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Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis

Author: Adrian Constantin

Publisher: SIAM

Published: 2011-01-01

Total Pages: 333

ISBN-13: 9781611971873

This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest. It contains selected information about water-wave motion for which advanced mathematical study can be pursued, enabling readers to derive conclusions that explain observed phenomena to the greatest extent possible. The author discusses the underlying physical factors of such waves and explores the physical relevance of the mathematical results that are presented. The material is an expanded version of the author's lectures delivered at the NSF-CBMS Regional Research Conference in the Mathematical Sciences organized by the Mathematics Department of the University of Texas-Pan American in 2010.

Nonlinear Water Waves

Author: David Henry

Publisher: Springer Nature

Published: 2019-11-27

Total Pages: 218

ISBN-13: 3030335364

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The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume. Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.

Water Waves Generated by Underwater Explosion

Author: Bernard Le Mehaute

Publisher: World Scientific

Published: 1996

Total Pages: 398

ISBN-13: 9789810220839

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This is the first book on explosion-generated water waves. It presents the theoretical foundations and experimental results of the generation and propagation of impulsively generated waves resulting from underwater explosions. Many of the theories and concepts presented herein are applicable to other types of water waves, in particular, tsunamis and waves generated by the fall of a meteorite. Linear and nonlinear theories, as well as experimental calibrations, are presented for cases of deep and shallow water explosions. Propagation of transient waves on dissipative, nonuniform bathymetries together with laboratory simulations are analyzed and discussed.

Tsunami and Nonlinear Waves

Author: Anjan Kundu

Publisher: Springer Science & Business Media

Published: 2007-06-19

Total Pages: 319

ISBN-13: 3540712569

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The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

Optical Remote Sensing of Ocean Hydrodynamics

Author: Victor Raizer

Publisher: CRC Press

Published: 2019-03-04

Total Pages: 310

ISBN-13: 1351119168

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Optical Remote Sensing is one of the main technologies used in sea surface monitoring. Optical Remote Sensing of Ocean Hydrodynamics investigates and demonstrates capabilities of optical remote sensing technology for enhanced observations and detection of ocean environments. It provides extensive knowledge of physical principles and capabilities of optical observations of the oceans at high spatial resolution, 1-4m, and on the observations of surface wave hydrodynamic processes. It also describes the implementation of spectral-statistical and fusion algorithms for analyses of multispectral optical databases and establishes physics-based criteria for detection of complex wave phenomena and hydrodynamic disturbances including assessment and management of optical databases. This book explains the physical principles of high-resolution optical imagery of the ocean surface, discusses for the first time the capabilities of observing hydrodynamic processes and events, and emphasizes the integration of optical measurements and enhanced data analysis. It also covers both the assessment and the interpretation of dynamic multispectral optical databases and includes applications for advanced studies and nonacoustic detection. This book is an invaluable resource for researches, industry professionals, engineers, and students working on cross-disciplinary problems in ocean hydrodynamics, optical remote sensing of the ocean and sea surface remote sensing. Readers in the fields of geosciences and remote sensing, applied physics, oceanography, satellite observation technology, and optical engineering will learn the theory and practice of optical interactions with the ocean.

Extreme Ocean Waves

Author: Efim Pelinovsky

Publisher: Springer

Published: 2015-09-02

Total Pages: 242

ISBN-13: 3319215752

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This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented. This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects.

Nonlinear Water Waves

Author: Adrian Constantin

Publisher: Springer

Published: 2016-06-28

Total Pages: 237

ISBN-13: 3319314629

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This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiar with one branch of the study of water waves, to learn more about other areas.

The Water Waves Problem

Author: David Lannes

Publisher: American Mathematical Soc.

Published: 2013-05-08

Total Pages: 347

ISBN-13: 0821894706

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This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.

Analytical Properties of Nonlinear Partial Differential Equations

Author: Alexei Cheviakov

Publisher: Springer Nature

Published:

Total Pages: 322

ISBN-13: 3031530748

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Nonlinear Waves in Integrable and Non-integrable Systems

Author: Jianke Yang

Publisher: SIAM

Published: 2010-12-02

Total Pages: 452

ISBN-13: 0898717051

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Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).