Quasi-diffusion and correlations in models of anisotropic transport

This paper deals with scaling laws that describe transport and correlation effects in anisotropic mediums. Diffusion approximation of correlation effects is considered in a system of perpendicular random steady flows by using the Corrsin conjecture. The correlation properties of several well-known diffusive models in an anisotropic medium are investigated. We show that superdiffusive and subdiffusive behavior in the anisotropic medium with strong longitudinal correlations can be described by a single fractional differential equation. In the considered model we obtain the relationship between the Hurst exponent H, describing transverse diffusion and the correlation exponent α by the simple expression, H=1−α/4. This result is in agreement with an analogous scaling law for isotropic medium.