Asymptotic theory of neutral stability curve of the Couette flow of vibrationally excited gas

All-Russian conference on Nonlinear Waves: Theory and New Applications

Grigor'ev, Yu.N.^1 ; Ershov, I.V.^2

Institute of Computational Technologies of SB RAS, Novosibirsk

630090, Russia^1

Department of Information Systems and Technologies, Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk

630008, Russia^2

关键词: Algebraic equations;    Asymptotic theories;    Linear Stability;    Neutral stability;    Numerical solution;    Plane Couette flow;    System of ordinary differential equations;    Vibrationally excited;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012012/pdf
DOI  :  10.1088/1742-6596/722/1/012012

来源: IOP

【 摘 要 】

The asymptotic theory of neutral stability curve of the supersonic plane Couette flow of vibrationally excited gas is constructed. The system of two-temperature viscous gas dynamics equations was used as original mathematical model. Spectral problem for an eighth order linear system of ordinary differential equations was obtained from the system within framework of classical theory of linear stability. Transformations of the spectral problem universal for all shear flows were carried along the classical Dunn - Lin scheme. As a result the problem was reduced to secular algebraic equation with a characteristic division on "inviscid" and "viscous" parts which was solved numerically. The calculated neutral stability curves coincide in limits of 10% with corresponding results of direct numerical solution of original spectral problem.