Non-Linear Propagation of Directional Cylindrical 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 harmonic pulsations of a finite circular cylinder. For a uniform expansion, both the radial and axial distances need to be strained. The effect of dimensionless quantities upon the acoustic shock-formation distance is examined. The results show that the wave produced consists of a number of groups that propagate without any mutual interaction.
Journal of Sound and Vibration
Kelly, S. Graham and Nayfeh, A. H., "Non-Linear Propagation of Directional Cylindrical Waves" (1981). Mechanical Engineering Faculty Research. 873.