The Mathematical Theory of Permanent Progressive Water-Waves

The Mathematical Theory of Permanent Progressive Water-Waves

Author: Hisashi Okamoto

Publisher: World Scientific Publishing Company

Published: 2001-09-28

Total Pages: 244

ISBN-13: 9813102691

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This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered. The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.


Gravity Waves in Water of Finite Depth

Gravity Waves in Water of Finite Depth

Author: J. N. Hunt

Publisher: Computational Mechanics

Published: 1997

Total Pages: 346

ISBN-13:

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In this book linear and nonlinear theories of wave modification are considered. There are chapters focusing on linear wave scattering, nonlinear dispersive long waves and parabolic modelling, the interaction of waves with tidal and other currents, the trapping of wave energy in the vicinity of particular topographical features, and the mechanisms by which waves change the bed profile through sediment transport.


Waves in Fluids

Waves in Fluids

Author: Sir M. J. Lighthill

Publisher: Cambridge University Press

Published: 2001-11-15

Total Pages: 528

ISBN-13: 9780521010450

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A comprehensive textbook in which the author describes the science of waves in liquids and gases. Drawing on a subject of enormous extent and variety, he provides his readers with a thorough analysis of the most important and representative types of waves including sound waves, shock waves, waterwaves of all kinds, and the so-called internal waves (inside atmospheres and oceans) due to intensity stratification. Emphasis throughout is on the most generally useful fundamental ideas of wave science, including the principles of how waves interact with flows. This standard work on one of the great subdivisions of the dynamics of fluids is lucidly written and will be invaluable to engineers, physicists, geophysicists, applied mathematicians or any research worker concerned with wave motions or fluid fllows. It is especially suitable as a textbook for courses at the final year undergraduate or graduate level.


Solitary Waves in Fluids

Solitary Waves in Fluids

Author: R. Grimshaw

Publisher: WIT Press

Published: 2007

Total Pages: 209

ISBN-13: 1845641574

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Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.


Water Wave Mechanics For Engineers And Scientists

Water Wave Mechanics For Engineers And Scientists

Author: Robert G Dean

Publisher: World Scientific Publishing Company

Published: 1991-01-23

Total Pages: 369

ISBN-13: 9814365696

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This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.


Hydrodynamics of Coastal Zones

Hydrodynamics of Coastal Zones

Author: S.R. Massel

Publisher: Elsevier

Published: 1989-04-01

Total Pages: 349

ISBN-13: 0080870864

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This book discusses selected theoretical topics of coastal hydrodynamics, including basic principles and applications in coastal oceanography and coastal engineering. It is not intended as a handbook; the emphasis is placed on presentation of a number of basic problems, rather than giving detailed instructions for their application. The bulk of the material deals with surface waves. In the author's opinion there is still a strong need for a book on wave phenomena in the coastal waters, as general textbooks on sea surface dynamics focus most of their attention on the deep ocean. This book intends to fill this need by concentrating on the phenomena typical of the coastal zone.Based on lectures given at the Institute of Hydroengineering, Polish Academy of Sciences in Gdansk, the approach throughout is a combination of the theoretical and observational. A basic knowledge of ordinary and partial differential equations, as well as the statistical and spectral analysis of time series, is assumed. The reader should also be familiar with fundamental hydrodynamic concepts.The book comprises nine chapters. Governing equations and conservation laws are treated in Chapter 1, using the variational principles. The theory of regular surface waves is covered in Chapters 2 to 4. The nonlinear effect of wave train modulation and their breaking of beaches is examined in Chapter 5. Chapters 6 and 7 focus on the statistical and spectral treatment of waves induced by wind. Current generation and circulation pattern are the subject of Chapter 8, while sea level variations are examined in Chapter 9. References for further reading are given at the end of each chapter.


Internal Gravity Waves

Internal Gravity Waves

Author: Bruce R. Sutherland

Publisher: Cambridge University Press

Published: 2010-09-02

Total Pages: 395

ISBN-13: 1316184323

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The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.


Gravity-Capillary Free-Surface Flows

Gravity-Capillary Free-Surface Flows

Author: Jean-Marc Vanden-Broeck

Publisher: Cambridge University Press

Published: 2010-07-15

Total Pages: 331

ISBN-13: 0521811902

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Experienced and well-respected author; essential monograph for applied mathematicians and engineers.


Advances In Coastal And Ocean Engineering, Vol 5

Advances In Coastal And Ocean Engineering, Vol 5

Author: Philip L-f Liu

Publisher: World Scientific

Published: 1999-07-06

Total Pages: 338

ISBN-13: 9814495026

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In the last two decades, one of the most important research accomplishments in coastal hydrodynamics has been the development of accurate numerical models for nonlinear water wave propagation over a complex bathymetry from a relatively deep-water depth into the surf zone. This book contains five excellent papers reviewing different methodologies in various aspects of wave modeling; the authors are active researchers who have made original contributions to these subjects.