A Study On The Nonlocal Shallow Water Model Arising From The Full Water Waves With The Coriolis Effect

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A Study on the Nonlocal Shallow-water Model Arising from the Full Water Waves with the Coriolis Effect

Author : Junwei Sun
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis A Study on the Nonlocal Shallow-water Model Arising from the Full Water Waves with the Coriolis Effect by : Junwei Sun

Download or read book A Study on the Nonlocal Shallow-water Model Arising from the Full Water Waves with the Coriolis Effect written by Junwei Sun and published by . This book was released on 2017 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Equatorial Undercurrent is a significant feature of the geophysical waves near the equator, which is one of the key factors to explain El Niño phenomenon. However, based on [beta]-plane approximation, the classical theory of geophysical waves ignored the vertical structure of the Equatorial Undercurrent. To obtain a better description of the equatorial waves, in this dissertation, I study the rotational-Camassa-Holm (R-CH) equation, which is a mathematical model of long-crested water waves near the equator, propagating mainly in one direction with the effect of Earth's rotation under the f-plane approximation. R-CH equation can be derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solutions corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated.

A Study on Traveling Wave Solutions in the Shallow-water-type Systems

Author : Ting Luo
Publisher :
ISBN 13 :
Total Pages : 131 pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis A Study on Traveling Wave Solutions in the Shallow-water-type Systems by : Ting Luo

Download or read book A Study on Traveling Wave Solutions in the Shallow-water-type Systems written by Ting Luo and published by . This book was released on 2017 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of water waves reveals the physical principles of many phenomena of scientific and engineering interest. In this dissertation I consider three models: two-component Camassa-Holm system(2CH), generalized two-component Camassa-Holm equation(g2CH) and rotation-Camassa-Holm equation(R-CH). In the first part, we consider the stability of the Camassa-Holm peakons and antipeakons in the dynamics of the two-component Camassa-Holm system. The second part shows that the train of N-smooth traveling waves of this system is dynamically stable to perturbations in energy space with a range of parameters. In the third part, we formally derive the simplified phenomenological models with the Coriolis effect due to the Earth's rotation and justify rigorously that the solutions of these models are well approximated by the solutions of the rotation-Camassa-Holm equation. Furthermore, we demonstrate nonexistence of the Camassa-Holm-type peaked solution and classify various localized traveling-wave solutions to the rotation-Camassa-Holm equation.

Dispersive Shallow Water Waves

Author : Gayaz Khakimzyanov
Publisher : Springer Nature
ISBN 13 : 3030462676
Total Pages : 296 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Dispersive Shallow Water Waves by : Gayaz Khakimzyanov

Download or read book Dispersive Shallow Water Waves written by Gayaz Khakimzyanov and published by Springer Nature. This book was released on 2020-09-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

The Shallow Water Wave Equations: Formulation, Analysis and Application

Author : Ingemar Kinnmark
Publisher : Springer Science & Business Media
ISBN 13 : 3642826466
Total Pages : 212 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis The Shallow Water Wave Equations: Formulation, Analysis and Application by : Ingemar Kinnmark

Download or read book The Shallow Water Wave Equations: Formulation, Analysis and Application written by Ingemar Kinnmark and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.

Numerical Methods for Shallow-Water Flow

Author : C.B. Vreugdenhil
Publisher : Springer Science & Business Media
ISBN 13 : 9401583544
Total Pages : 273 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Numerical Methods for Shallow-Water Flow by : C.B. Vreugdenhil

Download or read book Numerical Methods for Shallow-Water Flow written by C.B. Vreugdenhil and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included. The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.

