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

^*Corresponding author for this work

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

38 Citations (Scopus)

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
Pages (from-to)	343-355
Number of pages	13
Journal	Analysis
Volume	35
Issue number	4
DOIs	https://doi.org/10.1515/anly-2015-0001
Publication status	Published - 1 Nov 2015
Externally published	Yes

Keywords

boundary layer
inviscid limit
Navier-Stokes
Prandtl

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title = "Spectral stability of Prandtl boundary layers: An overview",

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.",

keywords = "boundary layer, inviscid limit, Navier-Stokes, Prandtl",

author = "Emmanuel Grenier and Yan Guo and Nguyen, \{Toan T.\}",

note = "Publisher Copyright: {\textcopyright} 2015 by De Gruyter 2015.",

year = "2015",

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AU - Guo, Yan

AU - Nguyen, Toan T.

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N2 - 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.

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.

KW - boundary layer

KW - inviscid limit

KW - Navier-Stokes

KW - Prandtl

UR - https://www.scopus.com/pages/publications/84946846084

U2 - 10.1515/anly-2015-0001

DO - 10.1515/anly-2015-0001

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SN - 0174-4747

VL - 35

SP - 343

EP - 355

JO - Analysis

JF - Analysis

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ER -

Spectral stability of Prandtl boundary layers: An overview

Abstract

Keywords

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