Stability of the flow due to a linear stretching sheet

TL;DR

This study investigates the linear stability of a two-dimensional flow caused by a linearly stretching sheet, revealing instability to Tollmien-Schlichting waves contrary to previous beliefs that it was stable.

Contribution

The paper demonstrates that the flow is linearly unstable to Tollmien-Schlichting waves, challenging prior findings that suggested stability for this flow configuration.

Findings

Flow is linearly unstable to Tollmien-Schlichting waves.

Previous stability results are limited to Görtler-type disturbances.

Uses asymptotic analysis and spectral numerical methods.

Abstract

In this article we consider the linear stability of the two-dimensional flow induced by the linear stretching of a surface in the streamwise direction. The basic flow is a rare example of an exact analytical solution of the Navier-Stokes equations. Using results from a large Reynolds number asymptotic study and a highly accurate spectral numerical method we show that this flow is linearly unstable to disturbances in the form of Tollmien-Schlichting waves. Previous studies have shown this flow is linearly stable. However, our results show that this is only true for G\"{o}rtler-type disturbances.