Shallow Water Waves on the Rotating Earth

Author : Nathan Paldor
Publisher : Springer
ISBN 13 : 3319202618
Total Pages : 83 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Shallow Water Waves on the Rotating Earth by : Nathan Paldor

Download or read book Shallow Water Waves on the Rotating Earth written by Nathan Paldor and published by Springer. This book was released on 2015-08-12 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes new theoretical advances concerning analytical solutions of the Rotating Shallow Water Equations, which will make it of great interest to graduate students and scientists in the fields of Geophysical Fluid Dynamics, Physical Oceanography, Dynamical Meteorology and Applied Mathematics. The new dispersion relations and meridional amplitude variations of waves derived in this book can be applied to observations in the atmosphere and ocean and also provide alternatives to the Spherical Harmonics basis of global-scale spectral numerical models.

Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Author :
Publisher : Elsevier
ISBN 13 : 008048946X
Total Pages : 401 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances by :

Download or read book Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances written by and published by Elsevier. This book was released on 2007-04-03 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner. · Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Nonlinear Water Waves

Author : David Henry
Publisher : Springer Nature
ISBN 13 : 3030335364
Total Pages : 218 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Nonlinear Water Waves by : David Henry

Download or read book Nonlinear Water Waves written by David Henry and published by Springer Nature. This book was released on 2019-11-27 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Water Waves Problem

Author : David Lannes
Publisher : American Mathematical Soc.
ISBN 13 : 0821894706
Total Pages : 347 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Water Waves Problem by : David Lannes

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.

Wave Breaking for Nonlinear Nonlocal Shallow Water Equations

Author : Adrian Constantin
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (613 download)

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Book Synopsis Wave Breaking for Nonlinear Nonlocal Shallow Water Equations by : Adrian Constantin

Download or read book Wave Breaking for Nonlinear Nonlocal Shallow Water Equations written by Adrian Constantin and published by . This book was released on 1998 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Numerical Simulation of Nonlinear Water Waves

Author : Qingwei Ma
Publisher : World Scientific
ISBN 13 : 9812836500
Total Pages : 700 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Advances in Numerical Simulation of Nonlinear Water Waves by : Qingwei Ma

Download or read book Advances in Numerical Simulation of Nonlinear Water Waves written by Qingwei Ma and published by World Scientific. This book was released on 2010 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Model for fully nonlinear ocean wave simulations derived using Fourier inversion of integral equations in 3D / J. Grue and D. Fructus -- ch. 2. Two-dimensional direct numerical simulations of the dynamics of rogue waves under wind action / J. Touboul and C. Kharif -- ch. 3. Progress in fully nonlinear potential flow modeling of 3D extreme ocean waves / S.T. Grilli [und weitere] -- ch. 4. Time domain simulation of nonlinear water waves using spectral methods / F. Bonnefoy [und weitere] -- ch. 5. QALE-FEM method and its application to the simulation of free-responses of floating bodies and overturning waves / Q.W. Ma and S. Yan -- ch. 6. Velocity calculation methods in finite element based MEL formulation / V. Sriram, S.A. Sannasiraj and V. Sundar -- ch. 7. High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water / P.A. Madsen and D.R. Fuhrman -- ch. 8. Inter-comparisons of different forms of higher-order Boussinesq equations / Z.L. Zou, K.Z. Fang and Z.B. Liu -- ch. 9. Method of fundamental solutions for fully nonlinear water waves / D.-L. Young, N.-J. Wu and T.-K. Tsay -- ch. 10. Application of the finite volume method to the simulation of nonlinear water waves / D. Greaves -- ch. 11. Developments in multi-fluid finite volume free surface capturing method / D.M. Causon, C.G. Mingham and L. Qian -- ch. 12. Numerical computation methods for strongly nonlinear wave-body interactions / M. Kashiwagi, C. Hu and M. Sueyoshi -- ch. 13. Smoothed particle hydrodynamics for water waves / R.A. Dalrymple [und weitere] -- ch. 14. Modelling nonlinear water waves with RANS and LES SPH models / R. Issa [und weitere] -- ch. 15. MLPG_R method and Its application to various nonlinear water waves / Q.W. Ma -- ch. 16. Large Eddy simulation of the hydrodynamics generated by breaking waves / P. Lubin and J.-P. Caltagirone -- ch. 17. Recent advances in turbulence modeling for unsteady breaking waves / Q. Zhao and S.W. Armfield -- ch. 18. Freak waves and their interaction with ships and offshore structures / G.F. Clauss

