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

by Johannes Falnes

• ISBN13: 9780521782111
• ISBN10: 0521782112
• Format: Hardcover
• Copyright: 2002-04-08
• Publisher: Cambridge University Press

Summary

This book examines the interaction between ocean waves and oscillating systems. With a focus on linear analysis of low-amplitude waves, the text is designed to convey a thorough understanding of wave interactions. Topics covered include the background mathematics of oscillations, gravity waves on water, the dynamics of wave-body interactions, and the absorption of wave energy by oscillating bodies. Linear algebra, complex numbers, differential equations, and Fourier transformation are utilized as bases for the analysis, and each chapter ends with problems. While the book's focus is on linear theory, the practical application of energy storage and transport is interwoven throughout. This book will be appropriate for those with backgrounds in elementary fluid dynamics or hydrodynamics and mathematical analysis. Graduate students and researchers will find it an excellent source of wave energy theory and application.

Author Biography

Johannes Falnes is Professor of Experimental Physics at the Norwegian University of Science and Technology NTNU, where he has taught since 1965.

Table of Contents

Preface	ix
Introduction	1	(3)
Mathematical Description of Oscillations	4	(39)
Free and Forced Oscillations of a Simple Oscillator	4	(6)
Free Oscillation	5	(1)
Forced Oscillation	6	(3)
Electric Analogue: Remarks on the Quality Factor	9	(1)
Complex Representation of Harmonic Oscillations	10	(7)
Complex Amplitudes and Phasors	10	(3)
Mechanical Impedance	13	(4)
Power and Energy Relations	17	(3)
Harmonic Oscillation: Active Power and Reactive Power	18	(2)
State-Space Analysis	20	(3)
Linear Systems	23	(4)
The Delta Function and Related Distributions	25	(1)
Impulse Response: Time-Invariant System	26	(1)
Fourier Transform and Other Integral Transforms	27	(16)
Fourier Transformation in Brief	28	(3)
Time-Invariant Linear System	31	(2)
Kramers-Kronig Relations and Hilbert Transform	33	(4)
An Energy Relation for Non-sinusoidal Oscillation	37	(1)
Problems	38	(5)
Interaction Between Oscillations and Waves	43	(15)
Comparison of Waves on Water with Other Waves	43	(2)
Dispersion, Phase Velocity and Group Velocity	45	(1)
Wave Power and Energy Transport	46	(3)
Radiation Resistance and Radiation Impedance	49	(2)
Resonance Absorption	51	(7)
Problems	54	(4)
Gravity Waves on Water	58	(60)
Basic Equations: Linearisation	58	(6)
Harmonic Waves on Water of Constant Depth	64	(6)
Plane Waves: Propagation Velocities	70	(5)
Wave Transport of Energy and Momentum	75	(8)
Potential Energy	75	(1)
Kinetic Energy	76	(1)
Total Stored Energy	77	(1)
Wave-Energy Transport	77	(1)
Relation Between Energy Transport and Stored Energy	78	(1)
Momentum Transport and Momentum Density of a Wave	79	(2)
Drift Forces Caused by the Absorption and Reflection of Wave Energy	81	(2)
Real Ocean Waves	83	(4)
Circular Waves	87	(4)
A Useful Integral Based on Green's Theorem	91	(5)
Far-Field Coefficients and Kochin Functions	96	(8)
Waves in the Time Domain	104	(14)
Relation Between Wave Elevations at Two Locations	105	(4)
Relation Between Hydrodynamic Pressure and Wave Elevation	109	(1)
Problems	109	(9)
Wave-Body Interactions	118	(78)
Six Modes of Body Motion: Wave Forces and Moments	118	(7)
Six Modes of Motion	119	(2)
Hydrodynamic Force Acting on a Body	121	(2)
Excitation Force	123	(2)
Radiation from an Oscillating Body	125	(13)
The Radiation Impedance Matrix	125	(2)
Energy Interpretation of the Radiation Impedance	127	(1)
Wavemaker in a Wave Channel	128	(5)
Examples of Other Body Geometries	133	(5)
Impulse Response Functions in Hydrodynamics	138	(5)
The Kramers-Kronig Relations in Hydrodynamic Radiation	139	(2)
Non-causal Impulse Response for the Excitation Force	141	(2)
Reciprocity Relations	143	(6)
Radiation Resistance in Terms of Far-Field Coefficients	144	(3)
The Excitation Force: The Haskind Relation	147	(1)
Reciprocity Relation Between Radiation Resistance and Excitation Force	148	(1)
Several Bodies Interacting with Waves	149	(11)
Phenomenological Discussion	150	(1)
Hydrodynamic Formulation	151	(2)
Radiation-Impedance and Radiation-Resistance Matrices	153	(3)
Radiation-Reactance and Added-Mass Matrices	156	(2)
Excitation Force Vector: The Haskind Relation	158	(1)
Wide-Spacing Approximation	159	(1)
The Froude-Krylov Force and Small-Body Approximation	160	(8)
The Froude-Krylov Force and Moment	161	(2)
The Diffraction Force	163	(1)
Small-Body Approximation for a Group of Bodies	163	(2)
Small-Body Approximation for a Single Body	165	(3)
Axisymmetric Oscillating System	168	(11)
The Radiation Impedance	171	(1)
Radiation Resistance and Excitation Force	172	(3)
Numerical 2-Body Example	175	(4)
Two-Dimensional System	179	(2)
Motion Response and Control of Motion	181	(15)
Dynamics of a Floating Body in Heave	183	(4)
Problems	187	(9)
Wave-Energy Absorption by Oscillating Bodies	196	(29)
Absorption Considered as Wave Interference	196	(2)
Absorption by a Body Oscillating in One Mode of Motion	198	(6)
Maximum Absorbed Power	200	(1)
Upper Bound of Power-to-Volume Ratio	200	(2)
Maximum Converted Useful Power	202	(2)
Optimum Control for Maximising Converted Energy	204	(8)
Absorption by a System of Several Oscillators	212	(13)
Maximum Absorbed Power and Useful Power	214	(2)
Maximum Absorbed Power by an Axisymmetric Body	216	(2)
Maximum Absorbed Power in the Two-Dimensional Case	218	(4)
Maximum Absorbed Power with Amplitude Constraints	222	(1)
Problems	222	(3)
Wave Interaction with Oscillating Water Columns	225	(38)
The Applied-Pressure Description for a Single OWC	226	(12)
Absorbed Power and Radiation Conductance	229	(1)
Reactive Power and Radiation Susceptance	230	(1)
An Axisymmetric Example	230	(2)
Maximum Absorbed Power	232	(2)
Reciprocity Relations for an OWC	234	(2)
OWC with Pneumatic Power Takeoff	236	(2)
Systems of OWCs and Oscillating Bodies	238	(25)
Phenomenological Theory	239	(3)
Absorbed Power	242	(2)
Hydrodynamic Formulation	244	(2)
Hydrodynamic Parameters	246	(1)
Reciprocity Relations for Radiation Parameters	247	(4)
Extension of the Haskind Relation	251	(3)
Reciprocity Relations for the Radiation Damping Matrix	254	(2)
Axisymmetric Systems	256	(3)
Problems	259	(4)
Bibliography	263	(6)
Index	269

Excerpts

"This book will be appropriate for those with backgrounds in elementary fluid dynamics or hydrodynamics and mathematical analysis. Graduate students and researchers will find it an excellent source of wave-energy theory and application."--BOOK JACKET.