Instability of cumulation in converging cylindrical shock wave

Abstract

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 (λ=2πRs0/k, Rs0—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.