Stieltjes Integral Representation and Effective Diffusivity Bounds for Turbulent Transport.

摘要

The motion of a diffusive particle advected by a fluctuating velocity field is equivalent at large spatial scales and long times to an effective enhanced diffusive motion. An important physical quantity in turbulent transport is the effective diffusivity coefficient at large Peclet numbers which depends on the bare particle diffusivity as well as on the velocity statistics. A Stieltjes integral representation for the effective diffusivity in turbulent transport is developed. This formula is valid for all Peclet numbers and yields a rigorous resummation of the divergent perturbation series in Peclet number provided that all diagrams are computed exactly. Another consequence of the integral representation is convergent upper and lower bounds on effective diffusivity for all Peclet numbers utilizing a prescribed finite number of terms in their perturbation series. Reprints. (aw)