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

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 Couet...

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Bibliographic Details
Published in:Journal of mathematical fluid mechanics 2020, Vol.22 (2), Article 21
Main Authors: Kagei, Yoshiyuki, Teramoto, Yuka
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Compressibility
Concentric cylinders
Couette flow
Eigenvalues
Fluid dynamics
Fluid flow
Fluid mechanics
Fluid- and Aerodynamics
Linearization
Mach number
Mathematical analysis
Mathematical Methods in Physics
Navier-Stokes equations
Physics
Physics and Astronomy
Rotating cylinders
Rotation
Theoretical mathematics
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Summary: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.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-020-0485-7