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Finite Amplitude Solitary Water Waves
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Book Synopsis Finite-Amplitude Solitary Water Waves by : C. J. Amick
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).
Book Synopsis Computer Studies of Finite-amplitude Water Waves by : Stanford University. Department of Civil Engineering
Download or read book Computer Studies of Finite-amplitude Water Waves written by Stanford University. Department of Civil Engineering and published by . This book was released on 1969 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two numerical techniques are utilized to study the motion of two-dimensional, finite-amplitude water waves by using an electronic digital computer. The non-linear properties of water waves are of primary interest. The first part of the work introduces the Stanford-University-Modified MAC (SUMMAC) code which is proposed as a valid tool for analyzing incompressible, viscous flows with a free surface under transient conditions. The method is applied to the study of the solitary wave run-up on a vertical wall. The results are compared with the available experimental data and give a much better prediction of the wave run-up than the existing analytic theory. In the second part, Newton's process of successive corrections is applied to solve steady-state potential flows with free surface and gravity. A specific application to the analysis of solitary waves is made and all the wave characteristics are in excellent agreement with experiments. (Author).
Book Synopsis Small-amplitude steady water waves with vorticity by : Evgeniy Lokharu
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.
Book Synopsis Higher Approximation to Nonlinear Water Waves and the Limiting Heights of Cnoidal, Solitary, and Stokes' Waves by : Edmund V. Laitone
Download or read book Higher Approximation to Nonlinear Water Waves and the Limiting Heights of Cnoidal, Solitary, and Stokes' Waves written by Edmund V. Laitone and published by . This book was released on 1963 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: To obtain the first and second approximations to solitary and cnoidal waves the shallow water expansion method of Friedrichs and Keller is carried out to the fourth order. It is shown that the rigorous first approximation to these amplitude waves of permanent form is identical to the solution first given by Korteweg and deVries in 1895. The second approximation however results in some new expressions for predicting the behavior of long waves in shallow water. Limiting amplitude is found to be 8/11 of the free water depth for the solitary wave. The third approximation to Stokes waves in water of finite depth is verified by the use of the classical small-perturbation expansion method. For finite amplitude waves the series expansion is found to be in terms of a parameter most suitable for wavelengths shorter than 8 times the depth. Rather severe restrictions inherent in the well-known analogy between the nonlinear shallow water flow and two-dimensional perfect gas flow are pointed out. (Author).
Book Synopsis Solitary Waves in Fluids by : R. Grimshaw
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.
Book Synopsis Finite-amplitude, Shallow Water-waves of Periodically Recurring Form by : Cyril Jerome Galvin
Download or read book Finite-amplitude, Shallow Water-waves of Periodically Recurring Form written by Cyril Jerome Galvin and published by . This book was released on 1970 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solitary and Periodic Gravity-Capillary Waves of Finite Amplitude by : J. K. Hunter
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.
Book Synopsis Numerical Methods and FORTRAN Programming by : Daniel D. McCracken
Download or read book Numerical Methods and FORTRAN Programming written by Daniel D. McCracken and published by . This book was released on 1964 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic understanding of the numerical solution of problems in modern computing.
Book Synopsis Finite Amplitude Solitary Waves at the Interface Between Two Homogeneous Fluids by : D. I. Pullin
Download or read book Finite Amplitude Solitary Waves at the Interface Between Two Homogeneous Fluids written by D. I. Pullin and published by . This book was released on 1987 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Accurate Computations for Steep Solitary Waves by : J. K. Hunter
Download or read book Accurate Computations for Steep Solitary Waves written by J. K. Hunter and published by . This book was released on 1983 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite amplitude solitary waves in water of arbitrary uniform depth are considered. A numerical scheme based on collocation is presented to calculate the highest solitary wave. It is found that the ratio of the amplitude of the wave versus the depth is 0.83322. This value is about 0.006 higher than the values obtained by most previous investigators. In addition another numerical scheme based on an integro-differential formulation is derived to compute solitary waves of arbitrary amplitude. Thse calculations show that the results of Longuet-Higgins and Fenton are not accurate for very steep waves. Graphs and tables of the results are included.
Book Synopsis On the Breaking of Water Waves of Finite Amplitude on a Sloping Beach by : Harvey Philip Greenspan
Download or read book On the Breaking of Water Waves of Finite Amplitude on a Sloping Beach written by Harvey Philip Greenspan and published by . This book was released on 1957 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent paper Carrier + Greenspan showed that, within the framework of the non-linear shallow-water theory, there exist waves which do not break as they climb a sloping beach. The formation of a shock or bore is dependent on a variety of factors (wave shape, particle velocity) and, as yet, no general criteria for breaking have been found. Waves are considered which propagate shoreward into quiescent water; it is shown that any compressive wave (a wave of positive amplitude) which has a non-zero slope at the wave-front eventually breaks before reaching the coastline. In fact, an explicit relation is obtained between the initial conditions and the position where breaking occurs. (Author).
Book Synopsis Dispersive Long Waves of Finite Amplitiude Over an Uneven Bottom by : Ole Secher Madsen
Download or read book Dispersive Long Waves of Finite Amplitiude Over an Uneven Bottom written by Ole Secher Madsen and published by . This book was released on 1969 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Water Waves by : Kiyoshi Horikawa
Download or read book Nonlinear Water Waves written by Kiyoshi Horikawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear behaviour of water waves has recently drawn much attention of scientists and engineers in the fields of oceanography, applied mathematics, coastal engineering, ocean engineering, naval architecture, and others. The IUTAM Symposium on Non-linear Water Waves was organized with the aim of bringing together researchers who are actively studying non-linear water waves from various viewpoints. The papers contained in this book are related to the generation and deformation of non-linear water waves and the non-linear interaction between waves and bodies. That is, various types of non-linear water waves were analyzed on the basis of various well-known equations, experimental studies on breaking waves were presented, and numerical studies of calculating second-order non-linear wave-body interaction were proposed.
Book Synopsis Finite-Amplitude Steady Waves in Stratified Fluids by : J. L. Bona
Download or read book Finite-Amplitude Steady Waves in Stratified Fluids written by J. L. Bona and published by . This book was released on 1982 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exact theory regarding solitary internal gravity waves in stratified fluids is presented. Two-dimensional, inviscid, incompressible flows confined between plane horizontal rigid boundaries are considered. Variational techniques are used to demonstrate that the Euler equations possess solutions that represent progressing waves of permanent form. These are analogous to the surface, solitary waves so easily generated in a flume. Periodic wave trains of permanent form, the analogue of the classical cnoidal waves, are also found. Moreover, internal solitary-wave solutions are shown to arise as the limit of cnoidal wave trains as the period length grows unboundedly. (Author).
Book Synopsis Effect Weak Shear on Finite Amplitude Internal Solitary Waves by : S. R. Clarke
Download or read book Effect Weak Shear on Finite Amplitude Internal Solitary Waves written by S. R. Clarke and published by . This book was released on 1998 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Amplitude Waves in Liquids and Solids by :
Download or read book Finite Amplitude Waves in Liquids and Solids written by and published by . This book was released on 1963 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Water Wave Mechanics For Engineers And Scientists by : Robert G Dean
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.
