A model for the atmospheric shock wave produced by a strong volcanic explosion

Atmospheric shock waves are a common phenomenon in explosive volcanic eruptions. We consider the motion of a spherical shock wave generated by a point source in the strong shock approximation. The shock front corresponds to discontinuities in the gas velocity, density, pressure and temperature, which are calculated as functions of the energy of the explosion. The problem is solved analytically for the distributions of velocity, density, pressure and temperature in the atmosphere as functions of the distance from the source. The motion of the shock wave being supersonic, the solution is valid for a few seconds after the explosion, corresponding to a distance of few kilometres. The acoustic effect of the shock wave, expressed by the peak sound pressure level, is calculated and may reach hundreds of decibels. The pressure waveform that could be recorded in the vicinity of the volcano is calculated and compared with typical waveforms in weak shock conditions. The change in the refractive index of air due to density inhomogeneity is calculated and the conditions under which a condensation cloud is formed behind the shock front are investigated.