The new mode of instability in viscous high-speed boundary layer flows

TL;DR

This paper investigates a newly identified instability mode in viscous high-speed boundary layer flows, which arises under specific pressure gradient and heating conditions, but is unlikely to occur naturally at practical Reynolds numbers.

Contribution

It provides a viscous stability analysis of the new instability mode, clarifying its conditions of occurrence and its limited role in natural laminar-turbulent transition.

Findings

The new mode appears with certain pressure gradients and wall heating.

It rarely coexists with traditional instability modes at realistic Reynolds numbers.

The mode may only induce transition under artificial experimental conditions.

Abstract

The new mode of instability found by Tunney et al. is studied with viscous stability theory in this article. When the high-speed boundary layer is subject to certain values of favorable pressure gradient and wall heating, a new mode becomes unstable due to the appearance of the streamwise velocity overshoot ($U(y)>U_\infty$) in the base flow. The present study shows that under practical Reynolds numbers, the new mode can hardly co-exist with conventional first mode and Mack's second mode. Due to the requirement for additional wall heating, the new mode may only lead to laminar-turbulent transition under experimental (artificial) conditions.