Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction

Cover......Page 1
Half-title......Page 3
Ocean waves and oscillating systems: Linear interactions including wave-energy extraction......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1. Introduction......Page 13
2.1 Free and Forced Oscillations of a Simple Oscillator......Page 16
2.1.1 Free Oscillation......Page 17
2.1.2 Forced Oscillation......Page 18
2.1.3  Electric Analogue: Remarks on the Quality Factor......Page 21
2.2.1 Complex Amplitudes and Phasors......Page 22
2.2.2 Mechanical Impedance......Page 25
2.3 Power and Energy Relations......Page 29
2.3.1 Harmonic Oscillation: Active Power and Reactive Power......Page 30
2.4 State-Space Analysis......Page 32
2.5 Linear Systems......Page 35
2.5.1 The Delta Function and Related Distributions......Page 37
2.5.2 Impulse Response: Time-Invariant System......Page 38
2.6 Fourier Transform and Other Integral Transforms......Page 39
2.6.1 Fourier Transformation in Brief......Page 40
2.6.2 Time-Invariant Linear System......Page 43
2.6.3  Kramers-Kronig Relations and Hilbert Transform......Page 45
2.6.4 An Energy Relation for Non-sinusoidal Oscillation......Page 49
Problem 2.3: Forced Oscillation......Page 50
Problem 2.6: Complex Representations of Harmonic Oscillation......Page 51
Problem 2.10: State-Space Description of Oscillation......Page 52
Problem 2.13: Convolution with Sinusoidal Oscillation......Page 53
Problem 2.15: Mechanical Impedance at  Zero Frequency......Page 54
3.1 Comparison of Waves on Water with Other  Waves......Page 55
3.2 Dispersion, Phase Velocity and Group Velocity......Page 57
3.3 Wave Power and Energy Transport......Page 58
3.4 Radiation Resistance and Radiation Impedance......Page 61
3.5 Resonance Absorption......Page 63
Problem 3.2: Capillary-Gravity Surface Wave......Page 66
Problem 3.5: Acoustic Point Absorber......Page 67
Problem 3.7: Optimum Load Resistance......Page 68
Problem 3.9: Power Radiated from Oscillating Submerged Body......Page 69
4.1 Basic Equations: Linearisation......Page 70
4.2 Harmonic Waves on Water of Constant Depth......Page 76
4.3 Plane Waves: Propagation Velocities......Page 82
4.4.1 Potential Energy......Page 87
4.4.2 Kinetic Energy......Page 88
4.4.4 Wave-Energy Transport......Page 89
4.4.5 Relation Between Energy Transport and Stored Energy......Page 90
4.4.6 Momentum Transport and Momentum Density of a Wave......Page 91
4.4.7 Drift Forces Caused by the Absorption and Reflection of Wave Energy......Page 93
4.5 Real Ocean Waves......Page 95
4.6 Circular Waves......Page 99
4.7 A Useful Integral Based on Green’s Theorem......Page 103
4.8 Far-Field Coefficients and Kochin Functions......Page 108
4.9 Waves in the Time Domain......Page 116
4.9.1 Relation Between Wave Elevations at Two Locations......Page 117
Problem 4.1: Deriving Dispersion Relation Including Capillarity......Page 121
Problem 4.3: Vertical Functions for Evanescent Solutions......Page 122
Problem 4.5: Reflection of Plane Wave at Vertical Wall......Page 123
Problem 4.8: Kinetic Energy Density......Page 124
Problem 4.11: Slowly Varying Water Depth and Channel Width......Page 125
Problem 4.13: Transmission and Reflection at a Barrier......Page 127
Problem 4.15: Wave-Energy Transport with Two Waves......Page 129
5.1 Six Modes of Body Motion: Wave Forces and Moments......Page 130
5.1.1 Six Modes of Motion......Page 131
5.1.2 Hydrodynamic Force Acting on a Body......Page 133
5.1.3 Excitation Force......Page 135
5.2.1 The Radiation Impedance Matrix......Page 137
5.2.2 Energy Interpretation of the Radiation Impedance......Page 139
5.2.3 Wavemaker in a Wave Channel......Page 140
5.2.4 Examples of Other Body Geometries......Page 145
5.3 Impulse Response Functios in Hydrodynamics......Page 150
