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

Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

13 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 languageEnglish
Pages (from-to)5-18
Number of pages14
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume89
Issue number1
DOIs
Publication statusPublished - 2008 Jan
Externally publishedYes

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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