Tsunamis and Hurricanes: A mathematical approach

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