Article,
Large-scale effects on meso-scale modeling for scalar transport
Physica D: Nonlinear Phenomena, 220 (2): 146--156 (August 2006)
Abstract
The transport of scalar quantities passively advected by velocity fields with a component at small scale l can be modeled at scales larger than l by means of an effective drift and an effective diffusivity, which can be determined by means of multiple-scale techniques. We show that the presence of a weak flow at large scales L>>l induces interesting effects on the scalar transport at the meso-scales (i.e. at scales intermediate between l and L). In particular, it gives rise to non-isotropic and non-homogeneous corrections to the meso-scale drift and diffusivity. We discuss an approximation that allows us to retain the second-order effects caused by the large-scale flow. This provides a rather accurate meso-scale modeling for both asymptotic and pre-asymptotic scalar transport properties. Numerical simulations in model flows are used to illustrate the importance of such large-scale effects.
