Tsunamis and Hurricanes, 2006 A Mathematical Approach

This book presents new research on the mathematical description of tsunamis and hurricanes. 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.

1 Introduction to wave physics

1.1 Types of waves

1.2 Linear wave equations

1.3 Solutions of linear wave equations

1.4 Nonlinear wave equations

1.5 Physics of nonlinear wave equations

2 Basic flow equations

2.1 Units and properties of substances

2.2 Conservation ofmass

2.3 The equation of motion

2.4 Conservation of energy

2.5 Thermodynamics

2.6 Vorticity theorems

2.7 Potential flow in incompressible fluids

2.8 Potential flow in compressible fluids4

2.9 The DARBOUX solution of plane waves in non-dissipative gases

2.10 The equivalence theorem

3 Water waves

3.1 The variety of water waves

3.2 Gravity water waves

3.3 Capillarity waves

3.4 Solitons

3.5 Dissipationless tsunamis2

3.6 Wave equation for dissipative tsunamis

3.7 The tsunami wave equations

4. Hurricanes

4.1 Terminology and basics

4.2 The excitation of vorticity in cyclones

4.3 Mathematical modelling of cyclones

4.4 Multifluid cyclone modelling

References

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.

Detailed mathematical analysis of tsunamis

First exact description of large amplitude waves

Combination of old (unknown) and new research