Dissipative instability of shock waves

TL;DR

This paper introduces a new condition for the linear dissipative instability of strong plane shock waves, highlighting the role of flow instability behind the shock front and emphasizing the importance of viscosity effects.

Contribution

It provides a novel criterion for shock wave instability considering viscosity, improving the alignment between theoretical predictions and experimental observations.

Findings

Low viscosity enhances the growth rate of one-dimensional disturbances.

One-dimensional disturbances grow faster than two-dimensional ones.

The new instability condition aligns better with experimental data.

Abstract

A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known dissipative instability in the boundary layer for the Tollmien-Schlichting waves. It is found that within the limit of low viscosity the one-dimensional longitudinal disturbances grow much faster than the two-dimensional corrugation ones. It points to a better correspondence to experiment of the new condition for the absolute instability of the shock in comparison with theory, which does not take viscosity into account.