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| Author | : David Lannes |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 347 |
| Release | : 2013-05-08 |
| Genre | : Mathematics |
| ISBN | : 0821894706 |
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.
| Author | : Birendra Nath Mandal |
| Publisher | : CRC Press |
| Total Pages | : 375 |
| Release | : 2015-05-21 |
| Genre | : Mathematics |
| ISBN | : 1498705537 |
The theory of water waves is most varied and is a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers, and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special configurations that are of interes
| Author | : James Johnston Stoker |
| Publisher | : Courier Dover Publications |
| Total Pages | : 593 |
| Release | : 2019-04-17 |
| Genre | : Science |
| ISBN | : 0486839923 |
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
| Author | : Robin Stanley Johnson |
| Publisher | : Cambridge University Press |
| Total Pages | : 468 |
| Release | : 1997-10-28 |
| Genre | : Mathematics |
| ISBN | : 9780521598323 |
This text considers classical and modern problems in linear and non-linear water-wave theory.
| Author | : David Henry |
| Publisher | : Birkhäuser |
| Total Pages | : 218 |
| Release | : 2019-12-06 |
| Genre | : Mathematics |
| ISBN | : 9783030335359 |
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.
| Author | : Robert G Dean |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 369 |
| Release | : 1991-01-23 |
| Genre | : Technology & Engineering |
| ISBN | : 9814365696 |
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.
| Author | : Nikolaĭ Germanovich Kuznet︠s︡ov |
| Publisher | : Cambridge University Press |
| Total Pages | : 528 |
| Release | : 2002-07-11 |
| Genre | : Mathematics |
| ISBN | : 9780521808538 |
This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'
| Author | : B. N. Mandal |
| Publisher | : WIT Press (UK) |
| Total Pages | : 376 |
| Release | : 1997 |
| Genre | : Science |
| ISBN | : |
The mathematical techniques used to handle various water wave problems are varied and fascinating. This book highlights a number of these techniques in connection with investigations of some classes of water wave problems by leading researchers in this field. The first eight chapters discuss linearised theory while the last two cover nonlinear analysis. This book will be an invaluable source of reference for advanced mathematical work in water wave theory.
| Author | : Frederic Dias |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 264 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180510X |
The proceedings featured in this book grew out of a conference attended by 40 applied mathematicians and physicists which was held at the International Center for Research in Mathematics in Luminy, France, in May 1995. This volume reviews recent developments in the mathematical theory of water waves. The following aspects are considered: modeling of various wave systems, mathematical and numerical analysis of the full water wave problem (the Euler equations with a free surface) and of asymptotic models (Korteweg-de Vries, Boussinesq, Benjamin-Ono, Davey-Stewartson, Kadomtsev-Petviashvili, etc.), and existence and stability of solitary waves.
| Author | : J. J. Stoker |
| Publisher | : John Wiley & Sons |
| Total Pages | : 598 |
| Release | : 2011-08-15 |
| Genre | : Mathematics |
| ISBN | : 1118031350 |
Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.
