Mack modes in supersonic boundary layer

TL;DR

This paper investigates Mack modes, unstable acoustic waves, in supersonic boundary layers, developing a novel mathematical approach to understand their role in transition to turbulence in high-speed aerodynamics.

Contribution

The paper introduces an inner-outer gluing iteration method to solve complex hyperbolic-elliptic systems modeling Mack modes in supersonic boundary layers.

Findings

Identification of multiple unstable Mack modes

Development of a new solution method for mixed-type systems

Insights into the transition process in supersonic flows

Abstract

Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.