Diffussion of a scalar field in a compressible turbulent medium

The diffusion of scalar fields (temperature, density number of some admixture) in a compressible medium showing an isotropic, homogeneous and stationary turbulence is considered. The derived formulae for turbulent diffusivity χ_T(ξ) hold up to ξ ≈ 1, where ξ = u₀ τ₀/R₀ (u₀, τ₀, and R₀ are characteristic velocity, life-time, and correlation length of turbulent pulsations, respectively. The velocity field of turbulent motions u(r, t) is assumed to be known and the influence of the scalar field onto u(r, t) is neglected. It is shown that the velocity correlators, which change their signs in dependence on the space corrdinates, may give negative values for ξ_T(ξ) when ξ ≠ 0.