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Stability of unstably stratified shear flow in a channel under non-Boussinesq conditions. (English) Zbl 0868.76029
The stratified plane Poiseuille flow of an ideal gas between two horizontal plates is subject to a vertical temperature gradient. The temperature variations are very high. The linear stability of this thermodynamic phenomenon is investigated numerically on the bases of the equations of mass, momentum and energy conservation containing four real parameters. The coefficients of thermal conductivity and dynamic viscosity depend on the temperature according to the Sutherland law. The perturbation equations are deduced by a Laplace and Fourier transform. The obtained eigenvalue problem is shown to have only two types of eigensolutions. The Squire’s theorem is shown to hold. Finally, the authors solve numerically the generalized Orr-Sommerfeld equations by means of a Chebyshev pseudo-spectral method. The comparison with the Boussinesq case is done.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76V05 Reaction effects in flows
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
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