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.

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.

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

This solutions manual is a companion to the workbook, Practical Numerical Mathematics with MATLAB: A workbook. It is intended for use by individual students independently studying the workbook and provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. It is also valuable for classroom instructors to help pinpoint the author's intent in each exercise and to provide a model for graders.

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 self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.