Simulation of Water Waves by Boussinesq Models

Author : Ge Wei
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Simulation of Water Waves by Boussinesq Models by : Ge Wei

Download or read book Simulation of Water Waves by Boussinesq Models written by Ge Wei and published by . This book was released on 1997 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new set of time-dependent Boussinesq equations is derived to simulate nonlinear long wave propagation in coastal regions. Following the approaches by Nwogu and later by Chen and Liu, the velocity (or velocity potential) at a certain water depth corresponding to the optimum linear dispersion property is used as a dependent variable. Therefore, the resulting equations are valid in intermediate water depth as well as for highly nonlinear waves. Coefficients for second order bound waves and the third order Schrodinger equation are derived and compared with exact solutions. A numerical model using a combination of second and fourth order schemes to discretize equation terms is developed for obtaining solutions to the equations. A fourth order predictor-corrector scheme is employed for time stepping and the first order derivative terms are finite differenced to fourth order accuracy, making the truncation errors smaller than the dispersive terms in the equations. Linear stability analysis is performed to determine the corresponding numerical stability range for the model. To avoid the problem of wave reflection from the conventional incident boundary condition, internal wave generation by source function is employed for the present model. Numerical filtering is applied at specified time steps in the model to eliminate short waves (about 2 to 5 times of the grid size) which are generated by the nonlinear interaction of long waves. To simulate the wave breaking process, additional terms for artificial eddy viscosity are included in the model equations to dissipate wave energy. The dissipation terms are activated when the horizontal gradient of the horizontal velocity exceeds the specified breaking criteria. Some of the existing models for simulating the process of wave runup are reviewed and we attempt to incorporate the present model to simulate the process by maintaining a thin layer of water over the physically dry grids.

Linear Water Waves

Author : Nikolaĭ Germanovich Kuznet︠s︡ov
Publisher : Cambridge University Press
ISBN 13 : 9780521808538
Total Pages : 528 pages
Book Rating : 4.8/5 (85 download)

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Book Synopsis Linear Water Waves by : Nikolaĭ Germanovich Kuznet︠s︡ov

Download or read book Linear Water Waves written by Nikolaĭ Germanovich Kuznet︠s︡ov and published by Cambridge University Press. This book was released on 2002-07-11 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

The Solitary Wave and Periodic Waves in Shallow Water

Author : Joseph B Keller
Publisher : Legare Street Press
ISBN 13 : 9781021437471
Total Pages : 0 pages
Book Rating : 4.4/5 (374 download)

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Book Synopsis The Solitary Wave and Periodic Waves in Shallow Water by : Joseph B Keller

Download or read book The Solitary Wave and Periodic Waves in Shallow Water written by Joseph B Keller and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed study of solitary waves and periodic waves in shallow water. The author, Joseph B. Keller, is a renowned mathematician with extensive expertise in applied mathematics. In this book, he provides a comprehensive analysis of the physical phenomena associated with the propagation of waves in shallow water. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Lectures on the Theory of Water Waves

Author : Thomas J. Bridges
Publisher : Cambridge University Press
ISBN 13 : 1316558940
Total Pages : 299 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Lectures on the Theory of Water Waves by : Thomas J. Bridges

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: In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics.

A Study on the Two Component Periodic Shallow Water Systems

Author : Caixia Chen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (822 download)

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Book Synopsis A Study on the Two Component Periodic Shallow Water Systems by : Caixia Chen

Download or read book A Study on the Two Component Periodic Shallow Water Systems written by Caixia Chen and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we study the generalized periodic two-component Camassa- Holm system and the generalized periodic two-component Dullin-Gottwald-Holm system, which can be derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, the sufficient conditions for global solutions are established.

Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis

Author : Adrian Constantin
Publisher : SIAM
ISBN 13 : 1611971861
Total Pages : 325 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis by : Adrian Constantin

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.