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Analytical modeling of the evolution of cylindrical and spherical shock waves(shocks) during an implosion in water is presented for an intermediate range ofconvergence radii. Up to now this range is determined only in experimentsobservations as a range of implosion radii which are already far from thepiston influence, but yet not described by well-known self-similar solutions.The model is based on an analysis of the change in pressure and kinetic energydensity, as well as on the corresponding fluxes of internal and kinetic energydensities behind the shock front. It shows that the spatial evolution of theshock velocity strongly depends on the initial compression, the adiabatic indexof water, and the geometry of convergence. The model also explains thetransition to a rapid like self-similar increase in the shock velocity at onlya certain radius of the shock that is observed in experiments. The dependenceof the threshold radius, where the shock implosion follows the power law (quasiself-similarity), on the initial compression is determined. It is stated thatin the entire range of the shock radii the internal and kinetic energy densityfluxes are equal, which is in agreement with known experimental data.

Energy density balance during shock wave implosion in water