Lectures on the Theory of Water Waves PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on the Theory of Water Waves PDF full book. Access full book title Lectures on the Theory of Water Waves by Thomas J. Bridges. Download full books in PDF and EPUB format.
Author: Thomas J. Bridges
Publisher: Cambridge University Press
ISBN: 1316558940
Category : Science
Languages : en
Pages : 299
Get Book Here
Book Description
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.
Author: Thomas J. Bridges
Publisher: Cambridge University Press
ISBN: 1316558940
Category : Science
Languages : en
Pages : 299
Get Book Here
Book Description
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.
Author: Thomas J. Bridges
Publisher: Cambridge University Press
ISBN: 1107565561
Category : Mathematics
Languages : en
Pages : 299
Get Book Here
Book Description
A range of experts contribute introductory-level lectures on active topics in the theory of water waves.
Author: Robin Stanley Johnson
Publisher: Cambridge University Press
ISBN: 9780521598323
Category : Mathematics
Languages : en
Pages : 468
Get Book Here
Book Description
This text considers classical and modern problems in linear and non-linear water-wave theory.
Author: Massimiliano Berti
Publisher: Springer
ISBN: 3319994867
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
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.
Author: A. Tørum
Publisher: Springer Science & Business Media
ISBN: 9400905319
Category : Technology & Engineering
Languages : en
Pages : 751
Get Book Here
Book Description
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.
Author: Adrian Constantin
Publisher: SIAM
ISBN: 9781611971873
Category : Mathematics
Languages : en
Pages : 333
Get Book Here
Book Description
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.
Author: Richard Manasseh
Publisher: CRC Press
ISBN: 1000464784
Category : Mathematics
Languages : en
Pages : 312
Get Book Here
Book Description
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.
Author: Sergey Nazarenko
Publisher: Springer Science & Business Media
ISBN: 3642159419
Category : Science
Languages : en
Pages : 287
Get Book Here
Book Description
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.
Author: Lokenath Debnath
Publisher: Academic Press
ISBN:
Category : Mathematics
Languages : en
Pages : 576
Get Book Here
Book Description
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.
Author: R. Shankar
Publisher: Yale University Press
ISBN: 0300249586
Category : Science
Languages : en
Pages : 523
Get Book Here
Book Description
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.
