Analytical Properties of the Effective-Diffusion Coefficient in Periodic Flows
Pavel Kalugin, Alexander Sokol, E. B. Tatarinova · Europhysics Letters (EPL) · 1990
Motion of a passive component in a periodic incompressible steady flow is studied in the presence of intrinsic diffusivity of a medium. It is rigorously proven that for large distance and time the transport can be described as an effective anisotropic diffusion. Analytical properties of the effective diffusivity D n * for a given direction n as a function of complex P 2 ( P is the Peclet number) are discussed. It is shown that the function D n *( P 2 ) is meromorphic and both poles and zeroes of D n *( P 2 ) are real and negative. It is proven that D n * < D (1 + const P 2 ) for any real P . New algorithm based on the continued fractions is given to compute D n *( P 2 ).