WAVE MECHANICS FOR OCEAN ENGINEERING

Transcription

1 Elsevier Oceanography Series, 64 WAVE MECHANICS FOR OCEAN ENGINEERING P. Boccotti Faculty of Engineering University of Reggio-Calabria Feo di Vito Reggio-Calabria Italy 2000 ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo

2 XIX LIST OF CONTENTS Chapter 1 Periodic wave pattern: the approach of differential calculus The irrotational flow, the continuity equation, the Bernoulli equation The differential equations of an irrotational flow with a free surface Introduction to wave mechanics Stokes' theory to the first order Analysis of the linear dispersion rule The flow field Stokes' theory to the second order Non-linearity effects Wave-current interaction. Part I: velocity potential and wavelength Preliminary remarks on three dimensional waves Wave reflection Wave diffraction References Chapter 2 Periodic wave pattern: the control volume approach 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 Wave-current interaction. Part II: shoaling and set-down References

3 XX List of contents Chapter 3 Wave effects on coasts 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 The sea state The theory of the sea states Some basic relations in the theory of the sea states How to obtain the input data of the theory A mathematical form of the wind wave spectrum Possibility of testing small scale models in sea or lakes Inferring the nature of waves from the bandwidth References Chapter 5 Analysis of the sea states: the time domain 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 Experimental verification

4 List of contents XXI Characteristic wave heights The maximum expected wave height in a sea state of given duration References Chapter 6 The wave climate The function H s (t) The probability of the significant wave height The probability of the significant wave height for a given direction of wave advance Probabilities of the significant wave height for a few areas of the globe The maximum expected wave height in a storm with a given history The concept of "equivalent triangular storm" Storm durations References Chapter 7 Design waves and risk analysis The return period of a sea storm where the significant wave height exceeds a fixed threshold The significant wave height and its persistence vs the return period The encounter probability The chain: lifetime, encounter probability => return period => significant wave height Coastal structures: the design sea state The return period of a wave with a height exceeding a fixed threshold The return period of a sea storm containing at least one wave higher than a fixed threshold Offshore structures: the design wave Calculations for different wave directions Corollary of risk analysis: a general relation between the confidence interval and the sampling rate References Chapter 8 Analysis of the sea states in the space-time The concept of homogeneous wave field The wave field in the open sea

5 XXII List of contents 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 Chapter 9 The theory of quasi-determinism 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 The first way to employ the theory A three dimensional wave group The waves are higher on the time domain than on the space domain! Effects of water depth and of spectrum shape on the wave group Shoaling and refraction of the wave group Explanation of the first big difference between sea waves and periodic waves Explanation of the second big difference between sea waves and periodic waves The second way to employ the theory The "genetic code" of the sea waves The determinism arises from within the random waves References

6 List of contents XXIII 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 Calculation of the wave forces on a, gravity offshore platform Calculation of the wave forces on a space frame structure Design of a submerged tunnel. I: calculation of the wave forces Design of a submerged tunnel. II: the effect of currents Design of a submerged tunnel. Ill: the risk of resonance Chapter 13 Stability analysis of coastal structures Wave pressure on a wall Forces on a vertical breakwater Design of vertical breakwaters Further verifications of the vertical breakwaters The Japanese practice The problem of the rubble mound breakwaters References Chapter 14 Topics calling for an overall overview of offshore and coastal engineering ' A comparison between tsunami and wind waves from the open sea to the coast Small scale models Wave measurements References

7 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 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