Instability of Plane Poiseuille Flow in Viscous Compressible Gas
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Instability of plane Poiseuille flow in viscous compressible gas is investigated. A condition for the Reynolds and Mach numbers is given in order for plane Poiseuille flow to be unstable. It turns out that plane Poiseuille flow is unstable for Reynolds numbers much less than the critical Reynolds number for the incompressible flow when the Mach number is suitably large. It is proved by the analytic perturbation theory that the linearized operator around plane Poiseuille flow has eigenvalues with positive real part when the instability condition for the Reynolds and Mach numbers is satisfied.
KeywordsCompressible Navier-Stokes equation Poiseuille flow instability
Mathematics Subject Classification35Q30 76N15
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