Tsunami And Nonlinear Waves

The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

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 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.

The theory of waves is generalized on cases of strongly nonlinear waves, multivalued waves, and particle–waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects. Extreme waves emerging in different artificial and natural systems from atom scale to the Universe are explored. Vast amounts of experimental data and comparisons of them with the results of the developed theory are presented. The book was written for graduate students as well as for researchers and engineers in the fields of geophysics, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It is designed as a professional reference for those working in the wave analysis and modeling fields.

This book describes the forecasting and risk evaluation of tsunamis by tectonic motion, land slides, explosions, run-up, and maps the tsunami sources in the world's oceans. It presents stochastic Monte-Carlo simulations and focusing mechanisms for rogue waves, nonlinear wave models, breather formulas, and the kinematics of the Draupner wave. Coverage also reveals the full story about the discovery of the very large oceanic internal waves.

This book presents a study of neuroscience models and natural phenomena, such as tsunami waves and tornados. The first part discusses various mathematical models of tsunamis, including the Korteweg–de Vries equation, shallow water equations and the Camassa–Holm equation (CH). In order to study the dynamics of these models, the text uses the Cellular Nonlinear Networks (CNN) approach to discretize the governing equation using a suitable mathematical grid. The second part discusses some of the models arising in the field of neuroscience. It examines the Fitzhugh-Nagumo systems, which are very important for understanding the qualitative nature of nerve impulse propagation. The volume will be of interest to a wide-ranging audience, including PhD students, mathematicians, physicists, engineers and specialists in the domain of nonlinear waves and their applications.

Till the very end of the twentieth century tsunami waves (or ‘waves in a harbour’, translated from Japanese) were considered an extremely rare and exotic natural p- nomenon, originating in the ocean and unexpectedly falling upon the seaside as gigantic waves. The 26th of December 2004, when tsunami waves wiped out, in a single day, more than 250,000 human lives, mourned in many countries, turned out to be a tragic date for all mankind. The authors of this book, who have studied tsunami waves for many years, - tended it to be a systematic exposition of modern ideas concerning • The mechanisms of tsunami wave generation • The peculiarities of tsunami wave propagation in the open ocean and of how waves run-up beaches • Methods for tsunami wave registration and the operation of a tsunami warning system • The mechanisms of other catastrophic processes in the ocean related to the se- mic activity of our planet The authors considered their main goal to be the creation of book prese- ing modern knowledge of tsunami waves and of other catastrophes in the ocean to scienti?c researchers and specialists in geophysics, oceanography, seismology, hydroacoustics, geology, geomorphology, civil and seaside engineering, postgr- uate students and students of relevant professions.

This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented. This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects.

This monograph aims at presenting a unified approach to numerical modeling of tsunami as long waves based on finite difference methods for 1D, 2D and 3D generation processes, propagation, and runup. Many practical examples give insight into the relationship between long wave physics and numerical solutions and allow readers to quickly pursue and develop specific topics in greater depth. The aim of this book is to start from basics and then continue into applications. This approach should serve well the needs of researchers and students of physics, physical oceanography, ocean/civil engineers, computer science, and emergency management staff. Chapter 2 is particularly valuable as it fully describes the application of finite-difference methods to the study of long waves by demonstrating how physical properties of water waves, especially phase velocity, are connected to the chosen numerical algorithm. Basic notions of numerical methods, i.e. approximation of the relevant differential equations, stability of the numerical scheme, and computational errors are explained through application to long waves. Finite-difference methods are further developed in major chapters to deal with complex problems that arise in the study of recent tsunamis.