https://doi.org/10.1007/s100510170261
Passive tracer dynamics in 4 point-vortex flow
1
Dipartimento di Energetica "S. Stecco", Università degli Studi di Firenze, INFN and INFM, Via di
Santa Marta 3, 50139 Firenze, Italy
2
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA
3
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
4
Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA
Corresponding author: a leoncini@cims.nyu.edu
Received:
28
September
2000
Revised:
9
February
2001
Published online: 15 April 2001
The advection of passive tracers in a system of 4 identical point vortices is
studied when the motion of the vortices is chaotic. The phenomenon of vortex-pairing
has been observed and statistics of the pairing time is computed. The distribution
exhibits a power-law tail with exponent 
implying finite average
pairing time. This exponents is in agreement with its computed analytical estimate
of 
. Tracer motion is studied for a chosen initial condition of
the vortex system. Accessible phase space is investigated. The size of the cores
around the vortices is well approximated by the minimum inter-vortex distance
and stickiness to these cores is observed. We investigate the origin of stickiness
which we link to the phenomenon of vortex pairing and jumps of tracers between
cores. Motion within the core is considered and fluctuations are shown to scale
with tracer-vortex distance 
as 
. No outward or inward diffusion
of tracers are observed. This investigation allows the separation of the accessible
phase space in four distinct regions, each with its own specific properties:
the region within the cores, the reunion of the periphery of all cores, the
region where vortex motion is restricted and finally the far-field region. We
speculate that the stickiness to the cores induced by vortex-pairings influences
the long-time behavior of tracers and their anomalous diffusion.
PACS: 05.45.Ac – Low-dimensional chaos
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
