Energy estimate of the critical Reynolds numbers in the Couette flow of a vibrationally nonequilibrium molecular gas

The equation of energy balance is deduced for plane-parallel flows of a vibrationally excited molecular gas in the context of the energy theory of the hydrodynamic stability. The flow is described by a system of equations of two-temperature aerodynamics. The dependence of the transport coefficients on the flow temperature is taken into account. The variational problem of calculating the critical Reynolds numbers is considered on the basis of the energy equation. The obtained asymptotical estimates of the critical Reynolds numbers are shown to have in the main order the typical dependence on the Mach number, bulk viscosity, degree of non-equilibrium of the vibrational energy, and time of the vibrational relaxation.