Dissipative instability of converging cylindrical shock wave

TL;DR

This paper derives the linear instability condition for converging cylindrical shock waves in viscous media, highlighting differences from plane shock waves and showing that viscosity influences the growth of perturbations.

Contribution

It provides the first analytical instability condition for converging cylindrical shock waves considering viscosity effects in large radius limits.

Findings

Instability condition differs from plane shock waves due to lack of chiral symmetry.

Positive exponential growth rate occurs only with nonzero viscosity at high Reynolds numbers.

The analysis extends the understanding of shock wave stability in cylindrical geometries.

Abstract

The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump relations as for the plane SW. This condition of instability is substantially different from the condition of instability for the plane SW because a cylindrical SW does not have chiral symmetry in the direction of the SW velocity (from left to right or vice versa) as in the case of a plane SW. The exponential growth rate of perturbations for the converging cylindrical SW is positive only for nonzero viscosity in the limit of high, but finite, Reynolds numbers as well as for the instability of a plane SW.