A Stieltjes integral representation for the effective diffusivity of a passive scalar in time-dependent, incompressible flows is developed. The representation provides a summability formula for the perturbative expansion of the diffusivity in powers of the Péclet number. In particular, upper and lower bounds on the effective diffusivity are obtained from Padé approximants of the series.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics