9780521782111

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

by
  • ISBN13:

    9780521782111

  • ISBN10:

    0521782112

  • Format: Hardcover
  • Copyright: 2002-04-08
  • Publisher: Cambridge University Press
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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.

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