Absolute and convective instabilities in an inviscid compressible mixing layer

TL;DR

This paper analyzes the stability of a compressible shear flow mixing layer, focusing on how Mach number and temperature differences influence the transition between absolute and convective instabilities, with implications for heliopause stability.

Contribution

It introduces a numerical eigenvalue analysis of compressible mixing layer stability, exploring the effects of flow parameters on instability types and their transition.

Findings

Mach number influences the transition between instabilities.

Temperature and velocity ratios affect stability regimes.

Results have implications for heliopause stability.

Abstract

We consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. The velocity and temperature profiles in this mixing layer are hyperbolic tangents. The normal mode analysis of the flow stability reduces to an eigenvalue problem for the pressure perturbation. We briefly describe the numerical method that we used to solve this problem. Then, we introduce the notions of the absolute and convective instabilities and examine the effects of Mach number, and the velocity and temperature ratios of each stream on the transition between convective and absolute instabilities. Finally, we discuss the implication of the results presented in this paper for the heliopause stability.