Physics and Astronomy

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1 Wind-Waves in Oceans Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy ONLINE LIBRARY

2 Physics of Earth and Space Environments The series Physics of Earth and Space Environments is devoted to monograph texts dealing with all aspects of atmospheric, hydrospheric and space science research and advanced teaching. The presentations will be both qualitative as well as quantitative, with strong emphasis on the underlying (geo )physical sciences. Of particular interest are contributions which relate fundamental research in the aforementioned fields to present and developing environmental issues viewed broadly concise accounts of newly emerging important topics that are embedded in a broader framework in order to provide quick but readable access of new material to a larger audience The books forming this collection will be of importance for graduate students and active researchers alike. Series Editors: Professor Dr. Rodolfo Guzzi Responsabile di Scienze della Terra Head of Earth Sciences Via di Villa Grazioli, Roma, Italy Professor Dr. Dieter Imboden ETH ZUrich Honggerberg 8093 ZUrich, Switzerland Dr. Louis J. Lanzerotti Bell Laboratories, Lucent Technologies 700 Mountain Avenue Murray Hill, NJ 07974, USA Professor Dr. Ulrich Platt Ruprecht-Karls-Universitat Heidelberg Institut fur Umweltphysik lm Neuenheimer Feld Heidelberg, Germany

3 Igor V. Lavrenov Wind-Waves in Oceans Dynamics and Numerical Simulations With 121 Figures ~ Springer

4 Professor Dr. Igor V. Lavrenov Arctic and Antartic Research Institute 38 Bering Str St. Petersburg Russia Library of Congress Cataloging-in-Publication Data: Lavrenov, I.V. (Igor' Viktorovich) Wind-waves in oceans: dynamics and numerical simulations/!. V. Lavrenov. p.cm.- (Physics of earth and space environments, ISSN ) Includes bibliographical references and index. ISBN ISBN (ebook) DOI / Wind waves-mathematical models. I. Title. II. Series. QC880.4.W3 L '022' dc ISBN This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003 Softcover reprint of the hardcover 1st edition 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the author Data conversion by LE-TEX, Leipzig Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper SPIN: /3111/tr

5 To my teachers

6 Preface The study of sea waves has always been in the focus of mankind's attention. This is attributed not only to a desire to understand the behaviour in seas and oceans, but also, it has some practical necessity. Developing up-todate wind wave numerical methods requires detailed mathematical modelling, starting with wave generation, development, propagation and transformation on the surface in different water areas under quasi-stationary conditions, up to a synthesis of climatic features observed under different wave generation conditions in oceans, sea or coastal areas. The present monograph considers wind waves in terms of the most general formulation of the problem as a probable hydrodynamic process with wide spatial variability. It ranges between the global scale of the oceans, whose typical size is comparable with the Earth's radius, to the regional and local scales of the seas, including water areas limited in space with significant current or depth gradients in coastal zones, where waves cease their existence having propagated tens of thousand miles. The importance of mathematical wind wave modelling as a random hydrodynamic process with a wide range of spatial-temporal variability at different scales is due to the stricter requirements for detailing, completeness and reliability of wave characteristic data. This is necessary for improving wave forecasting, elaborating principally new ocean diagnostic methods and means, and expanding areas of resource exploration of the world's oceans and their shelves. It is also important for an increasing number of tasks concerning special hydrometeorological (weather) services for marine and oceanic operations. The essence of mathematical wind wave modelling in the ocean in conditions of spatial non-uniformity, taking into account currents, uneven bottoms and ice influencing the generation, evolution and propagation of wind waves, is presented in this monograph. Considerable attention has been given to this problem during the last few years, but the methodical presentation of the modern theory is undertaken here for the first time. The monograph begins with the most general problem formulation of the mathematical wind wave modeling of the world's oceans. Some new approaches and optimal numerical methods of the solution of the problem are presented. The Earth's spherical effect on wave propagation is considered for global distances in the ocean. The main attention is given to the problem of

