On the Spectrum of the Linearized Operator Around Compressible Couette Flows Between Two Concentric Cylinders

Yoshiyuki Kagei, Yuka Teramoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The spectrum of the linearized operator around the Couette flow of the compressible Navier–Stokes equations between two concentric rotating cylinders is studied when the Mach number is sufficiently small. It is shown that, for sufficiently small Mach numbers, the linearized operator around the Couette flow has a critical eigenvalue which crosses the origin when the rotating speed of the cylinder increases. The critical eigenvalue and the associated eigenprojection converge to the ones for the incompressible Navier–Stokes equations as the Mach number goes to zero.

Original languageEnglish
Article number21
JournalJournal of Mathematical Fluid Mechanics
Volume22
Issue number2
DOIs
Publication statusPublished - Jun 1 2020
Externally publishedYes

Keywords

  • Compressible Navier–Stokes equations
  • Couette flow
  • Instability

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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