TY - JOUR

T1 - Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

AU - Grigor’ev, Yu N.

AU - Ershov, I. V.

N1 - Publisher Copyright: © 2017, Pleiades Publishing, Ltd.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. 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 within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the “inviscid” and “viscous” parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

AB - An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. 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 within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the “inviscid” and “viscous” parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

KW - critical Reynolds number

KW - linear stability theory

KW - neutral stability curve

KW - vibrationally excited gas

KW - LINEAR-STABILITY

UR - http://www.scopus.com/inward/record.url?scp=85015612586&partnerID=8YFLogxK

U2 - 10.1134/S0021894417010011

DO - 10.1134/S0021894417010011

M3 - Article

AN - SCOPUS:85015612586

VL - 58

SP - 1

EP - 16

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 1

ER -