Distribution Patterns of Eigenvalues of Laminar Pipe Flow 3rd Report, Effect of the Reynolds Number

Yoshikazu Suematsu, Toshiyuki Hayase, Kenji Hase, Tadaya Ito

Research output: Contribution to journalArticlepeer-review


This study investigates the structure and dynamic behavior of a linear system which describes the perturbation of a laminar pipe flow. In the preceding papers a numerical method for calculating the eigenvalues with sufficient accuracy was proposed, and the characteristic distribution pattern of eigenvalues for Poiseuille pipe flow and the classification of the modes of the perturbations were presented. This paper discusses the effects of the Reynolds number on the distribution pattern of eigenvalues. In the first place, for the Poiseuille pipe flow, it is shown how the distribution of eigenvalues in a complex phase velocity plane takes a tree like shape as the Reynolds number increases. Then the distributions of eigenvalues are calculated for the laminar developing pipe flow and the Poiseuille pipe flow with rigid rotation, which are known to be unstable for high Reynolds number. It is found that these distribution patterns take the same shape as that of Poiseuille pipe flow, and that the unstable eigenvalues belong to the specified modes of perturbations, as predicted in the former report.

Original languageEnglish
Pages (from-to)2433-2440
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series B
Issue number505
Publication statusPublished - 1988
Externally publishedYes


  • Developing Flow
  • Distribution of Eigenvalues
  • Fluid Mechanics
  • Hagen-Poiseuillle Flow
  • Laminar Pipe Flow
  • Poiseuile Flow with Rigid Rotation
  • Stability

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering


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