Contents -- Preface -- 1 Introduction -- 2 Mathematical Preliminaries -- 2.1 Introduction -- 2.2 Symbols Functions and Linear Operators -- 2.2.1 Landau Order Symbols 0(E) and o(E) (Nayfeh 1973 Chapter 1.3 and Olver 1990 Chapter 12.1.1) -- 2.2.2 Heaviside Step Function U(x-E) -- 2.2.3 Kronecker Delta 8mn Function and Dirac Delta 8(x-E) Distribution -- 2.2.4 Levi-Civita Symbol Eijk(Arfken 1985) -- 2.2.5 Gamma Functions T(o) (Andrews 1985) -- 2.2.6 Error Functions Erf(o) and Erfc(o) (Barcilon 1990 p. 351) -- 2.2.7 Gradient Vector Operator V(o) -- 2.2.8 Curl Vector Operator w = V x (o) -- 2.2.9 Laplacian Operator V2(o) = A(o) -- 2.2.10 Stokes Material Derivative Operator D(o)/Dt -- 2.2.11 Leibnitz's Rule for Differentiation of Integrals with Parameters (Hildebrand 1976 Chapter 7.9) -- 2.2.12 Signum (sign + ) Function -- 2.3 Properties of Series -- 2.3.1 Power Series (Hildebrand 1976 Chapter 4.1) -- 2.3.2 Function Series -- 2.3.3 Maclauren and Taylor Series (Hildebrand 1976 Chapters 4.1 and 7.5) -- 2.3.4 Binomial Expansion (Wylie and Barrett 1982 p.938) -- 2.4 Elementary and Special Functions (Hildebrand 1976 Chapter 10.2) -- 2.4.1 Trigonometric and Hyperbolic Identities -- 2.4.2 Euler's Constant yE (Barcilon 1990 p. 346) -- 2.4.3 Bessel Functions (Hildebrand 1976 Chapters 4.8 to 4.10) -- 2.4.4 Orthogonal Polynomials -- 2.5 Linear Ordinary Differential Equations (Hildebrand 1976 Chapters 1.1 to 1.11) and Operational Calculus (Friedman 1956) -- 2.5.1 Initial and Boundary Data (Stakgold 1979) -- 2.5.2 First Order Linear Ordinary Differential Equations (Hildebrand 1976 Chapter 1.4) -- 2.5.3 Variation of Parameters and the Duhamel Convolution Integral (Hildebrand 1976 Chapter 1.9).

2.5.4 Properties of Linear Differential Operators L(o) (Hildebrand 1976 Chapter 1.7) -- 2.5.5 Method of Frobenius (Hildebrand 1976 Chapter 4.4) -- 2.5.6 Method of Undetermined Coefficients (Hildebrand 1976 Chapter 1.5) -- 2.6 Sturm-Liouville Systems (Morse and Feshbach 1953 Chapter 6.3 -- Hildebrand 1976 Chapter 5.6 -- Oates 1990 Chapter 3.6.5 and Benton 1990 Chapter 6.6) -- 3 Fundamentals of Fluid Mechanics -- 3.1 Introduction -- 3.2 Conservation of Mass (Continuity Field Equation) -- 3.3 Momentum Principle -- 3.3.1 Inertial Forces -- 3.3.2 Surface Stresses -- 3.3.3 Body Forces -- 3.3.4 Navier-Stokes Equations (Lamb 1932) -- 3.3.5 Euler's Equations (Lamb 1932) -- 3.4 Mechanical Energy Principle -- 3.5 Scaling of Equations -- 3.6 Dimensional Analyses -- 3.7 Problems -- 4 Long-Crested Linear Wave Theory (LWT) -- 4.1 Introduction -- 4.2 Dimensional Boundary Value Problem (BVP) for LWT -- 4.3 Solutions to Dimensional Boundary Value Problem (BVP) for Long-Crested Linear Wave Theory (LWT) -- 4.3.1 Wave Celerity C and Computing the Eigenvalue k from the Frequency Dispersion Equation -- 4.4 Eulerian Kinematic Fields and Lagrangian Particle Displacements -- 4.5 Eulerian Dynamic Fields Energy and Energy Flux Conservation Principles for Long-Crested Linear Waves -- 4.6 Wave Transformations for Long-Crested Progressive Linear Waves: Shoaling and Refraction -- 4.7 Problems -- 5 Wavemaker Theories -- 5.1 Introduction -- 5.2 Planar Wavemakers in a 2D Channel -- 5.2.1 Computation of the Eigenvalues Kn by the Newton-Raphson Method -- 5.2.2 Rate of Decay of Evanescent Eigenmodes: n > 2 -- 5.2.3 Orthogonality of Orthonormal Eigenfunctions Wn(Kn z/h) -- 5.2.4 Evaluation of Coefficients Cn by Wavemaker Vertical Displacement X(z/h) -- 5.2.5 Determination of Wave Amplitude from Wavemaker Motion.

