Tsunamis and hurricanes have had a devastating impact on the population living near the coast during the year 2005. The calculation of the power and intensity of tsunamis and hurricanes are of great importance not only for engineers and meteorologists but also for governments and insurance companies. This book presents new research on the mathematical description of tsunamis and hurricanes. A combination of old and new approaches allows to derive a nonlinear partial differential equation of fifth order describing the steepening up and the propagation of tsunamis. The description includes dissipative terms and does not contain singularities or two valued functions. The equivalence principle of solutions of nonlinear large gas dynamics waves and of solutions of water wave equations will be used. An extension of the continuity equation by a source term due to evaporation rates of salt seawater will help to understand hurricanes. Detailed formula, tables and results of the calculations are given.
Introduction: Types of waves; Wave equations; Classification of partial differential equations; Single particle motion and waves; Nonlinear wave equations; Solitons.- Basic flow equations: Conservation of mass; Conservation of momentum; Conservation of energy; Nonlinearity effects; Viscosity and dissipation; Flow equations and statistics; Potential flow; Compressible media; Similarity transformations.- Water wave solutions and Tsunamis: Surface waves; Gravity waves; Combined surface and gravity waves; Solitons; Korteweg-de-Vries equation; Darboux equation; Riemann invariants; The Bechert solution; The Shivamoggi picture of a tsunami; "Mathematica" Code.- Hurricanes: The motion of winds on the rotating Earth; Water evaporation; Formation of hurricanes; Vortexes.- Bibliography.- Index.
The author Ferdinand Cap is Professor Emeritus for Theoretical Physics at the University of Innsbruck, Austria. He holds a MS and PhD (under the honourable auspices of the President of the Republic of Austria) and was awarded the Rutherford Medal of the Soviet Academy of Sciences. His career includes serving as assistant to Erwin Schroedinger, Senior Research Associate at NASA and the University of Princeton, NJ, Plasma Laboratory. He has been guest or visiting Professor at leading institutions around the world including the USA, Russia, South Africa, Japan, India and nearly all European countries. He specializes in hydrodynamics and plasma physics as well as mathematical methods in physics and engineering, and has written several textbooks in these fields.
... This book is useful for researchers working in mathematical modeling and hydrodynamics. Zentralblatt MATH 11/2007