Download or read book Lectures on the Theory of Water Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2016-02-04 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.
Download or read book Lectures on the Theory of Water Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2016-02-04 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A range of experts contribute introductory-level lectures on active topics in the theory of water waves.
Download or read book The Water Waves Problem written by David Lannes and published by American Mathematical Soc.. This book was released on 2013-05-08 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Modern Introduction to the Mathematical Theory of Water Waves written by Robin Stanley Johnson and published by Cambridge University Press. This book was released on 1997-10-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers classical and modern problems in linear and non-linear water-wave theory.
Download or read book Almost Global Solutions of Capillary Gravity Water Waves Equations on the Circle written by Massimiliano Berti and published by Springer. This book was released on 2018-11-02 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
Download or read book Nonlinear Water Waves with Applications to Wave Current Interactions and Tsunamis written by Adrian Constantin and published by SIAM. This book was released on 2011-01-01 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Water Wave Kinematics written by A. Tørum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 751 pages. Available in PDF, EPUB and Kindle. Book excerpt: Water wave kinematics is a central field of study in ocean and coastal engineering. The wave forces on structures as well as sand erosion both on coastlines and in the ocean are to a large extent governed by the local distribution of velocities and accelerations of the water particles. Our knowledge of waves has generally been derived from measurements of the water surface elevations. The reason for this is that the surface elevations have been of primary interest and fairly cheap and reliable instruments have been developed for such measurements. The water wave kinematics has then been derived from the surface elevation information by various theories. However. the different theories for the calculation of water particle velocities and acceleration have turned out to give significant differences in the calculated responses of structures. In recent years new measurement techniques have made it possible to make accurate velocity measurements. Hence. the editors deemed it to be useful to bring together a group of experts working actively as researchers in the field of water wave kinematics. These experts included theoreticians as well as experimentalists on wave kinematics. It was also deemed useful to include experts on the response of structures to have their views from a structural engineering point of view on what information is really needed on water wave kinematics.
Download or read book Fluid Waves written by Richard Manasseh and published by CRC Press. This book was released on 2021-11-17 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book derives the mathematical basis for the most-encountered waves in fluids in science and engineering. It gives professionals in important occupations such as maritime engineering, climate science, urban noise control, and medical diagnostics the key formulae needed for calculations. The book begins with the basis of fluid dynamics and subsequent chapters cover surface gravity waves, sound waves, internal gravity waves, waves in rotating fluids, and introduce some nonlinear wave phenomena. Basic phenomena common to all fluid waves such as refraction are detailed. Thereafter, specialized application chapters describe specific contemporary problems. All concepts are supported by narrative examples, illustrations, and problems. FEATURES • Explains the basis of wave mechanics in fluid systems. • Provides tools for the analysis of water waves, sound waves, internal gravity waves, rotating fluid waves and some nonlinear wave phenomena, together with example problems. • Includes comprehensible mathematical derivations at the expense of fewer theoretical topics. • Reviews cases describable by linear theory and cases requiring nonlinear and wave-interaction theories. This book is suitable for senior undergraduates, graduate students and researchers in Fluid Mechanics, Applied Mathematics, Meteorology, Physical Oceanography, and in Biomedical, Civil, Chemical, Environmental, Mechanical, and Maritime Engineering.
Download or read book Linear Water Waves written by Nikolaĭ Germanovich Kuznet︠s︡ov and published by Cambridge University Press. This book was released on 2002-07-11 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.'
Download or read book Wave Turbulence written by Sergey Nazarenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
Download or read book Nonlinear Water Waves written by Lokenath Debnath and published by Academic Press. This book was released on 1994-03-29 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave motion in water is one of the most striking observable phenomena in nature. Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant. In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability phenomena. New solutions are now available for waves modulatedin both space and time, which exhibit new phenomena as diverse as solitons, resonant interactions, side-band instability, and wave-breaking. Other achievements include the discovery of soliton interactions, and the Inverse Scattering Transform method forfinding the explicit exact solution for several canonical nonlinear partial differential equations. This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.
Download or read book Fundamentals of Physics I written by R. Shankar and published by Yale University Press. This book was released on 2019-08-20 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beloved introductory physics textbook, now including exercises and an answer key, explains the concepts essential for thorough scientific understanding In this concise book, R. Shankar, a well-known physicist and contagiously enthusiastic educator, explains the essential concepts of Newtonian mechanics, special relativity, waves, fluids, thermodynamics, and statistical mechanics. Now in an expanded edition—complete with problem sets and answers for course use or self-study—this work provides an ideal introduction for college-level students of physics, chemistry, and engineering; for AP Physics students; and for general readers interested in advances in the sciences. The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics.
Download or read book Nonlinear Water Waves written by David Henry and published by Springer Nature. This book was released on 2019-11-27 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Waves in Fluids written by Sir M. J. Lighthill and published by Cambridge University Press. This book was released on 2001-11-15 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Hydrodynamics and Water Waves written by Bernard LeMéhauté and published by . This book was released on 1969 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Water Wave Mechanics For Engineers And Scientists written by Robert G Dean and published by World Scientific Publishing Company. This book was released on 1991-01-23 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to PDEs and Waves for the Atmosphere and Ocean written by Andrew Majda and published by American Mathematical Soc.. This book was released on 2003 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.
