On the global behaviour of sonic waves of arbitrary shape in gas flows with vibrational relaxation

The propagation of sonic discontinuities of arbitrary shape has been studied in a 3-dimensional gas flow with vibrational relaxation. The law of propagation is determined and the problem of growth and decay of waves has been solved. The effects of the wave geometry and that of vibrational relaxation on the global behavior of the wave amplitude have been studied. It is found that the vibrational relaxation has a stabilizing effect on the wave in the sense that either it disallows or delays the shock formation. The two cases of diverging and converging waves have been discussed separately.