Nonlinear Water Waves

Cetraro, Italy 2013

Author: Adrian Constantin,Joachim Escher,Robin Stanley Johnson,Gabriele Villari

Publisher: Springer

ISBN: 3319314629

Category: Mathematics

Page: 228

View: 6506

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.

Symmetry, Phase Modulation and Nonlinear Waves

Author: Thomas J. Bridges

Publisher: Cambridge University Press

ISBN: 1107188849

Category: Mathematics

Page: 242

View: 2340

Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

Proceedings of the Conference on Water Waves: Theory and Experiment, Howard University, USA, 13-18 May 2008

Author: M. F. Mahmood,Diane Henderson,Harvey Segur

Publisher: World Scientific

ISBN: 9814304247

Category: Electronic books

Page: 212

View: 8854

The objective of this book is to introduce new researchers to the rich dynamical system of water waves, and to show how (some) abstract mathematical concepts can be applied fruitfully in a practical physical problem and to make the connection between theory and experiment. It provides a coherent set of lectures on the current status of water wave theory, including identification of some open problems.

Mechanics of Deformable Bodies

Lectures on Theoretical Physics

Author: Arnold Sommerfeld

Publisher: Academic Press

ISBN: 1483220273

Category: Science

Page: 408

View: 9764

Mechanics of Deformable Bodies: Lectures on Theoretical Physics, Volume II covers topics on the mechanics of deformable bodies. The book discusses the kinematics, statics, and dynamics of deformable bodies; the vortex theory; as well as the theory of waves. The text also describes the flow with given boundaries. Supplementary notes on selected hydrodynamic problems and supplements to the theory of elasticity are provided. Physicists, mathematicians, and students taking related courses will find the book useful.

Collected Lectures on the Preservation of Stability Under Discretization

Author: Donald J. Estep,Simon Tavener

Publisher: SIAM

ISBN: 9780898715200

Category: Mathematics

Page: 267

View: 9711

The 13 lectures are intended to be accessible to new graduate students of mathematics, sacrificing some detail in order to offer an accessible introduction to the fundamentals of stability that can provide a foundation for further study. Presenters from the US and Britain cover preserving qualitative stability features and structural stability, and investigating physical stability and model stability. Annotation copyrighted by Book News, Inc., Portland, OR

Introduction to PDEs and Waves for the Atmosphere and Ocean

Author: Andrew Majda

Publisher: American Mathematical Soc.

ISBN: 9780821883495

Category: Mathematics

Page: 234

View: 5751

Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.

Lectures on Light

Delivered in the United States in 1872-'73

Author: John Tyndall

Publisher: N.A


Category: Light

Page: 194

View: 4583

Water Waves and Ship Hydrodynamics

An Introduction

Author: A.J. Hermans

Publisher: Springer Science & Business Media

ISBN: 9789400700963

Category: Technology & Engineering

Page: 169

View: 6944

In this book an introduction is given to aspects of water waves that play a role in ship hydrodynamics and offshore engineering. At first the equations and linearized boundary conditions are derived describing the non-viscous free surface water waves, with special attention to the combination of steady and non-steady flow fields. Then some simple kinds of free wave solutions are derived, such as plane waves and cylindrical waves. For several situations, steady and unsteady, the source singularity function is derived. These functions play a role in numerical codes used to describe the motion of ships and offshore structures. These codes are mostly based on a boundary integral formulation; therefore we give an introduction to these methods. It is shown how first order ship motions can be determined. In offshore engineering the second order wave drift motions play an important role. An introduction to this phenomenon is given and the effects which have to be taken into account are explained by means of a simple example where we can determine nearly all the aspects analytically. An interesting example that is worked out is the motion of very large floating flexible platforms with finite draft. Finally an introduction to the theory of shallow water non-linear dispersive waves is presented, and shallow water ship hydrodynamics, that plays a role in coastal areas and channels is treated. Here attention is paid to the interaction between passing ships in restricted water. In the appendix a short introduction to some of the mathematical tools is given.

