Non-Linear Propagation of General 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 the general harmonic pulsations of a sphere. For a uniform expansion, only the radial distance needs to be strained. The effect of dimensionless quantities upon the shock-formation distance is examined.
Journal of Sound and Vibration
Kelly, S. Graham and Nayfeh, A. H., "Non-Linear Propagation of General Directional Spherical Waves" (1981). Mechanical Engineering Faculty Research. 872.