Instability of cumulation in converging cylindrical shock wave

The conditions of linear instability for a converging cylindrical shock wave in an arbitrary inviscid medium are obtained. The initial continuous cylindrical symmetry of the shock wave front is exchanged on a discrete symmetry that is determined by the most unstable small azimuthal dimensionless wave numbers 0 < k < kth < 1 of corrugation perturbations. Due to the long azimuthal wavelengths ( lambda = 2 pi R-s0/k, R-s0-the radius of the shock wave) of perturbations, the shape of the resulting shock wave front is not changed significantly, but the corresponding restriction of the internal energy cumulation can be caused by the intensification of the rotation of the medium behind the front. The instability and the restriction of cumulation are also possible in the case of the exponential rapid growth of the one-dimensional perturbations with k = 0, when the shape of the shock front is not changed at all. The correspondence of present theory to the experimental and simulation data on underwater electrical explosion is considered. Published under an exclusive license by AIP Publishing.

Automated summary

The linear instability conditions for a converging cylindrical shock wave in an arbitrary inviscid medium have been examined. By analyzing the most unstable small dimensionless wave numbers, the influence of perturbations on the shape of the shock wave front and the cumulation of internal energy was discussed. The correspondence of this theory to experimental and simulation data on underwater electrical explosion was also considered.