Instability results for transonic flows past airfoils

TL;DR

This paper demonstrates that transonic flow solutions around airfoils are highly sensitive to Mach number perturbations, with instability arising unless the elliptic regions are analytically affected, highlighting challenges in flow stability analysis.

Contribution

It provides a new instability result for transonic flows, emphasizing the necessity of analytic conditions for stability under Mach number perturbations.

Findings

Perturbations in Mach number can destabilize transonic flows.

Instability occurs unless elliptic regions are analytically affected.

Highlights the sensitivity of transonic solutions to boundary perturbations.

Abstract

In this short note we present an instability result for transonic flows with respect to perturbations of the Mach number at infinity. More specifically we show that a perturbation of a transonic solution in the context of a Cauchy problem for the 2-dimensional steady, isentropic and irrotational Euler equations, which is a solution that solves an elliptic equation in certain parts of its domain and a hyperbolic equation in other parts, can only take place in the analytic category if the elliptic part of the domain is affected.