7 VIII Preface wave interaction with the bottom, non-uniform currents and ice cover. The effects of spectrum evolution, wave reflection and blocking are considered at a current. The monograph gives a spectral model description of "abnormal waves", which are very dangerous to ship navigation. Practical recommendations are given, for the first time here, in order to estimate the wave elements in a non-uniform current. The monograph can be used by specialists from many disciplines: oceanographers, meteorologists, hydraulic engineers and others, whose activity is connected with the ocean. It may also be used as an additional textbook for students in higher educational establishments for its methodical presentation of problems concerning physics and mathematical wind wave modelling. Although the author's results serve as a basis for the monograph, I am sincerely grateful to persons who participated in scientific discussions, assisted in solving theoretical problems and carrying out field measurements at sea. They are V. Dymov, T. Pasechnik and others (Arctic and Antarctic Research Institute, St. Petersburg); I. Davidan, Ye. Gutshabash, V. Ryvkin, V. Rozhkov, L. Lopatukhin, B. Shatov and others (Branch of the State Oceanographic Institute in St. Petersburg); Yu. Abuzyarov and V. Ryabinin (Hydrometeorological Centre, Moscow); V. Zakharov, M. Zaslavskii and V. Krasitskii (Institute of Oceanology, the Russian Academy of Sciences); G. Matushevskiy and V. Polnikov (State Oceanographic Institute, Moscow); I. Kantarzhi (STANKIN); V. Korobov (NORDECO); S. Strekalov (Hydroproject, Moscow), E. Pelinovskiy (Institute of Applied Physics, Nizniy Novgorod); V. Kudriavtcev (Marine Hydrophysical Institute, Ukraine); V. Makin, G. Komen, and J. Onvlee (KNMI, Netherlands); F.J. Ocampo-Torres (CICESE, Mexico); D. Resio (ERDC, US); L. Cavaleri (ISDGM, Italy); H. Krogstad (NTNU, Norway); and G. Athanassoulis (NTUA, Greece). The author is also grateful ton. Yakovleva for her assistance in the design of the monograph; and S. Kozhevnikov and M. Arsenchuk for helping in translation. Acknowledgements. The monograph includes the results of some scientific programmes concerning fundamental studies and data retrieval undertaken at the Arctic and Antarctic Research Institute in with support of the Russian Foundation for Basic Research (RFBR) and by the INTAS Projects:99-666; ; ; St. Petersburg November 2002 Igor V. Lavrenov

8 Contents Introduction General Problem Formulation of Wind Wave Modelling in a Non-Uniform Ocean Hydrodynamic Problem of Surface Wave Generation by Air Flow Geometric Optics Approximation Wave Action Conservation Law Statistical Wind Wave Description Kinetic Equation of the Evolution of the Wind Wave Spectrum General Problem Formulation for Determining the Wave Action Spectral Density in the Ocean Spatial-Temporal Scale Considerations in the Analysis of Problem Solution Mathematical Simulation of Wave Propagation at Global Distances Problem Formulation of Ocean Wind Wave Modelling Using Spherical Variables Correspondence of Local and Global Coordinate Systems Numerical Simulation of Swell Propagation Using the Method of Characteristics The Influence of Current on the Evolution of Waves at the Global Scale Numerical Implementation of the Wave Energy Balance Equation Statement of the Problem Formulation of the Wave Propagation Problem Standard Numerical Propagation Schemes Elimination of the "Garden Sprinkler Effect" Interpolation-Ray (INTERPOL) Method Comparison of Results of Numerical Wave Propagation Schemes

9 X Contents 3.7 Numerical Integration of the Source FUnction Conclusions Study of Physical Mechanisms Forming the Wind Wave Energy Spectrum in Deep Water Non-Linear Energy Transfer in Wind Wave Spectrum Problem Review Optimal Algorithm of Computation of Non-linear Energy Transfer Calculation Results of Non-linear Energy Transfer in Wind Wave Spectrum Numerical Study of Non-Stationary Solution of the Hasselmann Equation Wind Wave Energy Input Wave Energy Dissipation in Deep Water Influence of Mesoscale Effects on Wind Wave Evolution Wave Evolution in Non-uniform Currents in Deep Water Formulation of the Problem in the Local Coordinate System Frequency-Angular Spectrum Evolution in a Current Spectral Model of Rips Estimation of Non-Linear Wave Interaction in the Rip Spectrum Wave Element Transformations in Current, Varying Along its Direction Wave Diffraction Around a Caustic Wind Wave Transformation in Cross-Velocity Shear Current Freak Wave Problem Influence of Vertical Non-Uniform Current on Wind Wave Transformation Wind Wave Generation in a Current Some Practical Recommendations for Estimation of Current Influence on Waves Wave Transformation in Shallow Water Spectrum Transformation Due to Wave Refraction in Shallow Water Weak Non-Linear Wave Interaction in Shallow Water Joint Influence of Bottom and a Non-Uniform Current on Wave Transformation Wave Energy Dissipation in Shallow Water Numerical Model of Wind Wave Transformation in a Coastal Area

10 6.6 Wind Wave Spectrum Transformation According Contents XI to the Black Sea International Experiment Wave Transformation in Ice-Covered Water Wave Problem Formulation in Water with Ice Cakes Wave Spectrum Evolution in Water with Ice Cakes Kinetic Equation for Non-linear Waves in Sea with Ice Cakes Estimation of Non-Linear Energy Transfer in the Wave Spectrum in Water with Ice Cakes Numerical Simulation of Surface Gravity Wave Interaction with Elastic Ice Floes Conclusion Bibliography Index