The linear stability of an inviscid shear flow of a thermally non-equilibrium molecular gas
The problem of the llnear stablllty of plane-parallel shear flows of a vlbratlonally exclted molecular gas ls lnvestlgated uslng a two-temperature gas dynamlcs model. The Raylelgh condltlons and the semlclrcle theorem (Howard''s semlclrcle theorem) are generallzed to the case of a thermally non-equlllbrlum gas. It ls shown that the lnstablllty ln a shear flow ls necessarlly developed under the flrst Raylelgh condltlon stated ln the same form as for a homogeneous and stratlfled lncompresslble llquld and ldeal gas. However, a more rlgld restriction (known as the semlclrcle theorem) on the complex phase speed can be obtalned only under some addltlonal condltlons. In addltlon, a generallzed condltlon about the necessity of existence of an inflection point on an unstable speed profile (the second Rayleigh condition) is obtained.