Self-similar blast wave

A self-similar blast wave is an expanding shock wave whose post-shock profiles retain their shape in a rescaled radius or distance. A fixed explosion energy, ambient mass density and geometry set the front scaling through conservation of total energy. The dimensionless coefficient requires the profiles and an energy-normalization convention.

For a planar adiabatic explosion with energy per unit area $E$ in a uniform medium of mass density ${\rho }_0$, the conserved energy has form $E=I{\rho }_{0}Z{\dot{Z}}^2$, with a finite positive integral $I$ of the similarity profiles. Hence $Z=C(E/{\rho }_0{)}^{1/3}{t}^{2/3}$. If $E$ is shared by two fronts, its fraction assigned to either side is absorbed into $C$.