Spectral stability of Prandtl boundary layers: an overview

TL;DR

This paper reviews the spectral stability of Prandtl boundary layers, connecting it to shear flow stability in Navier-Stokes equations, and discusses classical instability results and conjectures on boundary layer expansions.

Contribution

It provides an overview linking Prandtl boundary layer stability to shear flow stability and discusses the construction of unstable modes and related conjectures.

Findings

Connection established between boundary layer and shear flow stability

Classical instability results summarized

Conjecture proposed on boundary layer expansion validity

Abstract

In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier Stokes equations. We then recall classical physical instability results, and give a short educational presentation of the construction of unstable modes for Orr Sommerfeld equations. We end the paper with a conjecture concerning the validity of Prandtl boundary layer asymptotic expansions.