HAMSYS2014 CONTRIBUTED TALK
Author: Arturo Olvera
IIMAS-UNAM
Mexico
email: aoc@mym.iimas.unam.mx
Title: Self-consistent chaotic transport in fluids and periodic orbits of
high-dimensional twist maps.
Abstract:
In this talk we study the self-consistend chaotic transport in a two
dimensional incompressible shear flow. In an active transport problem
the advected field determines the velocity field through a dynamical
constrain. The advection-diffusion equation (Vlasov-Poisson) equation
can be reduced to an area preserving self-consistent map obtained
from a space-time discretization of the single wave model [del
Castillo, Chaos, 2000]. In our case, the map is defined by a
infinite set of twist maps which are coupled by the perturbation
parameter and the phase variable. In this work, we consider that the
chaotic transport is controlled by the set of periodic orbits of the
map. Our goal is to study the set of periodic orbits for the case
when the number of maps is N. The main idea is to find symmetric
periodic orbit, these orbits correspond to find a low-dimensional
periodic orbit and replicate it in order to obtain a full periodic
orbit. These symmetric orbits can be continued from the uncoupled
case (where the twist maps are uncoupled). We use normal forms to
describe these orbits and to find the dependence of the orbits with
the parameters of the advected field. Numerical methods are used to
verify the prediction obtained from the asymptotic methods. This work
is with the collaboration of Diego del Castillo (OakRidge Nat. Lab.),
David Martinez and Renato Calleja (UNAM).