Wave Mechanics for Ocean Engineering
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Table of contents
- Cover
- List of ContentsXIX
- Chapter 1. Periodic wave pattern: the approach of differential calculus1
- 1.1 The irrotational flow, the continuity equation, the Bernoulli equation1
- 1.2 The differential equations of an irrotational flow with a free surface5
- 1.3 Introduction to wave mechanics7
- 1.4 Stokes’ theory to the first order9
- 1.5 Analysis of the linear dispersion rule13
- 1.6 The flow field16
- 1.7 Stokes’ theory to the second order19
- 1.8 Non-linearity effects21
- 1.9 Wave-current interaction. Part I: velocity potential and wavelength23
- 1.10 Preliminary remarks on three dimensional waves28
- 1.11 Wave reflection29
- 1.12 Wave diffraction34
- Conclusive note38
- References38
- Chapter 2. Periodic wave pattern: the control volume approach39
- 2.1 The linear momentum equation for a control volume39
- 2.2 The energy equation for a control volume42
- 2.3 Radiation stress, mean energy flux, mean wave energy per unit surface46
- 2.4 Formulae for radiation stress and mean energy flux of progressive waves48
- 2.5 The problem of the control volume extending from deep to shallow water54
- 2.6 Practical consequences of the control volume problem58
- 2.7 A current associated with the wave motion61
- 2.8 Wave refraction for an arbitrary configuration of the seabed65
- 2.9 The group celerity70
- 2.10 Wave-current interaction. Part II: shoaling and set-down74
- Conclusive note85
- References86
- Chapter 3. Wave effects on coasts87
- 3.1 The control volume from the breaker line to the beach87
- 3.2 The run-up88
- 3.3 The longshore transport92
- 3.4 The analytical approach to the problem of beach planform evolution94
- 3.5 Problem of beach planform evolution: the case of contour lines parallel up to deep water95
- 3.6 Problem of beach planform evolution: the case of contour lines parallel only within a certain di100
- 3.7 Planform evolution of a natural shoreline103
- 3.8 Stability of a nourished beach104
- 3.9 Planform evolution of beach nourishment projects107
- 3.10 A useful simplification111
- 3.11 Beach planform evolution caused by structures113
- Conclusive note116
- References118
- Chapter 4. Wind generated waves: basic concepts119
- 4.1 The sea state119
- 4.2 The theory of the sea states121
- 4.3 Some basic relations in the theory of the sea states123
- 4.4 How to obtain the input data of the theory126
- 4.5 A mathematical form of the wind wave spectrum136
- 4.6 Possibility of testing small scale models in sea or lakes140
- 4.7 Inferring the nature of waves from the bandwidth145
- Conclusive note150
- References151
- Chapter 5. Analysis of the sea states: the time domain153
- 5.1 Why the surface displacement represents a stationary Gaussian process153
- 5.2 Joint probability of surface displacements157
- 5.3 Rice's problem159
- 5.4 Rice's logic161
- 5.5 Corollaries of Rice's problem162
- 5.6 Solved and still unsolved problems166
- 5.7 The period of a very high wave and the wave height probability under general bandwidth assumptio167
- 5.8 Experimental verification172
- 5.9 Characteristic wave heights175
- 5.10 The maximum expected wave height in a sea state of given duration177
- Conclusive note180
- References181
- Chapter 6. The wave climate183
- 6.1 The function Hs (t)183
- 6.2 The probability of the significant wave height186
- 6.3 The probability of the significant wave height for a given direction of wave advance191
- 6.4 Probabilities of the significant wave height for a few areas of the globe196
- 6.5 The maximum expected wave height in a storm with a given history199
- 6.6 The concept of "equivalent triangular storm"200
- 6.7 Storm durations204
- Conclusive note206
- References206
- Chapter 7. Design waves and risk analysis207
- 7.1 The return period of a sea storm where the significant wave height exceeds a fixed threshold207
- 7.2 The significant wave height and its persistence vs the return period211
- 7.3 The encounter probability213
- 7.4 The chain: lifetime, encounter probability – return period – significant wave height221
- 7.5 Coastal structures: the design sea state223
- 7.6 The return period of a wave with a height exceeding a fixed threshold226
- 7.7 The return period of a sea storm containing at least one wave higher than a fixed threshold228
- 7.8 Offshore structures: the design wave235
- 7.9 Calculations for different wave directions239
- 7.10 Corollary of risk analysis: a general relation between the confidence interval and the sampling242
- Conclusive note246
- References247
- Chapter 8. Analysis of the sea states in the space-time249
- 8.1 The concept of homogeneous wave field249
- 8.2 The wave field in the open sea251
- 8.3 The directional spectrum254
- 8.4 Shoaling and refraction of the wind-generated waves257
- 8.5 Reflection of the wind-generated waves263