5.3.1 The Kramers-Kronig Relations in Hydrodynamic Radiation......Page 151
5.3.2 Non-causal Impulse Response for the Excitation Force......Page 153
5.4 Reciprocity Relations......Page 155
5.4.1 Radiation Resistance in Terms of Far-Field Coefficients......Page 156
5.4.2 The Excitation Force: the Haskind Relation......Page 159
5.4.3 Reciprocity Relation Between Radiation Resistance and Excitation Force......Page 160
5.5 Several Bodies Interacting with Waves......Page 161
5.5.1 Phenomenological Discussion......Page 162
5.5.2 Hydrodynamic Formulation......Page 163
5.5.3 Radiation-Impedance and Radiation-Resistance Matrices......Page 165
5.5.4 Radiation-Reactance and Added-Mass Matrices......Page 168
5.5.5 Excitation Force Vector: the Haskind Relation......Page 170
5.5.6 Wide-Spacing Appoximation......Page 171
5.6 The Froude-Krylov Force and Small-Body Approximation......Page 172
5.6.1 The Froude-Krylov Force and Moment......Page 173
5.6.3 Small-Body  Approximation for a Group of Bodies......Page 175
5.6.4 Small-Body Approximation for a Single Body......Page 177
5.7 Axisymmetric Oscillating System......Page 180
5.7.1 The Radiation Impedance......Page 183
5.7.2 Radiation Resistance and Excitation Force......Page 184
5.7.3 Numerical 2-Body Example......Page 187
5.8 Two-Dimensional System......Page 191
5.9 Motion Response and Control of Motion......Page 193
5.9.1 Dynamics of a Floating Body in Heave......Page 195
Problem 5.3: Radiation Resistance for a Vertical Plate......Page 199
Problem 5.5: Pivoting Vertical Plate as a Wave Generator......Page 200
Problem 5.8: Excitation-Force Impulse Response......Page 201
Problem 5.11: Heave Excitation Force for a Semisubmerged Sphere......Page 202
Problem 5.12: Radiation Resistance for a Cylindric Body......Page 203
Problem 5.14: Reciprocity Relations Between Diffracted Waves......Page 204
Problem 5.15: Diffracted and Radiated Two-Dimensional Waves......Page 205
Problem 5.16: Rectangular Piston in the End Wall of a Wave Channel......Page 206
6.1  Absorption Considered as Wave Interference......Page 208
6.2 Absorption by Body Oscillating in One Mode of Motion......Page 210
6.2.2 Upper Bound of Power-to-Volume Ratio......Page 212
6.2.3 Maximum Converted Useful Power......Page 214
6.3 Optimum Control for Maximising Converted Energy......Page 216
6.4 Absorption by a System of Several Oscillators......Page 224
6.4.1 Maximum Absorbed Power and Useful Power......Page 226
6.4.2 Maximum Absorbed Power by an Axisymmetric Body......Page 228
6.4.3 Maximum Absorbed Power in the Two-Dimensional Case......Page 230
Problem 6.1: Power Absorbed by Heaving Buoy......Page 234
Problem 6.3: Maximum Absorbed Power by an Axisymmetric Body......Page 235
Problem 6.5: Maximum Absorbed Power with Optimised Amplitude......Page 236
7. Wave Interaction with Oscillating Water Columns......Page 237
7.1 The Applied-Pressure Description for a Single OWC......Page 238
7.1.1 Absorbed Power and Radiation Conductance......Page 241
7.1.3 An Axisymmetric Example......Page 242
7.1.4 Maximum Absorbed Power......Page 244
7.1.5 Reciprocity Relations for an OWC......Page 246
7.1.6 OWC with Pneumatic Power Takeoff......Page 248
7.2 Systems of OWCs and Oscillating Bodies......Page 250
7.2.1 Phenomenological Theory......Page 251
7.2.2 Absorbed Power......Page 254
7.2.3 Hydrodynamic Formulation......Page 256
7.2.4 Hydrodynamic Parameters......Page 258
7.2.5 Reciprocity Relations for Radiation Parameters......Page 259
7.2.6 Extension of  the Haskind Relation......Page 263
7.2.7 Reciprocity Relations for the Radiation Damping Matrix......Page 266
7.2.8 Axisymmetric Systems......Page 268
Problem 7.3: Linear Electric 2-Port......Page 271
Problem 7.4: Maximum Absorbed Power......Page 272
Problem 7.5: Maximum Absorbed Wave Power......Page 273
Bibliography......Page 275
Index......Page 281