The linear stability of an inviscid shear flow of a thermally non-equilibrium molecular gas

The problem of the linear stability of plane-parallel shear flows of a vibrationally excited molecular gas is investigated using a two-temperature gas dynamics model. The Rayleigh conditions and the semicircle theorem (Howard's semicircle theorem) are generalized to the case of a thermally non-equilibrium gas. It is shown that the instability in a shear flow is necessarily developed under the first Rayleigh condition stated in the same form as for a homogeneous and stratified incompressible liquid and ideal gas. However, a more rigid restriction (known as the semicircle theorem) on the complex phase speed can be obtained only under some additional conditions. In addition, a generalized condition about the necessity of existence of an inflection point on an unstable speed profile (the second Rayleigh condition) is obtained.