Projects per year
Abstract
A standard model for the study of scalar dispersion through the combined effect of advection and molecular diffusion is a twodimensional periodic flow with closed streamlines inside periodic cells. Over long time scales, the dispersion of a scalar released in this flow can be characterized by an effective diffusivity that is a factor Pe(1/2) larger than molecular diffusivity when the Peclet number Pe is large. Here we provide a more complete description of dispersion in this regime by applying the largedeviation theory developed in Part 1 of this paper. Specifically, we derive approximations to the rate function governing the scalar concentration at large time t by carrying out an asymptotic analysis of the relevant family of eigenvalue problems. We identify two asymptotic regimes and, for each, make predictions for the rate function and spatial structure of the scalar. Regime I applies to distances vertical bar x vertical bar from the scalar release point that satisfy vertical bar x vertical bar = O(Pe(1/4)t). The concentration in this regime is isotropic at large scales, is uniform along streamlines within each cell, and varies rapidly in boundary layers surrounding the separatrices between adjacent cells. The results of homogenization theory, yielding the O(Pe(1/2)) effective diffusivity, are recovered from our analysis in the limit vertical bar x vertical bar
Original language  English 

Pages (fromto)  351377 
Number of pages  27 
Journal  Journal of Fluid Mechanics 
Volume  745 
DOIs  
Publication status  Published  Apr 2014 
Keywords
 chaotic advection
 laminar reacting flows
 mixing and dispersion
 BOUNDARYLAYERS
 DIFFUSION
 TRANSPORT
 SPEED
Projects
 1 Finished

Passive scalars in complex fluid flows: variability and extreme events
1/10/11 → 30/11/14
Project: Research
Profiles

Jacques Vanneste
 School of Mathematics  Personal Chair in Fluid Dynamics
Person: Academic: Research Active