5.2.6 Hydrodynamic Pressure Force and Moment (Added Mass and Radiation Damping) -- 5.3 Circular Wavemakers -- 5.3.1 Determination of Wave Amplitude from Wavemaker Motion -- 5.3.2 Hydrodynamic Pressure Force and Moment (Added Mass and Radiation Damping) -- 5.4 Double-Actuated Wavemaker -- 5.5 Directional Wavemaker -- 5.6 Sloshing Waves in a 2D Wave Channel -- 5.7 Conformal and Domain Mapping of WMBVP -- 5.7.1 Conformal Mapping -- 5.7.2 Domain Mapping -- 5.8 Problems -- 6 Nonlinear Wave Theories -- 6.1 Introduction -- 6.2 Classical Stokes: The Method of Successive Approximations -- 6.3 Traditional Stokes: Lindstedt-Poincare 4th Order Perturbation Solution -- 6.3.1 Traditional Stokes: Stokes Drift -- 6.4 Method of Multiple Scales (MMS)2 -- 6.5 Stream Function Solutions -- 6.6 Breaking Progressive Waves -- 6.7 Second-Order Nonlinear Planar Wavemaker Theory -- 6.8 Chaotic Cross Waves: Generalized Melnikov Method (GMM) and Liapunov Exponents -- 6.9 Problems -- 7 Deterministic Dynamics of Small Solid Bodies -- 7.1 Introduction -- 7.2 Small Body Hypothesis (Morison Equation) -- 7.3 Drag dFd and Inertia dFm Forces -- 7.3.1 Inertia Forces -- 7.4 Comparison Between a Fixed Cylinder in Accelerating Flow and an Accelerating Cylinder in Still Fluid -- 7.4.1 Accelerating Cylinder in Still Fluid -- 7.4.2 Fixed Cylinder in an Accelerating Flow -- 7.5 Maximum Static-Equivalent Force/Moment (Fixed-Free Beam) -- 7.6 Parametric Dependency of Force Coefficients Cm and Cd -- 7.6.1 Relative Importance of dFm(zi t) and dFd(zi t) -- 7.6.2 Computing the Force Coefficients Cm and Cd -- 7.6.3 Methods of Analyses -- 7.6.4 Linearized Drag Force -- 7.6.5 Laboratory U-Tube Data -- 7.6.6 Ocean Wave Data -- 7.7 The Dean Eccentricity Parameter and Data Condition.

7.7.1 Dean Error Ellipse and Eccentricity Parameter E (Geometric) -- 7.7.2 Amplitude/Phase Method (Geometric) -- 7.7.3 Matrix Condition Numbers (Numerical) -- 7.8 Modified Wave Force Equation (WFE Relative Motion Morison Equation) -- 7.8.1 Articulated Circular Cylindrical Tower: SDOF System -- 7.8.2 Two Semi-Immersed Horizontal Circular Cylinders: MDOF System -- 7.9 Transverse Forces on Bluff Solid Bodies -- 7.10 Stability of Marine Pipelines -- 7.11 Problems -- 8 Deterministic Dynamics of Large Solid Bodies -- 8.1 Dynamic Response of Large Bodies: An Overview -- 8.2 Linearized MDOF Large Solid Body Dynamics -- 8.2.1 Kinematic Body Boundary Conditions (KBBC) -- 8.2.2 Dynamic Body Boundary Condition (DBBC) -- 8.3 Froude-Kriloff Approximations for Potential Theory -- 8.3.1 Froude-Kriloff Load in 2-D Cartesian Coordinates -- 8.3.2 Froude-Kriloff Load in Circular Cylindrical Coordinates -- 8.4 Diffraction by a Full-Draft Vertical Circular Cylinder -- 8.5 Reciprocity Relationships -- 8.6 Green's Functions and Fredholm Integral Equations -- 8.6.1 Orthonormal Eigenfunction Expansion of Green's Function for 2D Wavemaker -- 8.7 Wave Loads Computed by the FEM -- 8.8 Problems -- 9 Real Ocean Waves -- 9.1 Introduction -- 9.2 Fourier Analyses -- 9.3 Ocean Wave Spectra -- 9.3.1 Generic Four-Parameter Wave Density Spectrum -- 9.3.2 Wave and Spectral Parameters Computed from Spectral Moments mn -- 9.3.3 Multi-Parameter Theoretical Spectra -- 9.3.4 Spectral Directional Spreading Functions -- 9.3.5 Confidence Intervals for FFT Estimates -- 9.4 Probability Functions for Random Waves -- 9.4.1 Gaussian (Normal) Probability Distribution -- 9.4.2 Rayleigh Probability Distribution -- 9.4.3 Distribution of the Maxima -- 9.5 Wave Groups -- 9.5.1 Resolving Incident and Reflected Random Wave Time Series -- 9.6 Random Wave Simulations.

9.6.1 Conditional Wave Simulations -- 9.7 Data Analyses: An Example from Hurricane CARLA -- 9.8 Random Wave Forces on Small Circular Members -- 9.8.1 Probability Density Function p(Y) (pdf) and Covariance Function CFTFT(T) for Nondeterministic Wave Force per Unit Length for a Small Vertical Circular Pile -- 9.8.2 Stochastic Response of Space-Frame Offshore Structure -- 9.9 Frequency Domain Input-Output Transfer Functions -- 9.10 Problems -- Bibliography -- Author Index -- Subject Index.