Diffusion Stability of Mechanical Equilibrium in Compressible Isothermal Gases
— This paper is presented stability condition of mechanical equilibrium for diffusion of compressible isothermal gases in a cylindrical domain. Two general cases of the divergent stable motions were considered when density depended on the conditions 0  u div  and 0  u div . Stability criterion of mechanical equilibrium for the compressible gas mixture is proposed by defining continuous dependence of the velocity vector for the compressible flows in the Navier-Stokes problem from initial date. Using the parametrix method of theory nonlinear partial differential equations were obtained the velocity components for the transient compressible flows. Introduced stability condition for isothermal gases was predicted in the principal form by the energy conservation law and based on the transport equation for an appropriate convergent-divergent turbulent gas motion.
Convective regimes of mixing in binary systems with the mechanical equilibrium instability of a gas mixture
Experimental data on pressure that correspond to the diffusion-concentration-induced convection are presented. Stability analysis carried out with allowance for the channel geometry realized in the experiment shows the existence of various modes of perturbations, in good agreement with experimental data.
Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis
Linear stability analysis is applied to the problem of a density-stratified fluid contained in an inclined slot being subjected to a lateral temperature gradient. Stability equations are solved using the Galerkin technique with 12 terms in the truncated expansion series. Within the range of θ considered, |θ| < 75°, critical instability was found to be of the stationary type. Results of critical thermal Rayleigh numbers and wavenumbers at all inclination angles are in good agreement with the experimental results obtained earlier (Paliwal & Chen 1980). Contrary to intuition, these results show that the system is more stable when the lower wall is heated. This is shown to be the result of the increased vertical solute gradient in the steady state prior to the onset of instabilities when the heating is from below.