Le Mehaute 



both of which are mathematically tractible. 



The Compressible Hydrodynamic Phase 

 The Incompressible Phase 



The first is arrived at by defining the conditions which prevail at the 

 location of the explosion and in its immediate neighborhood. The 

 second makes use of this input as an initial condition to calculate the 

 water waves at a distance far from the explosion. 



2, 1 The Compressible Hydrodynamic Phase 



The compressible phase of an underwater detonation lasts 

 for a relatively short tinae. Initially, upon detonation, there is im- 

 mediate vaporization of water around the weapon due to intense 

 radiation. This takes place in a time scale of microseconds. As 

 the shock wave propagates outward, the bubble front initailly coin- 

 cides with the shock front (Fig, 2), Only the initial phase of the 

 formation of the bubble need be considered compressible. Bubble 

 migration, expansion, and collapse can be treated as incompressible. 



BUBBLE FRONT / .SMOCK FRONT 



DISTANCE FROM EXPLOSION, r 



Fig. 2 Qualitative relationship between shock front 

 and bubble front 



or, perhaps more correctly, as quasi-incompressible, since subse- 

 quent shock waves are emitted at each minimum of the bubble history. 

 It is obvious that, from the point of view of wave generation, the only 

 problems of importance during the compressible phase concern the 

 fluid motions generated in the vicinity of the bubble and the effect 

 of reflected shocks. The early, compressible phase of bubble (cavity) 

 expansion can be treated by the particle-in-cell technique, which has 

 been successfully employed in many similar cases of compressible 

 flow, both in fluids and in solids (Mader [ 1967] ). 



74 



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