A study of eigenvalue sensitivity for hydrodynamic stability operators

Peter J. Schmid; Dan S. Henningson; Mehdi R. Khorrami; Mujeeb R. Malik

doi:10.1007/BF00417929

A study of eigenvalue sensitivity for hydrodynamic stability operators

Peter J. Schmid, Dan S. Henningson, Mehdi R. Khorrami, Mujeeb R. Malik

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31 Scopus citations

Abstract

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of ε-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem. © 1993 Springer-Verlag.

Original language	English (US)
Pages (from-to)	227-240
Number of pages	14
Journal	Theoretical and Computational Fluid Dynamics
Volume	4
Issue number	5
DOIs	https://doi.org/10.1007/BF00417929
State	Published - Jul 1 1993
Externally published	Yes

ASJC Scopus subject areas

Computational Mechanics
General Engineering
Fluid Flow and Transfer Processes
Condensed Matter Physics

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title = "A study of eigenvalue sensitivity for hydrodynamic stability operators",

abstract = "The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of ε-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem. {\textcopyright} 1993 Springer-Verlag.",

author = "Schmid, {Peter J.} and Henningson, {Dan S.} and Khorrami, {Mehdi R.} and Malik, {Mujeeb R.}",

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AU - Schmid, Peter J.

AU - Henningson, Dan S.

AU - Khorrami, Mehdi R.

AU - Malik, Mujeeb R.

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-13

PY - 1993/7/1

Y1 - 1993/7/1

N2 - The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of ε-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem. © 1993 Springer-Verlag.

AB - The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of ε-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem. © 1993 Springer-Verlag.

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JO - Theoretical and Computational Fluid Dynamics

JF - Theoretical and Computational Fluid Dynamics

IS - 5

ER -

A study of eigenvalue sensitivity for hydrodynamic stability operators

Abstract

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