Contents 



1. The Sequence of Events in an Underwater Explosion 



1.1 The Initial Conditions 3 



1.2 Dynamical Properties of Water 4 



1.3 The Shock Wave 5 



1.4 iMotion of the Gas Sphere 7 



1.5 Secondary Pressure Pulses 10 



1.6 Surface and Other Effects 11 



2. Hydrodynamical Relations 



2.1 The Differential Equations for Ideal Fluids 14 



2.2 Waves of Small Amplitude 18 



2.3 Waves of Finite Amplitude 23 



2.4 Kirkwood-Bethe Propagation Theory 28 



2.5 Conditions at a Shock Front in a Fluid 33 



2.6 Properties of Water at a Shock Front 36 



2.7 The Thickness of Shock Fronts 44 



2.8 Conditions at a Boundary between Two Different Media 47 



2.9 Reflection of Acoustic Waves 51 



2.10 Reflection of Finite Amplitude Waves 55 



3. The Detonation Process in Explosives 



3.1 Explosive Materials 67 



3.2 Detonation Waves 71 



3.3 The Equation of State for Explosives 78 



3.4 Calculated Conditions at the Shock Front 85 



3.5 Adiabatic Pressure-Density Relation after Detonation 91 



3.6 The Form of the Detonation Wave 94 



3.7 The Approximation of Adiabatic Explosion at Constant 



Volume 101 



3.8 Boundary Conditions and Initial Motion of the Gas 



Sphere 102 



4. Theory of the Shock Wave 



4.1 The Principle of Similarity 110 



4.2 The Detailed Evaluation of Shock Wave Propagation 



(Kirkwood-Bethe Theory) 114 



4.3 The Asymptotic Behavior of Spherical Shock Waves 124 



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