Stability of the flow due to a linear stretching sheet

Paul Griffiths*, Sharon Stephen, Mair Khan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 that this flow is linearly stable. However, our results show that this is only true for Görtler-type disturbances.
Original languageEnglish
Article number084106
Number of pages13
JournalPhysics of Fluids
Issue number8
Early online date6 Aug 2021
Publication statusPublished - 31 Aug 2021

Bibliographical note

© 2021 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Griffiths, P, Stephen, S & Khan, M 2021, 'Stability of the flow due to a linear stretching sheet', Physics of Fluids, vol. 33, 084106 and may be found at


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