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This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins with a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicity. A further four chapters discuss sea severity, extreme sea state, directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally, the stochastic properties of nonGaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitable as a text for graduate students of naval, ocean and coastal engineering. It will also serve as a useful reference for research scientists and engineers working in this field.
CAMBRIDGE OCEAN TECHNOLOGY SERIES: 6 General editors: I. Dyer, R. Eatock Taylor, J. N. Newman, W. G. Price
OCEAN WAVES
Cambridge Ocean Technology Series 1. 2. 3. 4.
Faltinsen: Sea Loads on Ships and Offshore Structures Burcher & Rydill: Concepts in Submarine Design Breslin & Andersen: Hydrodynamics of Ship Propellers Shenoi & Wellicome (eds.): Composite Materials in Maritime Structures, Volume 13 Fundamental Aspects 5. Shenoi & Wellicome (eds.): Composite Materials in Maritime Structures, Volume 23 Practical Considerations 6. Ochi: Ocean Waves
OCEAN WAVES The Stochastic Approach
Michel K. Ochi University of Florida
CAMBRIDGE UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521563789 © Michel K.Ochi 1998 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1998 This digitally printed first paperback version 2005 A catalogue recordfor this publication is available from the British Library Library of Congress Cataloguing in Publication data Ochi, Michel K. Ocean waves / Michel K. Ochi. p. cm. - (Cambridge ocean technology series ; 6) ISBN 0 521 56378 X (he) 1. Ocean waves. I. Title. II. Series. GC211.2.026 1998 551.47'02-dc21 97-16355 CIP ISBN-13 978-0-521-56378-9 hardback ISBN-10 0-521-56378-X hardback ISBN-13 978-0-521-01767-1 paperback ISBN-10 0-521-01767-X paperback
CONTENTS
Preface
xi
1 Description of random seas 1.1 Stochastic concept as applied to ocean waves 1.1.1 Introduction 1.1.2 Ocean waves as a Gaussian random process 1.1.3 Random seas 1.2 Mathematical presentation of random waves 1.3 Stochastic prediction of wave characteristics 2 Spectral analysis 2.1 Spectral analysis of random waves 2.1.1 Fundamentals of stochastic processes 2.1.2 Auto-correlation function 2.1.3 Spectral density function (spectrum) 2.1.4 Wiener-Khintchine theorem 2.1.5 Spectral analysis of two wave records 2.1.6 Wave-number spectrum 2.1.7 Wave velocity and acceleration spectra 2.2 Characteristics of wave spectra 2.3 Wave spectral formulations 2.3.1 Pierson-Moskowitz spectrum 2.3.2 Two-parameter spectrum 2.3.3 Spectral formulation as a function of ) Syx(-o>)=Sxy(w)
(2-26)
where S^y(a)) is the complex conjugate of Sxy((o). The cro