On the Propagation and Structure of the Blast Wave, I

Concerning blast waves with front surfaces of plane, cylindrical and spherical shape, the propagation velocity U and the distribution of hydrodynamical quantities are discussed. The solutions are constructed in the form of power series in ( C / U ) 2 , where C is the sound velocity of undisturbed fluid. Especially R , the distance of shock front from the charge, is represented as, {aligned} (C/U)²({R₀}{R})α+1{=}J₀[1+λ₁(C/U)²+1/2λ₂(C/U)⁴+⋯⋯], {aligned} where R 0 is the characteristic length related to the energy of explosion, J 0 and λ i are constants, and α=0,1,2 correspond to plane, cylindrical and spherical case, respectively. In this paper the first approximations for α=0,1 are discussed (The case α=2 has been discussed by G. I. Taylor). The solution is obtained numerically for the case of the adiabatic index λ=1.4. The approximate solution is also considered. Using these solutions, J 0 is found to be: