Download or read book Small amplitude steady water waves with vorticity written by Evgeniy Lokharu and published by Linköping University Electronic Press. This book was released on 2017-01-30 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of describing two-dimensional traveling water waves is considered. The water region is of finite depth and the interface between the region and the air is given by the graph of a function. We assume the flow to be incompressible and neglect the effects of surface tension. However we assume the flow to be rotational so that the vorticity distribution is a given function depending on the values of the stream function of the flow. The presence of vorticity increases the complexity of the problem and also leads to a wider class of solutions. First we study unidirectional waves with vorticity and verify the Benjamin-Lighthill conjecture for flows whose Bernoulli constant is close to the critical one. For this purpose it is shown that every wave, whose slope is bounded by a fixed constant, is either a Stokes or a solitary wave. It is proved that the whole set of these waves is uniquely parametrised (up to translation) by the flow force which varies between its values for the supercritical and subcritical shear flows of constant depth. We also study large-amplitude unidirectional waves for which we prove bounds for the free-surface profile and for Bernoulli’s constant. Second, we consider small-amplitude waves over flows with counter currents. Such flows admit layers, where the fluid flows in different directions. In this case we prove that the initial nonlinear free-boundary problem can be reduced to a finite-dimensional Hamiltonian system with a stable equilibrium point corresponding to a uniform stream. As an application of this result, we prove the existence of non-symmetric wave profiles. Furthermore, using a different method, we prove the existence of periodic waves with an arbitrary number of crests per period.
Download or read book Large amplitude Solitary Water Waves with Discontinuous Vorticity written by Adelaide Akers and published by . This book was released on 2017 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a two-dimensional body of water with constant density which lies below a vacuum. The ocean bed is assumed to be impenetrable, while the boundary which separates the fluid and the vacuum is assumed to be a free boundary. Under the assumption that the vorticity is only bounded and measurable, we prove that for any upstream velocity field, there exists a continuous curve of large-amplitude solitary wave solutions. This is achieved via a local and global bifurcation construction of weak solutions to the elliptic equations which constitute the steady water wave problem. We also show that such solutions possess a number of qualitative features; most significantly that each solitary wave is a symmetric, monotone wave of elevation.
Download or read book Ideal MHD written by Jeffrey P. Freidberg and published by Cambridge University Press. This book was released on 2014-06-26 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive, self-contained, and clearly written, this book describes the macroscopic equilibrium and stability of high temperature plasmas.
Download or read book Steady Water Waves with Vorticity written by Mikyoung Hur and published by . This book was released on 2006 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Twenty Second Symposium on Naval Hydrodynamics written by National Research Council and published by National Academies Press. This book was released on 2000-03-02 with total page 1039 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Twenty-Second Symposium on Naval Hydrodynamics was held in Washington, D.C., from August 9-14, 1998. It coincided with the 100th anniversary of the David Taylor Model Basin. This international symposium was organized jointly by the Office of Naval Research (Mechanics and Energy Conversion S&T Division), the National Research Council (Naval Studies Board), and the Naval Surface Warfare Center, Carderock Division (David Taylor Model Basin). This biennial symposium promotes the technical exchange of naval research developments of common interest to all the countries of the world. The forum encourages both formal and informal discussion of the presented papers, and the occasion provides an opportunity for direct communication between international peers.
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 Differential Equations with Operator Coefficients written by Vladimir Kozlov and published by Springer Science & Business Media. This book was released on 1999-01-19 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.
Download or read book The Interaction of Ocean Waves and Wind written by Peter Janssen and published by Cambridge University Press. This book was released on 2004-10-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.
Download or read book Mass Transport in Water Waves written by Chiang C. Mei and published by . This book was released on 1972 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a fluid is in periodic wave motion, a fluid particle is carried by a velocity field varying from place to place. At different instants the location of the particle differs and so does the velocity field in its immediate neighborhood. As a result the time-averaged velocity of a particle may be different from the local velocity field. In particular, a fluid particle may have a net mean drift even if the local velocity field has zero mean; this is indeed the case in irrotational gravity waves. In a viscous fluid, the wave-induced Reynolds stress imparts a steady momentum to the fluid; a steady shear is set up to balance it and hence a further mean velocity field results. The sum of these two steady currents provides the total drift by which a fluid particle migrates, and is termed the mass transport velocity. It is of importance to the study of sediment motion in coastal waters. The present report describes a coordinated inquiry into both theoretical and experimental aspects of mass transport by waves. In accordance with the division of effort, it is separated into two parts. However, nearly all ideas expressed and actions taken in both parts have been influenced by extensive mutual discussions. Part I (Theory) begins with a review of the basic assumptions underlying existing theories. General formulas of mass transport velocity components throughout the Stokes boundary layer near a solid body are then derived; details of two examples are calculated. The three-dimensional mass transport distribution throughout the cross section of a wave tank is worked out for progressive waves of very small amplitudes. The effects of finite width is studied with the assumption that vorticity is diffused by molecular viscosity throughout the entire cross section. For a wave obliquely incident and reflected from a vertical sea wall, the structure in the second boundary layer between the Stokes layer and the inviscid core is investigated. This is appropriate for amplitudes much greater than the Stokes layer thickness. Part II (Experiments), were intended in part to check and to evaluate the theoretical deductions in Part I. In particular, extensive measurements were made for the longitudinal mass transport velocity in a progressive wave in a long tank with a smooth bottom. For standing waves and partially standing waves, possible features of erosion and deposition were observed by spreading (1) a small amount of sand on a smooth bottom and (2) a thick layer of sand on the bottom. The relevance of mass transport very near the bottom to the bed load transport is discussed in the light of the real beach environment.
Download or read book Water Waves The Mathematical Theory with Applications written by James Johnston Stoker and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Water Waves written by Adrian Constantin and published by Springer. This book was released on 2016-06-28 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiar with one branch of the study of water waves, to learn more about other areas.
Download or read book The Mathematical Theory of Permanent Progressive Water waves written by Hisashi Okamoto and published by World Scientific. This book was released on 2001 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Water Waves written by Gordon David Crapper and published by . This book was released on 1984 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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.
