OCEAN WAVES AND OSCILLATING SYSTEMS

Transcription

1 OCEAN WAVES AND OSCILLATING SYSTEMS LINEAR INTERACTIONS INCLUDING WAVE-ENERGY EXTRACTION JOHANNES FALNES Department of Physics Norwegian University of Science and Technology NTNU CAMBRIDGE UNIVERSITY PRESS

2 Contents Preface page ix 1 Introduction 1 2 Mathematical Description of Oscillations Free and Forced Oscillations of a Simple Oscillator Free Oscillation Forced Oscillation Electric Analogue: Remarks on the Quality Factor Complex Representation of Harmonic Oscillations Complex Amplitudes and Phasors Mechanical Impedance Power and Energy Relations Harmonic Oscillation: Active Power and Reactive Power State-Space Analysis Linear Systems The Delta Function and Related Distributions Impulse Response: Time-Invariant System Fourier Transform and Other Integral Transforms Fourier Transformation in Brief Time-Invariant Linear System Kramers-Kronig Relations and Hilbert Transform An Energy Relation for Non-sinusoidal Oscillation 37 Problems 38 3 Interaction Between Oscillations and Waves Comparison of Waves on Water, with Other Waves Dispersion, Phase Velocity and Group Velocity Wave Power and Energy Transport Radiation Resistance and Radiation Impedance Resonance Absorption 51 Problems 54

3 vi CONTENTS 4 Gravity Waves on Water Basic Equations: Linearisation Harmonic Waves on Water of Constant Depth Plane Waves: Propagation Velocities Wave Transport of Energy and Momentum Potential Energy Kinetic Energy Total Stored Energy Wave-Energy Transport Relation Between Energy Transport and Stored Energy Momentum Transport and Momentum Density of a Wave Drift Forces Caused by the Absorption and Reflection of Wave Energy Real Ocean Waves Circular Waves A Useful Integral Based on Green's Theorem Far-Field Coefficients and Kochin Functions Waves in the Time Domain Relation Between Wave Elevations at Two Locations Relation Between Hydrodynamic Pressure and Wave Elevation \ 109 Problems Wave-Body Interactions Six Modes of Body Motion: Wave Forces and Moments Six Modes of Motion Hydrodynamic Force Acting on a Body Excitation Force Radiation from an Oscillating Body ' The Radiation Impedance Matrix Energy Interpretation of the Radiation Impedance Wavemaker in a Wave Channel Examples of Other Body Geometries Impulse Response Functions in Hydrodynamics The Kramers-Kronig Relations in Hydrodynamic Radiation Non-causal Impulse Response for the Excitation Force Reciprocity Relations Radiation Resistance in Terms of Far-Field Coefficients The Excitation Force: The Haskind Relation Reciprocity Relation Between Radiation Resistance and Excitation Force Several Bodies Interacting with Waves Phenomenological Discussion Hydrodynamic Formulation Radiation-Impedance and Radiation-Resistance Matrices 153

4 CONTENTS vii Radiation-Reactance and Added-Mass Matrices Excitation Force Vector: The Haskind Relation Wide-Spacing Approximation The FroudV-Krylov Force and Small-Body Approximation The Froude-Krylov Force and Moment The Diffraction Force Small-Body Approximation for a Group of Bodies Small-Body Approximation for a Single Body Axisymmetric Oscillating System The Radiation Impedance Radiation Resistance and Excitation Force Numerical 2-Body Example Two-Dimensional System Motion Response and Control of Motion Dynamics of a Floating Body in Heave 183 Problems Wave-Energy Absorption by Oscillating Bodies Absorption Considered as Wave Interference Absorption by a Body Oscillating in One Mode of Motion Maximum Absorbed Power Upper Bound of Power-to-Volume Ratio Maximum Converted Useful Power Optimum Control for Maximising Converted Energy Absorption by a System of Several Oscillators Maximum Absorbed Power and Useful Power Maximum Absorbed Power by an Axisymmetric Body Maximum Absorbed Power in the Two-Dimensional Case Maximum Absorbed Power with Amplitude Constraints 222 Problems Wave Interaction with Oscillating Water Columns The Applied-Pressure Description for a Single OWC Absorbed Power and Radiation Conductance Reactive Power and Radiation Susceptance An Axisymmetric Example Maximum Absorbed Power Reciprocity Relations for an OWC OWC with Pneumatic Power Takeoff Systems of OWCs and Oscillating Bodies Phenomenological Theory Absorbed Power Hydrodynamic Formulation Hydrodynamic Parameters Reciprocity Relations for Radiation Parameters Extension of the Haskind Relation 251

5 viii CONTENTS Reciprocity Relations for the Radiation Damping Matrix Axisymmetric Systems 256 Problems 259 Bibliography 263 Index 269