Asymptotic scaling laws for imploding thin fluid shells

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the (A, M) parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A, M >> 1. It is shown that there exists a critical value gamma(cr) = 1 + 2/nu (nu = 1, 2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density rho(s) and pressure P-s with the peak value M-0 of the Mach number is obtained.