Shock instability in dissipative gases

TL;DR

This paper investigates shock wave instability in dissipative gases, demonstrating that clustering instability, rather than classical DK or BZT mechanisms, causes observed non-uniformities in shock structures.

Contribution

The study introduces a molecular model with inelastic collisions to identify the clustering instability as the primary cause of shock instability in dissipative gases.

Findings

Shock waves become unstable with finite dissipation.

Instability leads to high density non-uniformities and convective rolls.

Clustering instability explains the observed shock behavior.

Abstract

Previous experiments have revealed that shock waves in thermally relaxing gases, such as ionizing, dissociating and vibrationally excited gases, can become unstable. To date, the mechanism controlling this instability has not been resolved. Previous accounts of the D'yakov-Kontorovich instability, and Bethe-Zel'dovich-Thompson behaviour could not predict the experimentally observed instability. To address the mechanism controlling the instability, we study the propagation of shock waves in a simple two-dimensional dissipative hard disk molecular model. To account for the energy relaxation from translational degrees of freedom to higher modes within the shock wave structure, we allow inelastic collisions above an activation threshold. When the medium allows finite dissipation, we find that the shock waves are unstable and form distinctive high density non-uniformities and convective rolls on their surface. Using analytical and numerical results for the shock Hugoniot, we show that both DK and BZT instabilities can be ruled out. Instead, the results suggest that the clustering instability of Goldhirsch and Zanetti in dissipative gases is the dominant mechanism.