Ben Franklin Stilled the Waves

An Informal History of Pouring Oil on Water with Reflections on the Ups and Downs of Scientific Life in General

Author: Charles Tanford

Publisher: Oxford University Press on Demand

ISBN: 0192804944

Category: History

Page: 269

View: 3922

When Benjamin Franklin, the 18th-century American statesman and scientist, watched the calming effect of a drop of oil on the waves and ripples of a London pond, he was observing what Pliny the Elder and generations of seafarers had done before him. Franklin, though, was the first to wonder exactly what was happening to the oil, and to investigate this strange phenomenon.Following Franklin's lead, a motley crowd of scientists over the next two centuries and more chose to investigate the nature of atoms and molecules through the interaction of fluid membranes. They included Lord Rayleigh, an altruistic English Lord, Agnes Pockels, who conducted experiments in her kitchen and became one of the earliest women to make lasting contributions to science, the renowned Dutch pediatrician Evert Gorter, and Irving Langmuir, one of America's greatest industrialscientists. Building on Franklin's original experiments, their work has culminated in the discovery of the structure of cell membranes, research that continues to bear fruit today.Ben Franklin Stilled the Waves is far more than the story of oil on water; it is a voyage into the very nature of science and its place in our history.

Wind Over Waves

Forecasting and Fundamentals of Applications

Author: S G Sajjadi,J C R Hunt

Publisher: Elsevier

ISBN: 0857099531

Category: Science

Page: 250

View: 9551

This book addresses ocean wave processes and turbulence as they affect oceanography, meteorology, marine and coastal engineering. It will enable applied mathematicians, seafarers, and all others affected by these phenomena to predict and control wave effects on shipping safety, weather forecasting, offshore structures, sediment pollution, and ice dynamics in polar regions. The focus is on analytical and computational methods for solving equations of motion and studying non-linear aspects of waves and turbulence. Results included show how sudden gusts and winds over waves can modify the mechanisms of wave-breaking and oceanic turbulence. The book records the proceedings of the Wind Over Waves conference of the Institute of Mathematics and its Applications at Churchill College, Cambridge. Co-sponsors with the IMA are the Institute of Civil Engineers and the Royal Meteorological Society. Addresses ocean wave processes and turbulence as they affect oceanography, meteorology, marine and coastal engineering Focuses on analytical and computational methods for solving equations of motion and studying non-linear aspects of waves and turbulence Records the proceedings of the Wind Over Waves conference of the Institute of Mathematics and its Applications at Churchill College, Cambridge

The Mathematics of Diffusion

Author: Wei-Ming Ni

Publisher: SIAM

ISBN: 1611971969

Category: Mathematics

Page: 110

View: 3686

Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.

Nonlinear Water Waves

Author: Lokenath Debnath

Publisher: N.A


Category: Mathematics

Page: 544

View: 6015

Wave motion in water is one of the most striking observable phenomena in nature. Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant. In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability phenomena. New solutions are now available for waves modulatedin both space and time, which exhibit new phenomena as diverse as solitons, resonant interactions, side-band instability, and wave-breaking. Other achievements include the discovery of soliton interactions, and the Inverse Scattering Transform method forfinding the explicit exact solution for several canonical nonlinear partial differential equations. This monograph is the first to summarize the research on nonlinear wave phenomena over the past three decades, and it also presents numerous applications in physics, geophysics, and engineering.

Kinematic Wave Modeling in Water Resources, Surface-Water Hydrology

Author: Vijay P. Singh

Publisher: John Wiley & Sons

ISBN: 9780471109457

Category: Science

Page: 1399

View: 5237

Kinematic wave modeling methods are gaining wide acceptance as a fast and accurate way of handling a wide range of water modeling problems. This is the first book to provide a thorough reference to the application of KW methods to such problems as the spatial representation of watersheds, overland flow routing, and channel flow routing.

Lectures on the Analysis of Nonlinear Partial Differential Equations

Author: Fanghua Lin,Xueping Wang,Ping Zhang

Publisher: N.A

ISBN: 9781571462671

Category: Differential equations, Nonlinear

Page: 393

View: 8919

This volume presents some of the most recent progress in the mathematical theory of fluid mechanics. The eight papers herein originated in a series of seminars held in 2011 at the Chinese Academy of Sciences in Beijing. Among them are Nicolas Burq on the wellposedness of the water wave problem with rough data, Jean-Yves Chemin on the wellposedness of the Navier-Stokes system, and Isabelle Gallagher on the semiclassical limit of a geostrophic system. This third volume of the series is a good reference for those working on nonlinear partial differential equations, especially as applied to fluid mechanics equations and micro-local analysis.

Geomechanics and Fluidodynamics

With Applications to Reservoir Engineering

Author: Victor N. Nikolaevskiy

Publisher: Springer Science & Business Media

ISBN: 9780792337935

Category: Science

Page: 352

View: 4437

This monograph is based on subsurface hydrodynamics and applied geomechanics and places them in a unifying framework. It focuses on the understanding of physical and mechanical properties of geomaterials by presenting mathematical models of deformation and fracture with related experiments.