A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Yoshitaka Watanabe; Michael Plum; Mitsuhiro T. Nakao

doi:10.1002/zamm.200700158

A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Yoshitaka Watanabe^*, Michael Plum, Mitsuhiro T. Nakao

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.

Original language	English
Pages (from-to)	5-18
Number of pages	14
Journal	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume	89
Issue number	1
DOIs	https://doi.org/10.1002/zamm.200700158
Publication status	Published - 2008 Jan
Externally published	Yes

Keywords

Computer-assisted proof
Non-selfadjoint eigenvalue problem
Orr-sommerfeld equation
Poiseuille flow

ASJC Scopus subject areas

Applied Mathematics
Computational Mechanics

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10.1002/zamm.200700158

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abstract = "This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.",

keywords = "Computer-assisted proof, Non-selfadjoint eigenvalue problem, Orr-sommerfeld equation, Poiseuille flow",

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AB - This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.

KW - Computer-assisted proof

KW - Non-selfadjoint eigenvalue problem

KW - Orr-sommerfeld equation

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A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Abstract

Keywords

ASJC Scopus subject areas

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