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Calculating the power of tsunamis and hurricanes is of great importance to engineers and meteorologists as well as governments and insurance companies. This book presents new research on the mathematical description of tsunamis and hurricanes.
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 den Autor / die Autorin
Ferdinand Cap zählt zu den bedeutenden theoretischen Physikern der Gegenwart. Er lehrte an den Universitäten Wien, New York und Innsbruck und hatte Gastprofessuren an zahlreichen Universitäten in Europa, Afrika, Asien und den USA inne. Zahlreiche Vorträge und Publikationen auf den Gebieten der Relativitätstheorie, Nuklearphysik, Plasmaphysik und der angewandten Physik. In Diskussionen mit Theologen hat er sich seit vielen Jahren mit dem Verhältnis zwischen Naturwissenschaft und Religion intensiv auseinandergesetzt.
Zusammenfassung
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.
Zusatztext
"... This book is useful for researchers working in mathematical modeling and hydrodynamics." Zentralblatt MATH 11/2007
Bericht
"... This book is useful for researchers working in mathematical modeling and hydrodynamics." Zentralblatt MATH 11/2007
