Dynamics and Stability of Gravity-capillary Solitary Waves PDF Download
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Author: David Christopher Calvo Publisher: ISBN: Category : Languages : en Pages : 286
Book Description
(Cont.) The analysis followed in the free-surface problem is then generalized to examine the dynamics of gravity-capillary interfacial solitary waves in a layered two-fluid system. Here, the linear stability and limiting wave forms of free solitary waves are determined over a range of system parameters using the full hydrodynamic equations. Finally, a related problem of gravity-capillary envelope solitons is considered under the general situation of unequal phase and group speeds. By asymptotic and numerical techniques it is found that envelope solitons are generally nonlocal-tails are radiated owing to a resonance mechanism that is beyond the NLS equation.
Author: David Christopher Calvo Publisher: ISBN: Category : Languages : en Pages : 286
Book Description
(Cont.) The analysis followed in the free-surface problem is then generalized to examine the dynamics of gravity-capillary interfacial solitary waves in a layered two-fluid system. Here, the linear stability and limiting wave forms of free solitary waves are determined over a range of system parameters using the full hydrodynamic equations. Finally, a related problem of gravity-capillary envelope solitons is considered under the general situation of unequal phase and group speeds. By asymptotic and numerical techniques it is found that envelope solitons are generally nonlocal-tails are radiated owing to a resonance mechanism that is beyond the NLS equation.
Author: Hisashi Okamoto Publisher: World Scientific ISBN: 9789810244507 Category : Mathematics Languages : en Pages : 248
Book Description
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.
Author: Publisher: ISBN: Category : Languages : en Pages : 252
Book Description
Two particular nonlinear waves are considered in this thesis: wind ripples in the sea surface which are called capillary-gravity (CG) waves and flexural-gravity (FG) waves generated by the moving loads on floating ice sheets. Very short wind waves, predominantly in the capillary-gravity regime, are important because they affect energy, momentum and material fluxes through the sea surface. For the three-dimensional CG waves, a weakly nonlinear model equation based on a truncation using the Dirichlet to Neumann operator is developed in this thesis. Many solitary wave branches are found using the model, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers. The FG wave, modeling the deformation of a floating ice sheet, has applications in the polar regions, where ice cover is used for roads or runways. In the thesis, we show that solitary waves do occur in deep water for the full potential equation, though the associated Nonlinear Schrodinger equation is of defocusing type. These solitary waves are a new type in that they occur along a branch of generalized solitary waves that itself bifurcates from periodic waves of finite amplitude. When the problem is forced by a moving load, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. If the problem is forced at a speed in this range, very large unsteady responses are obtained, which may result in the ice break. When the forcing is released, a solitary wave is generated.
Author: David Henry Publisher: Springer Nature ISBN: 3030335364 Category : Mathematics Languages : en Pages : 218
Book Description
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: Mohammad F Mahmood Publisher: World Scientific ISBN: 9814465135 Category : Science Languages : en Pages : 214
Book Description
The objective of this book is to introduce new researchers to the rich dynamical system of water waves, and to show how (some) abstract mathematical concepts can be applied fruitfully in a practical physical problem and to make the connection between theory and experiment. It provides a coherent set of lectures on the current status of water wave theory, including identification of some open problems.
Author: Publisher: ScholarlyEditions ISBN: 1464965064 Category : Mathematics Languages : en Pages : 864
Book Description
Issues in Applied Mathematics / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Applied Mathematics. The editors have built Issues in Applied Mathematics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: David Christopher Calvo
Author: David Christopher Calvo
Author: R. Grimshaw
Author: Benjamin Fearing Akers
Author: Ashutosh Sharma
Author: Hisashi Okamoto
Author: 
Author: David Henry
Author: Mohammad F Mahmood
Author: Albert Ai
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