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 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 Wavetrains and Solitary Waves in Vortices written by Sidney Leibovich and published by . This book was released on 1989 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Finite Amplitude Solitary Water Waves written by C. J. Amick and published by . This book was released on 1979 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the existence problem for solutions of the free boundary value problem which arises from the question of the existence of solitary gravity waves, moving without changes of form, and with constant velocity, on the surface of ideal fluid in a horizontal canal of finite depth. The analysis imposes no restriction on either the slope or the amplitude of the wave, and we prove that there exists a connected set of solitary waves containing waves of all slope between 0 and pi/6. It is then proved that each of these solitary waves has finite mass, and, as a consequence, that F> 1, where F is the Froude number. This, in turn, tells us that the solitary wave decays faster than exp( -alpha abs.val.(x/h), where alpha is an element or (0, alpha-bar) and 1/alpha-bar tam(alph-bar) = f-squared. Finally, it is shown that, in a certain limit, these solitary waves converge to a solitary stokes wave of greatest height, and the validity of stokes' conjecture for solitary waves is considered, but not resolved. (Author).

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 2011-12-01 with total page 325 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 book is intended for mathematicians, physicists and engineers interested in the interplay between physical concepts and insights and the mathematical ideas and methods that are relevant to specific water-wave phenomena. 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 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 Solitary Waves of Large Amplitude written by Stephen A. Pennell and published by . This book was released on 1982 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rossby Vortices Spiral Structures Solitons written by Mikhail V. Nezlin and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be looked upon in more ways than one. On the one hand, it describes strikingly interesting and lucid hydrodynamic experiments done in the style of the "good old days" when the physicist needed little more than a piece of string and some sealing wax. On the other hand, it demonstrates how a profound physical analogy can help to get a synoptic view on a broad range of nonlinear phenomena involving self-organization of vortical structures in planetary atmo spheres and oceans, in galaxies and in plasmas. In particular, this approach has elucidated the nature and the mechanism of such grand phenomena as the Great of galaxies. A number of our Red Spot vortex on Jupiter and the spiral arms predictions concerning the dynamics of spiral galaxies are now being confirmed by astronomical observations stimulated by our experiments. This book is based on the material most of which was accumulated during 1981-88 in close cooperation with our colleagues, experimenters from the Plasma Physics Department of the Kurchatov Atomic Energy Institute (S. V. Antipov, A. S. Trubnikov, AYu. Rylov, AV. Khutoretsky) and astrophysics theoreticians from the Astronomical Council of the USSR Academy of Sciences (AM. Frid man) and from the Volgograd State University (AG. Morozov). To all of them we wish to express our gratitude. Whenever we speak of "our experiments", the participation of the entire team is implied.

Download or read book The Convergence of Periodic Waves to Solitary Waves in the Long Wave Limit written by John F. Toland and published by . This book was released on 1980 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that large amplitude solitary water-waves arise as the limit of periodic waves whose wavelengths increases indefinitely. This results is obtained after a new version of the Nekrasov integral equation for periodic waves has been derived. Its resemblance to the equation for solitary waves (1) leads to this convergence results once the global existence proof for solitary waves given in (1) has been taken into account. (Author).

Download or read book Elliptic and Parabolic Equations written by Joachim Escher and published by Springer. This book was released on 2015-06-04 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.

Download or read book Numerical Computation of Large Amplitude Internal Solitary Waves written by Tony F. C. Chan and published by . This book was released on 1981 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite amplitude internal solitary waves in a stratified fluid are computed numerically as solutions to a version of Long's equation. Newton's method is used to linearize the two dimensional nonlinear elliptic equation and numerical continuation techniques, both using the wave speed and a pseudo-arclength parameter, are used to trace out solution branches efficiently. Numerical results for the 'tanh' density profile are presented for various depths of the fluid. For shallow depths, solutions for a fixed wave speed are not unique and bore-like solutions with large amplitude have been found. In the deep water case, excellent agreement is obtained with the experimental data of Davis and Acrivos whereas traditional weakly nonlinear analysis fails to produce agreement in the large amplitude regime.

Download or read book Water Waves written by J. J. Stoker and published by John Wiley & Sons. This book was released on 1992-04-16 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Geometric Measure Theory and Free Boundary Problems written by Guido De Philippis and published by Springer Nature. This book was released on 2021-03-23 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.

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 Solitary and Periodic Gravity Capillary Waves of Finite Amplitude written by J. K. Hunter and published by . This book was released on 1982 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dimensional solitary and periodic waves in water of finite depth are considered. The wave propagate under the combined influence of gravity and surface tension. The flow, the surface profile, and the phase velocity are functions of the amplitude of the wave and parameters l = lambda/H and tau = T/g(H squared). Here lambda is the wavelength, H the depth, T the surface tension, rho the density and g the gravity. For small values of l and small values of the amplitude, the profile of the wave satisfies the Korteweg de Vries equation approximately. However, for tau close to 1/3 this equation becomes invalid. In the present paper a new equation valid for tau close to 1/3 is obtained. Moreover, a numerical scheme based on an integro-differential equation formulation is derived to solve the problem in the fully nonlinear case. Accurate solutions for periodic and solitary waves are presented. In addition, the limiting configuration for large amplitude solitary waves when tau> 1/2 is found analytically. Graphs of the results are included.

Download or read book An Introduction to Maximum Principles and Symmetry in Elliptic Problems written by L. E. Fraenkel and published by Cambridge University Press. This book was released on 2000-02-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.