TURBULENT BARODIFFUSION, TURBULENT THERMAL-DIFFUSION, AND LARGE-SCALEINSTABILITY IN GASES

Two effects, turbulent barodiffusion and turbulent thermal diffusion i n gases, are discussed. These phenomena are related to the dynamics of a gaseous admixture in compressible turbulent fluid flow with low Mac h numbers. Turbulent barodiffusion causes an additional mass flux of t he gaseous admixture directed to the maximum of the mean fluid pressur e, while turbulent thermal diffusion results in an accumulation of the gaseous admixture in the vicinity of the minimum of the mean-temperat ure of the surrounding fluid. At large Peclet and Reynolds numbers the se additional turbulent fluxes are considerably higher than those caus ed by molecular barodiffusion and molecular thermal diffusion. It is s hown that turbulent barodiffusion and turbulent thermal diffusion may contribute to the formation of large-scale inhomogeneous structures in a gaseous admixture advected by a low-Mach-number compressible turbul ent velocity field. The large-scale dynamics are studied by considerin g the stability of the equilibrium solution of the derived evolution e quation for the mean number density of the gaseous admixture in the li mit of large Peclet numbers. The resulting equation is reduced to an e igenvalue problem for a Schrodinger equation with a variable mass, and a modified Rayleigh-Ritz variational method is used to estimate the l owest eigenvalue (corresponding to the growth rate of the instability) . This estimate is in good agreement with obtained numerical solution of the Schrodinger equation.