Description and assessment of ocean waves can provide information vital for the design and operation of marine structures such as ships, offshore oil platforms, wave energy converters and breakwaters.
In view of the growing number of graduate students who have little background knowledge on ocean waves but want to start new research topics in coastal and ocean engineering, a textbook that is easy to read and understand, and that brings all the mathematical information required for wave study together is desirable. This book is self-contained, and almost all mathematical equations and engineering concepts are presented or derived in the text. Therefore, it is suitable for college seniors or first-year graduate students even without any basic education in applied mechanics. Besides, it can also work as a reference book for researchers and designers.
This book is limited to the linear water wave theory without discussing anything related to the nonlinear effect. It can be separated into two parts. The first one is mainly related to regular waves, which serve as the foundation of the second part, i.e., the irregular waves.
In the first part, it starts with a review of fluid mechanics and some basic concepts in vector analysis. The formulation and solution of the governing equations for boundary value problems are developed under the assumption of small-amplitude waves, and the corresponding wave properties in engineering are described in detail.
In the second part, besides the basic concepts of wave spectrum, it mainly provides uniform and concise information necessary to comprehend stochastic analysis and probabilistic prediction of ocean waves. Specific efforts are made in thisbook to explain the fundamental principles supporting current prediction techniques and to show practical applications of prediction methods. Each chapter concludes with several homework problems that exercise the material covered in each chapter.
The authors are indebted to many famous scholars and researchers who directly or indirectly inspired us to write this book. Many thanks should be given to those who provided us with financial support to publish this book. Finally, we would like to acknowledge the contribution of graduate students who helped us plot figures and edit equations in this book.
Chapter 3 Linear Solutions to the Equations of Motion 32
3.1 Formulation of the Boundary Value Problem 32
3.2 Linearized 2D Wave Boundary Conditions 34
3.3 Solution to the Boundary Value Problem 35
3.4 Stationary Wave and Progressive Wave 39
3.5 Linear Dispersion Relationship 41
3.6 Wavelength and Wave Celerity 42
3.7 Waves Propagating on a Current 45
3.8 Exercise 49
Chapter 4 Analysis of Wave Properties 50
4.1 Particle Kinematics for Progressive Waves 50
4.2 Pressure Field under Progressive Waves 54
4.3 Particle Kinematics for Stationary Waves 56
4.4 Pressure Field under Stationary Waves 59
4.5 Group Velocity 60
4.6 Wave Energy and Energy Flux 62
4.7 Oblique Waves 67
4.8 Exercise 70
Chapter 5 Wave Transformation at the Nearshore Region 71
5.1 Conservation of Wave Number 71
5.2 Wave Refraction 73
5.3 Conservation of Wave Energy 75
5.4 Wave Breaking 77
5.5 Wave Diffraction 79
5.6 Exercise 84
Chapter 6 Random Sea Surface 85
6.1 Representation of Random Surface Elevations 85
6.2 Wave Spectrum 93
6.3 Exercise 106
Chapter 7 Statistical Analysis of Irregular Waves 107
7.1 Distribution of Surface Displacements 107
7.2 Distribution of Wave Amplitudes 113
7.3 Distribution of Wave Heights 120
7.4 Joint Distribution of Wave Heights and Periods 127
7.5 Exercise 139
Chapter 8 Extreme Wave Statistics 140
8.1 Long-Term Wave Statistics 140
8.2 Data for Extreme Wave Analysis 142
8.3 Distribution Functions of Extreme Waves 145
8.4 Return Period and Return Value 152
8.5 Estimation of the Best-Fitting Distribution Function 153
8.6 Determination of Return Value 159
8.7 Selection of Return Period 161
8.8 Exercise 164