- 8.6 Diffraction of the wind-generated waves267
- 8.7 Long-crested random waves: the link between periodic waves and wind- generated waves270
- 8.8 Direct proportion between the maximum expected wave height and the diffraction coefficient274
- 8.9 Space-time covariances276
- Conclusive note279
- References279
- Chapter 9. The theory of quasi-determinism281
- 9.1 A sufficient condition for occurrence of a wave of given height very large281
- 9.2 A necessary condition for occurrence of a wave of given height very large286
- 9.3 The water surface on space-time, if a wave of given height very large occurs at a fixed point288
- 9.4 The velocity potential if a wave of given height very large occurs at a fixed point291
- 9.5 Theory's generality and consistency with Stokes' theory293
- 9.6 Formal proof of the necessary condition. Part I: symbols and assumptions294
- 9.7 Formal proof of the necessary condition. Part II: core of the proof296
- 9.8 Formal proof of the necessary condition. Part III: the central inequality300
- 9.9 Formal proof of the necessary condition. Part IV: conclusion303
- 9.10 Corollary: the closed solution for the wave height distribution306
- Chapter 10. Uses and consequences of the quasi-determinism theory311
- 10.1 The first way to employ the theory311
- 10.2 A three dimensional wave group317
- 10.3 The waves are higher on the time domain than on the space domain!318
- 10.4 Effects of water depth and of spectrum shape on the wave group320
- 10.5 Shoaling and refraction of the wave group324
- 10.6 Explanation of the first big difference between sea waves and periodic waves326
- 10.7 Explanation of the second big difference between sea waves and periodic waves335
- 10.8 The second way to employ the theory339
- 10.9 The "genetic code" of the sea waves346
- 10.10 The determinism arises from within the random waves350
- Conclusive note358
- References359
- Chapter 11. Analysis of the wave forces on offshore structures361
- 11.1 Wave forces on gravity offshore platforms361
- 11.2 Local perturbation of the flow field at an offshore structure364
- 11.3 Wave forces on submerged tunnels367
- 11.4 The diffraction coefficients of the forces373
- 11.5 Wave forces on space frame structures383
- 11.6 The long-structure problem387
- Conclusive note392
- References392
- Chapter 12. Calculation of the wave forces on offshore structures393
- 12.1 Calculation of the wave forces on a gravity offshore platform393
- 12.2 Calculation of the wave forces on a space frame structure397
- 12.3 Design of a submerged tunnel. I: calculation of the wave forces402
- 12.4 Design of a submerged tunnel. II: the effect of currents412
- 12.5 Design of a submerged tunnel. III: the risk of resonance413
- Chapter 13. Stability analysis of coastal structures419
- 13.1 Wave pressure on a wall419
- 13.2 Forces on a vertical breakwater427
- 13.3 Design of vertical breakwaters430
- 13.4 Further verifications of the vertical breakwaters436
- 13.5 The Japanese practice438
- 13.6 The problem of the rubble mound breakwaters441
- Conclusive note445
- References445
- Chapter 14. Topics calling for an overall overview of offshore and coastal engineering447
- 14.1 A comparison between tsunami and wind waves from the open sea to the coast447
- 14.2 Small scale models450
- 14.3 Wave measurements455
- Conclusive note461
- References461
- Appendix A: Appendix to chapters 6 and 7: use of wave hindcast and wave measurements from satellites463
- A.1 Long term wave statistics from satellite data463
- A.2 Wave hindcast464
- A.3 Trend in the wave climate and its effects on engineering470
- References473
- Appendix B: Appendix to chapters 9 and 10: the wave group of the maximum expected crest elevation, a475
- B.1 The first version of the quasi-determinism theory475
- B.2 Corollaries of the first version480
- B.3 The relationship between the two versions of the theory482
- Conclusive note485
- References485
- Subject Index487
- Author Index493
In a unitary way, this monograph deals with a wide range of subjects related to the mechanics of sea waves. The book highlights recent theoretical results on the dynamics of random wind-generated waves, on long-term wave statistics, and on beach planform evolution. A fresh approach is given to more traditional concepts. For example, new evidence from a recent series of small-scale field experiments is used to introduce some crucial topics like wave forces. Also, the book gives some worked examples for the design of offshore or coastal structures.
An exciting subject dealt with in the book is the quasi-deterministic mechanics of three-dimensional wave groups in sea storms, and the loads exerted by these wave groups on offshore structures.
The text is intended for researchers and graduate students in ocean engineering, but may also be understood by undergraduates. The more complex concepts are explained with examples or more extensive case studies.