Dissipative instability of converging cylindrical shock wave

Abstract

The condition of linear instability for the converging cylindrical strong shock wave (SW) in arbitrary viscous medium is obtained in the limit of 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 substantial different from the condition of instability for the plane SW because cylindrical SW have not chiral symmetry for the direction of the SW velocity (from the left to right or vice versa) as for the case of plane SW. The exponential increment of perturbations for the converging cylindrical SW is positive only for nonzero viscosity in the limit of high, but finite Reynolds numbers as for instability of plane SW.