Abstract
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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Notes
- 1.
The choice of the minus sign in the logarithm argument at \(\eta <0\) was justified in [2] by referring to W. Tollmien, who showed that this is necessary for profiles with \(U\,'_{s\,c}>0\) to ensure a correct jump of the phase of the perturbation of the streamwise velocity u across the critical layer.
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Grigoryev, Y.N., Ershov, I.V. (2017). Asymptotic Theory of Neutral Linear Stability Contours in Plane Shear Flows of a Vibrationally Excited Gas. In: Stability and Suppression of Turbulence in Relaxing Molecular Gas Flows. Fluid Mechanics and Its Applications, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-55360-3_4
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DOI: https://doi.org/10.1007/978-3-319-55360-3_4
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