Asymptotic Theory of Neutral Linear Stability Contours in Plane Shear Flows of a Vibrationally Excited Gas

  • Yurii N. GrigoryevEmail author
  • Igor V. Ershov
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 117)


An asymptotic theory of the neutral stability curve for plane shear flows of a vibrationally excited gas is developed in the chapter. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations. Unified transformations of the system for all shear flows are performed in accordance with the classical scheme. The spectral problem for the supersonic plane Couette flow with two boundary conditions, which was not considered previously even for perfect gas, is reduced to an algebraic secular equation with separation into the “inviscid” and “viscous” parts. The neutral stability curves obtained on the basis of the numerical solution of the secular equation agree well with the previously obtained results of the direct numerical solution of the original spectral problem.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computational TechnologiesRussian Academy of SciencesNovosibirskRussia

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