Waves and Wave Forces on Coastal and Ocean Structures (2005)(en)(932s)

Robert T. Hudspeth9789812386120, 981-238-612-2

This book focuses on: (1) the physics of the fundamental dynamics of fluids and of semi-immersed Lagrangian solid bodies that are responding to wave-induced loads; (2) the scaling of dimensional equations and boundary value problems in order to determine a small dimensionless parameter e that may be applied to linearize the equations and the boundary value problems so as to obtain a linear system; (3) the replacement of differential and integral calculus with algebraic equations that require only algebraic substitutions instead of differentiations and integrations; and (4) the importance of comparing numerical and analytical computations with data from laboratories and/or nature.

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Table of contents :
Contents……Page 8
Preface……Page 16
1 Introduction……Page 22
2.2.1 Landau Order Symbols 0(E) and o(E) (Nayfeh 1973 Chapter 1.3 and Olver 1990 Chapter 12.1.1)……Page 26
2.2.4 Levi-Civita Symbol Eijk(Arfken 1985)……Page 28
2.2.5 Gamma Functions T(o) (Andrews 1985)……Page 29
2.2.6 Error Functions Erf(o) and Erfc(o) (Barcilon 1990 p. 351)……Page 30
2.2.8 Curl Vector Operator w = V x (o)……Page 31
2.2.10 Stokes Material Derivative Operator D(o)/Dt……Page 32
2.3.1 Power Series (Hildebrand 1976 Chapter 4.1)……Page 34
2.3.2 Function Series……Page 35
2.3.3 Maclauren and Taylor Series (Hildebrand 1976 Chapters 4.1 and 7.5)……Page 36
2.3.4 Binomial Expansion (Wylie and Barrett 1982 p.938)……Page 38
2.4.1 Trigonometric and Hyperbolic Identities……Page 39
2.4.2 Euler’s Constant yE (Barcilon 1990 p. 346)……Page 41
2.4.3 Bessel Functions (Hildebrand 1976 Chapters 4.8 to 4.10)……Page 42
2.4.4 Orthogonal Polynomials……Page 47
2.5 Linear Ordinary Differential Equations (Hildebrand 1976 Chapters 1.1 to 1.11) and Operational Calculus (Friedman 1956)……Page 52
2.5.1 Initial and Boundary Data (Stakgold 1979)……Page 53
2.5.2 First Order Linear Ordinary Differential Equations (Hildebrand 1976 Chapter 1.4)……Page 55
2.5.3 Variation of Parameters and the Duhamel Convolution Integral (Hildebrand 1976 Chapter 1.9)……Page 56
2.5.4 Properties of Linear Differential Operators L(o) (Hildebrand 1976 Chapter 1.7)……Page 60
2.5.5 Method of Frobenius (Hildebrand 1976 Chapter 4.4)……Page 61
2.5.6 Method of Undetermined Coefficients (Hildebrand 1976 Chapter 1.5)……Page 66
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)……Page 69
3.1 Introduction……Page 74
3.2 Conservation of Mass (Continuity Field Equation)……Page 76
3.3 Momentum Principle……Page 78
3.3.1 Inertial Forces……Page 79
3.3.2 Surface Stresses……Page 84
3.3.4 Navier-Stokes Equations (Lamb 1932)……Page 90
3.4 Mechanical Energy Principle……Page 91
3.5 Scaling of Equations……Page 92
3.6 Dimensional Analyses……Page 102
3.7 Problems……Page 105
4.1 Introduction……Page 106
4.2 Dimensional Boundary Value Problem (BVP) for LWT……Page 108
4.3 Solutions to Dimensional Boundary Value Problem (BVP) for Long-Crested Linear Wave Theory (LWT)……Page 118
4.3.1 Wave Celerity C and Computing the Eigenvalue k from the Frequency Dispersion Equation……Page 126
4.4 Eulerian Kinematic Fields and Lagrangian Particle Displacements……Page 134
4.5 Eulerian Dynamic Fields Energy and Energy Flux Conservation Principles for Long-Crested Linear Waves……Page 142
4.6 Wave Transformations for Long-Crested Progressive Linear Waves: Shoaling and Refraction……Page 161
4.7 Problems……Page 165
5.1 Introduction……Page 170
5.2 Planar Wavemakers in a 2D Channel……Page 175
5.2.1 Computation of the Eigenvalues Kn by the Newton-Raphson Method……Page 191
5.2.2 Rate of Decay of Evanescent Eigenmodes: n > 2……Page 197
5.2.3 Orthogonality of Orthonormal Eigenfunctions Wn(Kn z/h)……Page 198
5.2.4 Evaluation of Coefficients Cn by Wavemaker Vertical Displacement X(z/h)……Page 201
5.2.5 Determination of Wave Amplitude from Wavemaker Motion……Page 206
5.2.6 Hydrodynamic Pressure Force and Moment (Added Mass and Radiation Damping)……Page 210
5.3 Circular Wavemakers……Page 222
5.3.1 Determination of Wave Amplitude from Wavemaker Motion……Page 240
