Spectral stability of Prandtl boundary layers: An overview

Emmanuel Grenier; Yan Guo; Toan T. Nguyen

doi:10.1515/anly-2015-0001

Spectral stability of Prandtl boundary layers: An overview

Emmanuel Grenier, Yan Guo, Toan T. Nguyen

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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.

Original language	English (US)
Pages (from-to)	343-355
Number of pages	13
Journal	Analysis (Germany)
Volume	35
Issue number	4
DOIs	https://doi.org/10.1515/anly-2015-0001
State	Published - Nov 1 2015

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

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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.",

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AB - 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.

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Spectral stability of Prandtl boundary layers: An overview

Abstract

All Science Journal Classification (ASJC) codes

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