Tsunamis and Hurricanes

A Mathematical Approach
2006
ISBN: 978-3-7091-1737-8
Verlag: Springer Vienna

Buch, Englisch, 197 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Tsunamis and hurricanes continue to have a devastating impact on the population living near the coast. 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 book uses the equivalence principle of solutions of nonlinear large gas dynamic waves and of solutions of water wave equations. An extension of the continuity equation by a source term due to evaporation rates of salt seawater help to understand hurricanes. Detailed formula, tables, and results of the calculations are given.

Zielgruppe

Research

Autoren/Hrsg.

Cap, Ferdinand

Fachgebiete

• Geowissenschaften Geologie Marine Geologie, Ozeanographie (Meereskunde)
• Geowissenschaften Geologie Meteorologie, Klimatologie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Geowissenschaften Geologie Geophysik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre

Inhaltsverzeichnis

From the contents:
Introduction to wave physics: Types of waves; Linear wave equations; Solutions of linear wave equations; Nonlinear wave equations; Physics of nonlinear wave equations.- Basic flow equations: Units and properties of substances; Conservation of mass; The equation of motion; Conservation of energy; Thermodynamics; Vorticity theorems; Potential flow in incompressible fluids; Potential flow in compressible fluids; The DARBOUX solution of plane waves in non-dissipative gases; The equivalence theorem.- Water waves: The variety of water waves; Gravity water waves; Capillarity waves; Solitons; Dissipationless tsunamis; Wave equation for dissipative tsunamis; The tsunami wave equations.- Hurricanes: Terminology and basics; The excitation of vorticity in cyclones; Mathematical modelling of cyclones; Multifluid cyclone modelling.- References.- Index.

Über Autor(innen)

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.