arXiv subjects

Emmanuelle Gouillart

Publications and source records attributed to Emmanuelle Gouillart.

21 records · Page 2Linked to original sources

arXiv2006

Topological Chaos in Spatially Periodic Mixers

Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various braids. For spatially periodic flows, in addition to the usual stirrer-exchange braiding motions, there are additional topologically-nontrivial motions corresponding to stirrers traversing the periodic directions. This leads to a study of the braid group on the cylinder and the torus. Methods for finding topological entropy lower bounds for such flows are examined. These bounds are then compared to numerical stirring simulations of Stokes flow to evaluate their sharpness. The sine flow is also examined from a topological perspective.

nlin.CD↗

arXiv2006

Topological Mixing with Ghost Rods

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call ghost rods, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.

nlin.CD↗

arXiv2005

The Size of Ghost Rods

'Ghost Rods' are periodic structures in a two-dimensional flow that have an effect on material lines that is similar to real stirring rods. An example is a periodic island: material lines exterior to it must wrap around such an island, because determinism forbids them from crossing through it. Hence, islands act as topological obstacles to material lines, just like physical rods, and lower bounds on the rate of stretching of material lines can be deduced from the motion of islands and rods. Here, we show that unstable periodic orbits can also act as ghost rods, as long as material lines can 'fold' around the orbit, which requires the orbit to be parabolic. We investigate the factors that determine the effective size of ghost rods, that is, the magnitude of their impact on material lines.

nlin.CD↗