Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation

Yoshiyuki Kagei, Takaaki Nishida

Research output: Contribution to journalArticle

Abstract

Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.

Original languageEnglish
JournalArchive for Rational Mechanics and Analysis
Volume231
Issue number1
DOIs
Publication statusPublished - Jan 22 2019

Fingerprint

Compressible Navier-Stokes Equations
Poiseuille Flow
Traveling Wave
Mach number
Reynolds number
Fluids
Periodic Traveling Waves
Eigenvalue
Complex conjugate
Compressible Fluid
Asymptotically Stable
Viscous Fluid
Operator

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation. / Kagei, Yoshiyuki; Nishida, Takaaki.

In: Archive for Rational Mechanics and Analysis, Vol. 231, No. 1, 22.01.2019.

Research output: Contribution to journalArticle

@article{e7f320decf884b81be450c3b3922ff06,
title = "Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation",
abstract = "Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.",
author = "Yoshiyuki Kagei and Takaaki Nishida",
year = "2019",
month = "1",
day = "22",
doi = "10.1007/s00205-018-1269-6",
language = "English",
volume = "231",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Traveling Waves Bifurcating from Plane Poiseuille Flow of the Compressible Navier–Stokes Equation

AU - Kagei, Yoshiyuki

AU - Nishida, Takaaki

PY - 2019/1/22

Y1 - 2019/1/22

N2 - Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.

AB - Plane Poiseuille flow in viscous compressible fluid is known to be asymptotically stable if Reynolds number R and Mach number M are sufficiently small. On the other hand, for R and M being not necessarily small, an instability criterion for plane Poiseuille flow is known, and the criterion says that, when R increases, a pair of complex conjugate eigenvalues of the linearized operator cross the imaginary axis. In this paper it is proved that a spatially periodic traveling wave bifurcates from plane Poiseuille flow when the critical eigenvalues cross the imaginary axis.

UR - http://www.scopus.com/inward/record.url?scp=85048523175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048523175&partnerID=8YFLogxK

U2 - 10.1007/s00205-018-1269-6

DO - 10.1007/s00205-018-1269-6

M3 - Article

AN - SCOPUS:85048523175

VL - 231

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 1

ER -