Non-Linear Propagation of Directional Spherical Waves
The method of renormalization is used to determine a uniformly valid expansion for the problem of non-linear waves produced in a fluid by spatially non-uniform simple harmonic motion of the surface of a sphere. The effect of dimensionless quantities upon the acoustic shock-formation distance is examined.
Journal of Sound and Vibration
Kelly, S. Graham and Nayfeh, A. H., "Non-Linear Propagation of Directional Spherical Waves" (1980). Mechanical Engineering Faculty Research. 871.