5.3.2 Hydrodynamic Pressure Force and Moment (Added Mass and Radiation Damping)……Page 252
5.4 Double-Actuated Wavemaker……Page 263
5.5 Directional Wavemaker……Page 272
5.6 Sloshing Waves in a 2D Wave Channel……Page 289
5.7 Conformal and Domain Mapping of WMBVP……Page 300
5.7.1 Conformal Mapping……Page 301
5.7.2 Domain Mapping……Page 322
5.8 Problems……Page 327
6.1 Introduction……Page 330
6.2 Classical Stokes: The Method of Successive Approximations……Page 331
6.3 Traditional Stokes: Lindstedt-Poincare 4th Order Perturbation Solution……Page 337
6.3.1 Traditional Stokes: Stokes Drift……Page 382
6.4 Method of Multiple Scales (MMS)2……Page 392
6.5 Stream Function Solutions……Page 415
6.6 Breaking Progressive Waves……Page 421
6.7 Second-Order Nonlinear Planar Wavemaker Theory……Page 426
6.8 Chaotic Cross Waves: Generalized Melnikov Method (GMM) and Liapunov Exponents……Page 444
6.9 Problems……Page 513
7.1 Introduction……Page 516
7.2 Small Body Hypothesis (Morison Equation)……Page 519
7.3 Drag dFd and Inertia dFm Forces……Page 526
7.3.1 Inertia Forces……Page 529
7.4 Comparison Between a Fixed Cylinder in Accelerating Flow and an Accelerating Cylinder in Still Fluid……Page 530
7.4.2 Fixed Cylinder in an Accelerating Flow……Page 531
7.5 Maximum Static-Equivalent Force/Moment (Fixed-Free Beam)……Page 536
7.6.1 Relative Importance of dFm(zi t) and dFd(zi t)……Page 541
7.6.2 Computing the Force Coefficients Cm and Cd……Page 543
7.6.3 Methods of Analyses……Page 545
7.6.4 Linearized Drag Force……Page 551
7.6.5 Laboratory U-Tube Data……Page 553
7.6.6 Ocean Wave Data……Page 556
7.7 The Dean Eccentricity Parameter and Data Condition……Page 559
7.7.1 Dean Error Ellipse and Eccentricity Parameter E (Geometric)……Page 562
7.7.2 Amplitude/Phase Method (Geometric)……Page 569
7.7.3 Matrix Condition Numbers (Numerical)……Page 576
7.8 Modified Wave Force Equation (WFE Relative Motion Morison Equation)……Page 580
7.8.1 Articulated Circular Cylindrical Tower: SDOF System……Page 584
7.8.2 Two Semi-Immersed Horizontal Circular Cylinders: MDOF System……Page 594
7.9 Transverse Forces on Bluff Solid Bodies……Page 620
7.10 Stability of Marine Pipelines……Page 626
7.11 Problems……Page 636
8.1 Dynamic Response of Large Bodies: An Overview……Page 640
8.2 Linearized MDOF Large Solid Body Dynamics……Page 657
8.2.1 Kinematic Body Boundary Conditions (KBBC)……Page 659
8.2.2 Dynamic Body Boundary Condition (DBBC)……Page 664
8.3 Froude-Kriloff Approximations for Potential Theory……Page 683
8.3.1 Froude-Kriloff Load in 2-D Cartesian Coordinates……Page 684
8.3.2 Froude-Kriloff Load in Circular Cylindrical Coordinates……Page 688
8.4 Diffraction by a Full-Draft Vertical Circular Cylinder……Page 693
8.5 Reciprocity Relationships……Page 703
8.6 Green’s Functions and Fredholm Integral Equations……Page 709
8.6.1 Orthonormal Eigenfunction Expansion of Green’s Function for 2D Wavemaker……Page 720
8.7 Wave Loads Computed by the FEM……Page 727
8.8 Problems……Page 737
9.1 Introduction……Page 740
9.2 Fourier Analyses……Page 741
9.3 Ocean Wave Spectra……Page 751
9.3.1 Generic Four-Parameter Wave Density Spectrum……Page 761
9.3.2 Wave and Spectral Parameters Computed from Spectral Moments mn……Page 768
9.3.3 Multi-Parameter Theoretical Spectra……Page 773
9.3.4 Spectral Directional Spreading Functions……Page 775
9.3.5 Confidence Intervals for FFT Estimates……Page 780
9.4 Probability Functions for Random Waves……Page 781
9.4.1 Gaussian (Normal) Probability Distribution……Page 786
9.4.2 Rayleigh Probability Distribution……Page 793
9.4.3 Distribution of the Maxima……Page 801
9.5 Wave Groups……Page 811
9.5.1 Resolving Incident and Reflected Random Wave Time Series……Page 824
9.6 Random Wave Simulations……Page 829
9.6.1 Conditional Wave Simulations……Page 834
9.7 Data Analyses: An Example from Hurricane CARLA……Page 844
9.8 Random Wave Forces on Small Circular Members……Page 852
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……Page 853
9.8.2 Stochastic Response of Space-Frame Offshore Structure……Page 864
9.9 Frequency Domain Input-Output Transfer Functions……Page 875
9.10 Problems……Page 885
Bibliography……Page 888
Author Index……Page 930
Subject Index……Page 938