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Nonlinear effects on the dispersion relation of waves in shallow water are examined with measurements collected on a mild sloping sandy beach during the recent Sandy Duck experiment. Four arrays of bottom pressure sensors were deployed in depths ranging from 3 - 6 m during August-November, 1997. For each of these arrays, a root-mean-square average wavenumber was estimated as a function of frequency from the cross-spectra of one-hour-long pressure records. The observed wavenumbers are compared to linear finite depth theory predictions and to predictions based on a stochastic formulation of weakly nonlinear Boussinesq equations that incorporate both frequency and amplitude dispersion effects. The observed wavenumbers are generally in agreement with the nonlinear theory predictions and deviate significantly (maximum errors averaged over the spectrum of about 25%) from the linear theory predictions. In high energy conditions with breaking or nearly breaking waves, the effects of amplitude and frequency dispersion tend to cancel, and all components of the wave spectrum travel with approximately the shallow water wave speed. These results are consistent with previous studies.
Nonlinear effects on the dispersion relation of waves in shallow water are examined with measurements collected on a mild sloping sandy beach during the recent Sandy Duck experiment. Four arrays of bottom pressure sensors were deployed in depths ranging from 3 - 6 m during August-November, 1997. For each of these arrays, a root-mean-square average wavenumber was estimated as a function of frequency from the cross-spectra of one-hour-long pressure records. The observed wavenumbers are compared to linear finite depth theory predictions and to predictions based on a stochastic formulation of weakly nonlinear Boussinesq equations that incorporate both frequency and amplitude dispersion effects. The observed wavenumbers are generally in agreement with the nonlinear theory predictions and deviate significantly (maximum errors averaged over the spectrum of about 25%) from the linear theory predictions. In high energy conditions with breaking or nearly breaking waves, the effects of amplitude and frequency dispersion tend to cancel, and all components of the wave spectrum travel with approximately the shallow water wave speed. These results are consistent with previous studies.
This book is intended as a handbook for professionals and researchers in the areas of Physical Oceanography, Ocean and Coastal Engineering and as a text for graduate students in these fields. It presents a comprehensive study on surface ocean waves induced by wind, including basic mathematical principles, physical description of the observed phenomena, practical forecasting techniques of various wave parameters and applications in ocean and coastal engineering, all from the probabilistic and spectral points of view. The book commences with a description of mechanisms of surface wave generation by wind and its modern modeling techniques. The stochastic and probabilistic terminology is introduced and the basic statistical and spectral properties of ocean waves are developed and discussed in detail. The bulk of material deals with the prediction techniques for waves in deep and coastal waters for simple and complex ocean basins and complex bathymetry. The various prediction methods, currently used in oceanography and ocean engineering, are described and the examples of practical calculations illustrate the basic text. An appendix provides a description of the modern methods of wave measurement, including the remote sensing techniques. Also the wave simulation methods and random data analysis techniques are discussed. In the book a lot of discoveries of the Russian and East European scientists, largely unknown in the Western literature due to the language barrier, are referred to.
In this classic study, a renowned student of ocean wave theory examines the data requirements and details of the power spectral analysis required to make the wave revolution intelligible. Although the discussions center on waves, once the techniques are understood, they can be applied to many other areas. After outlining the nature of waves and wave processes and their methods of measurement and classification, the author provides a detailed exploration that relies heavily on mathematical models. Topics include perturbations of irrotational motion, energy considerations, wave generations by wind, and much more. The text is enhanced and clarified by 270 photos, figures, and tables. A helpful bibliography and indexes conclude this indispensable addition to the oceanographer's library.
New Edition: Ocean Surface Waves: Their Physics and Prediction (3rd Edition)The book is an extended and updated edition of the book published in 1996 under the same title (World Scientific, ISBN 9810216866). It contains a very comprehensive and extensive study on surface ocean waves induced by wind, earthquakes and possible landslides and asteroids impacts. The basic mathematical principles, physical description of the observed phenomena, practical forecasting techniques of the various wave parameters and extended application in ocean and coastal engineering, are discussed from the stochastic point of view.All chapters were completely rewritten and supplemented with many new discoveries which were published since the first edition in 1996. In particular, new chapters are added on very interesting and contemporary topics such as: wave breaking mechanisms in deep- and shallow water, freak waves, tsunami, water circulation in porous sea bottom induced by surface waves, and waves propagation through mangrove forests.In terms of numerical modeling, the state of the art of the modern methodology of wave prediction models WAM and SWAN, as well as of the high sophisticated satellite methods of waves measurement and modern methods of signal processing, including wavelets approach and Hilbert Transform approach are presented. The book is supplemented with an extended list of relevant and extended, contemporary bibliography, subject index and author index.
This book is an extended and substantially updated edition of the previous book editions published in 1996 and 2013 under the same title. The 3rd edition is a one-volume, modern and comprehensive overview of the current knowledge of regular and random ocean surface waves in deep waters and in coastal zones.Since the previous editions many new theoretical advances have been made in the physical understanding and analytical and numerical treatment of various ocean wave problems. The revisions and supplements demanded by these advances have been substantial, therefore the scope of the book has been extended by adding a new chapter and substantially supplementing others.All chapters of the book have been rewritten to include and describe in detail many new discoveries made since the completion of the previous editions. In this 3rd edition a comprehensive and updated overview of the fundamentals of the regular wave mechanics, as well as the spectral and statistical properties of random waves are given. Except for the updated chapters dedicated to tsunami and extreme waves, a new chapter dealing with other types of impulsive waves starting from rest, are also included.The air-sea interaction processes as well as the last improvements in ocean wave modelling and presently available wave prediction models (WAM, WAVEWATCH III, UMWM, NEMO) are thoroughly discussed and their applications are demonstrated. The review of the present ocean observation methods encompasses the modern sea-truthing, as well as applications of data from presently operating marine satellites.In this revised edition, chapters on the behavior of surface waves in the vegetated environments such as coral reef, mangrove forest, seaweed and seagrass areas are substantially extended and updated to include the last discoveries.The explanations in the book are self-contained and detailed enough to capture the interest of the potential readers and to prompt them to explore the research literature. The list of rapidly growing number of the recent papers on the ocean waves has been extended substantially, up to about 900 titles.
This book contains a comprehensive study of the internal ocean waves, which play a very important role in ocean physics providing mechanisms for ocean water mixing and circulation, as well as the transportation of gases, nutrients, and a very large number of marine organisms in the ocean body. In contrast to surface waves, the literature on internal waves is not so numerous, mainly due to the difficulties in experimental data collection and in the mathematical description of internal wave propagation. In this book, the basic mathematical principles, a physical description of the observed phenomena, and practical theoretical methods of determination of wave parameters as well as the original method of observation using moving sensors are presented. Special attention is paid to internal wave propagation over changing bottom topographies in shallow seas such as the Baltic Sea. The book is supplemented with an extended list of relevant and extended bibliographies, a subject index, and an author index.
The aim of this book is to present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from the deterministic point of view. The bulk of the material deals with the linearized theory.