Reynolds number effects on mixing due to topological chaos
Abstract
Topological chaos has emerged as a powerful tool to investigate fluid mixing. While this theory can guarantee a lower bound on the stretching rate of certain material lines, it does not indicate what fraction of the fluid actually participates in this minimally mandated mixing. Indeed, the area in which effective mixing takes place depends on physical parameters such as the Reynolds number. To help clarify this dependency, we numerically simulate the effects of a batch stirring device on a 2D incompressible Newtonian fluid in the laminar regime. In particular, we calculate the finite time Lyapunov exponent (FTLE) field for three different stirring protocols, one topologically complex (pseudoAnosov) and two simple (finiteorder), over a range of viscosities. After extracting appropriate measures indicative of both the amount of mixing and the area of effective mixing from the FTLE field, we see a clearly defined Reynolds number range in which the relative efficacy of the pseudoAnosov protocol over the finiteorder protocols justifies the application of topological chaos. More unexpectedly, we see that while the measures of effective mixing area increase with increasing Reynolds number for the finiteorder protocols, they actually exhibit nonmonotonic behavior for the pseudoAnosov protocol.
 Publication:

Chaos
 Pub Date:
 March 2016
 DOI:
 10.1063/1.4943170
 arXiv:
 arXiv:1603.02234
 Bibcode:
 2016Chaos..26c3106S
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 10 pages, 9 figures