Anomalous diffusion of tracer in convection rolls

The dispersion of a passive tracer in a two-dimensional, spatially periodic stationary flow, such as convection rolls, is studied in the large Peclet number limit. In the case where injection, at time t=0, is localized in one roll, two regimes exist. First, there is an anomalous diffusion regime in which the number of invaded rolls grows like t1/3. This regime is due to the presence of separatrices between rolls that induce trapping of tracer within each roll. At a later time, when t≫Td (the diffusion time within a roll), the usual diffusion regime is recovered, yet with an effective diffusive coefficient κeff that is greater than the molecular diffusivity κ by a factor proportional to the square root of the Peclet number.