Elsevier Oceanography Series, 64 WAVE MECHANICS FOR OCEAN ENGINEERING P. Boccotti Faculty of Engineering University of Reggio-Calabria Feo di Vito 1-89060 Reggio-Calabria Italy 2000 ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo
XIX LIST OF CONTENTS Chapter 1 Periodic wave pattern: the approach of differential calculus 1 1.1 The irrotational flow, the continuity equation, the Bernoulli equation 5 1.2 The differential equations of an irrotational flow with a free surface 7 1.3 Introduction to wave mechanics 9 1.4 Stokes' theory to the first order 13 1.5 Analysis of the linear dispersion rule 16 1.6 The flow field 19 1.7 Stokes' theory to the second order 21 1.8 Non-linearity effects 23 1.9 Wave-current interaction. Part I: velocity potential and wavelength 28 1.10 Preliminary remarks on three dimensional waves 29 1.11 Wave reflection 34 1.12 Wave diffraction 38 38 References 39 42 46 48 54 58 61 65 70 74 85 86 Chapter 2 Periodic wave pattern: the control volume approach 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 The linear momentum equation for a control volume The energy equation for a control volume Radiation stress, mean energy flux, mean wave energy per unit surface Formulae for radiation stress and mean energy flux of progressive waves The problem of the control volume extending from deep to shallow water Practical consequences of the control volume problem A current associated with the wave motion Wave refraction for an arbitrary configuration of the seabed The group celerity 2.9 2.10 Wave-current interaction. Part II: shoaling and set-down References
XX List of contents 87 88 92 94 95 100 103 104 107 111 113 116 118 Chapter 3 Wave effects on coasts 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 The control volume from the breaker line to the beach The run-up The longshore transport The analytical approach to the problem of beach planform evolution Problem of beach planform evolution: the case of contour lines parallel up to deep water Problem of beach planform evolution: the case of contour lines parallel only within a certain distance from the shoreline Planform evolution of a natural shoreline Stability of a nourished beach Planform evolution of beach nourishment projects A useful simplification Beach planform evolution caused by structures References Chapter 4 Wind generated waves: basic concepts 119 4.1 The sea state 121 4.2 The theory of the sea states 123 4.3 Some basic relations in the theory of the sea states 126 4.4 How to obtain the input data of the theory 136 4.5 A mathematical form of the wind wave spectrum 140 4.6 Possibility of testing small scale models in sea or lakes 145 4.7 Inferring the nature of waves from the bandwidth 150 151 References 153 157 159 161 162 166 167 Chapter 5 Analysis of the sea states: the time domain 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Why the surface displacement represents a stationary Gaussian process Joint probability of surface displacements Rice's problem Rice's logic Corollaries of Rice's problem Solved and still unsolved problems The period of a very high wave and the wave height probability under general bandwidth assumptions 172 5.8 Experimental verification
List of contents XXI 175 5.9 Characteristic wave heights 177 5.10 The maximum expected wave height in a sea state of given duration 180 181 References Chapter 6 The wave climate 183 6.1 The function H s (t) 186 6.2 The probability of the significant wave height 191 6.3 The probability of the significant wave height for a given direction of wave advance 196 6.4 Probabilities of the significant wave height for a few areas of the globe 199 6.5 The maximum expected wave height in a storm with a given history 200 6.6 The concept of "equivalent triangular storm" 204 6.7 Storm durations 206 206 References Chapter 7 Design waves and risk analysis 207 7.1 The return period of a sea storm where the significant wave height exceeds a fixed threshold 211 7.2 The significant wave height and its persistence vs the return period 213 7.3 The encounter probability 221 7.4 The chain: lifetime, encounter probability => return period => significant wave height 223 7.5 Coastal structures: the design sea state 226 7.6 The return period of a wave with a height exceeding a fixed threshold 228 7.7 The return period of a sea storm containing at least one wave higher than a fixed threshold 235 7.8 Offshore structures: the design wave 239 7.9 Calculations for different wave directions 242 7.10 Corollary of risk analysis: a general relation between the confidence interval and the sampling rate 246 247 References Chapter 8 Analysis of the sea states in the space-time 249 8.1 The concept of homogeneous wave field 251 8.2 The wave field in the open sea
XXII List of contents 254 257 263 267 270 274 8.3 8.4 8.5 8.6 8.7 8.8 276 8.9 279 279 References The directional spectrum Shoaling and refraction of the wind-generated waves Reflection of the wind-generated waves Diffraction of the wind-generated waves Long-crested random waves: the link between periodic waves and windgenerated waves Direct proportion between the maximum expected wave height and the diffraction coefficient Space-time covariances 281 286 288 291 293 294 296 300 303 306 Chapter 9 The theory of quasi-determinism 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 A sufficient condition for occurrence of a wave of given height very large A necessary condition for occurrence of a wave of given height very large The water surface on space-time, if a wave of given height very large occurs at a fixed point The velocity potential if a wave of given height very large occurs at a fixed point Theory's generality and consistency with Stokes' theory Formal proof of the necessary condition. Part I: symbols and assumptions Formal proof of the necessary condition. Part II: core of the proof Formal proof of the necessary condition. Part III: the central inequality Formal proof of the necessary condition. Part IV: conclusion Corollary: the closed solution for the wave height distribution Chapter 10 Uses and consequences of the quasi-determinism theory 311 10.1 The first way to employ the theory 317 10.2 A three dimensional wave group 318 10.3 The waves are higher on the time domain than on the space domain! 320 10.4 Effects of water depth and of spectrum shape on the wave group 324 10.5 Shoaling and refraction of the wave group 326 10.6 Explanation of the first big difference between sea waves and periodic waves 335 10.7 Explanation of the second big difference between sea waves and periodic waves 339 10.8 The second way to employ the theory 346 10.9 The "genetic code" of the sea waves 350 10.10 The determinism arises from within the random waves 359 359 References
List of contents XXIII 361 364 367 373 383 387 392 Chapter 11 Analysis of the wave forces on offshore structures 11.1 Wave forces on gravity offshore platforms 11.2 Local perturbation of the flow field at an offshore structure 11.3 Wave forces on submerged tunnels 11.4 The diffraction coefficients of the forces 11.5 Wave forces on space frame structures 11.6 The long-structure problem 392 References Chapter 12 Calculation of the wave forces on offshore structures 393 12.1 Calculation of the wave forces on a, gravity offshore platform 397 12.2 Calculation of the wave forces on a space frame structure 402 12.3 Design of a submerged tunnel. I: calculation of the wave forces 412 12.4 Design of a submerged tunnel. II: the effect of currents 413 12.5 Design of a submerged tunnel. Ill: the risk of resonance Chapter 13 Stability analysis of coastal structures 419 13.1 Wave pressure on a wall 427 13.2 Forces on a vertical breakwater 430 13.3 Design of vertical breakwaters 436 13.4 Further verifications of the vertical breakwaters 438 13.5 The Japanese practice 441 13.6 The problem of the rubble mound breakwaters 445 445 References Chapter 14 Topics calling for an overall overview of offshore and coastal engineering ' 447 14.1 A comparison between tsunami and wind waves from the open sea to the coast 450 14.2 Small scale models 455 14.3 Wave measurements 461 461 References
XXIV List of contents Appendix A Appendix to chapters 6 and 7: use of wave hindcast and wave measurements from satellites 463 A.I Long term wave statistics from satellite data 464 A.2 Wave hindcast 470 A.3 Trend in the wave climate and its effects on engineering 473 References 475 480 482 485 485 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 B.I B.2 B.3 The first version of the quasi-determinism theory Corollaries of the first version The relationship between the two versions of the theory References