Spherical nonlinear wave propagation in a vibrationally relaxing gas

Abstract

The shock-free flow field emanating from a pulsating sphere in a vibrationally relaxing gas without viscosity and heat conduction is obtained by numerical integration of the exact equations. The method is applicable to air when models with either one or two vibrational modes are used. The results highlight the various effects of nonlinearity, attenuation, dispersion, spherical spreading, and source compactness. The special case of isentropic flow is first investigated in some detail. This gives information about the effects of nonlinear harmonic growth and of sphere compactness. Approximate solutions are found to be useful in explaining some of the effects observed. These solutions are reviewed, improved where possible, and compared with the numerical solutions. These appear to be particularly useful because they give details of the development of the wave profile whereas the approximate theories are essentially concerned with the changes in amplitude with distance.