusive note 486
References 486
Appendix A: Appendix to chapters 6 and 7: use of wave hindcast and wave measurements from satellites 488
A.1 Long term wave statistics from satellite data 488
A.2 Wave hindcast 489
A.3 Trend in the wave climate and its effects on engineering 495
References 498
Appendix B: Appendix to chapters 9 and 10: the wave group of the maximum expected crest elevation, and the wave group of the maximum expected crest-to-trough height 500
B.1 The first version of the quasi-determinism theory 500
B.2 Corollaries of the first version 505
B.3 The relationship between the two versions of the theory 507
Conclusive note 510
References 510
Subject Index 512
Author Index 518