Download or read book Model Equations for Gravity capillary Waves written by Benjamin Fearing Akers and published by . This book was released on 2008 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 269 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 Contributions to a Fifth Order Model Equation for Steady Capillary gravity Waves Over a Bump written by Chung-Hsien Tsai and published by . This book was released on 1999 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gravity capillary Waves in the Presence of Constant Vorticity written by Youngcheol Kang and published by . This book was released on 1998 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Nonlinear Gravity Capillary Waves on a Compressible Viscous Fluid with Edge Constraints written by M. C. Shen and published by . This book was released on 1983 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: An asymptotic method is developed for the study of gravity-capillary waves in a compressible viscous fluid with edge constraints in an inclined, straight channel. The Navier-Stokes equations subject to free surface and rigid bottom conditions are reduced to a sequence of elliptic boundary problems over a cross section of the channel. Their solutions are used to determine the wave speed and to construct the Burgers equation for the evolution of the gravity-capillary waves. The Burgers equation may become ill-posed when the Reynolds number exceeds some critical value. A criterion for the stability of the flow is then defined in terms of the critical Reynolds number. (Author).
Download or read book Solitary Waves in Fluids written by R. Grimshaw and published by WIT Press. This book was released on 2007 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Download or read book Numerical Calculations of Periodic Gravity capillary Waves written by James Warner Rottman and published by . This book was released on 1978 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Model Study of Water Gravity Waves Generated by Moving Circular Low Pressure Area written by G. Abraham and published by . This book was released on 1959 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave And Stability In Fluids written by Din-yu Hsieh and published by World Scientific. This book was released on 1994-12-16 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level textbook covers the topics of sound waves, water waves and stability problems in fluids. It also touches upon the subject of chaos which is related to stability problems. It aims to lead students in an accessible and efficient way to this important subject area in fluid mechanics and applied mathematics. The emphasis is on gaining an understanding of the essential features of the subject matter, thus often ignoring complicating details which may confuse non-experts. The topics chosen also reflect the personal bias and research activity of the authors.
Download or read book Quasi periodic Standing Wave Solutions of Gravity Capillary Water Waves written by Massimiliano Berti and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
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 On the Simpler Aspects of Nonlinear Fluctuating Deep Water Gravity Waves weak Interaction Theory written by Bruce J. West and published by . This book was released on 1981 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 On the Instability of Water Waves with Surface Tension written by Olga Trichtchenko and published by . This book was released on 2014 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the stability of solutions to Euler's equations in the presence of surface tension. First we compute stationary solutions to periodic Euler's equations in a traveling frame of reference and then we analyze their spectral stability. Depending on the coefficient of surface tension, we see resonant effects in the solutions. This results in a myriad of instabilities for gravity-capillary waves. Since the theory for analyzing the stability of water waves is general to all Hamiltonian systems, we extend the results to other equations, mainly ones that are used to model water waves in different asymptotic regimes. We compare the stability results for the model equations to those we obtain for the full water wave system and comment on the applicability of these models.
