Geodesic
Stability of the Couette flow of a vibrationally nonequilibrium of molecular~gas. Energy approach
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 76-88

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A variational problem of determining the critical Reynolds number of the laminar–turbulent transition is numerically solved in the context of the energy theory of hydrodynamic stability. Stability of various modes in the Couette flow of a vibrationally excited molecular gas is estimated by the method of collocations. The flow is described by a system of the equations of two-temperature aerodynamics. The transport coefficients depend on flow temperature. The calculations have shown that the critical Reynolds numbers depend on the Mach number, bulk viscosity, and vibrational relaxation time. In the realistic range of flow parameters for a diatomic gas, the minimum critical Reynolds numbers are reached on modes of streamwise disturbances and increase approximately by a factor of 2,5 as the flow parameters increase.
Keywords: energy theory, hydrodynamic stability, vibrational relaxation, equations of two-temperature aerodynamics, critical Reynolds number. 
@article{VTGU_2013_3_a9,
     author = {I. V. Ershov},
     title = {Stability of the {Couette} flow of a vibrationally nonequilibrium of molecular~gas. {Energy} approach},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {76--88},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_3_a9/}
}
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I. V. Ershov. Stability of the Couette flow of a vibrationally nonequilibrium of molecular~gas. Energy approach. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 76-88. http://geodesic.mathdoc.fr/item/VTGU_2013_3_a9/