https://doi.org/10.1140/epjst/e2017-70043-9
Regular Article
A snapshot attractor view of the advection of inertial particles in the presence of history force
1 Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
2 Institute for Theoretical Physics and MTA-ELTE Theoretical Physics Research Group, Eötvös University, P.O. Box 32, 1518 Budapest, Hungary
a e-mail: ksenia.guseva@uni-oldenburg.de
Received: 7 February 2017
Revised: 21 March 2017
Published online: 21 June 2017
We analyse the effect of the Basset history force on the sedimentation or rising of inertial particles in a two-dimensional convection flow. We find that the concept of snapshot attractors is useful to understand the extraordinary slow convergence due to long-term memory: an ensemble of particles converges exponentially fast towards a snapshot attractor, and this attractor undergoes a slow drift for long times. We demonstrate for the case of a periodic attractor that the drift of the snapshot attractor can be well characterized both in the space of the fluid and in the velocity space. For the case of quasiperiodic and chaotic dynamics we propose the use of the average settling velocity of the ensemble as a distinctive measure to characterize the snapshot attractor and the time scale separation corresponding to the convergence towards the snapshot attractor and its own slow dynamics.
© EDP Sciences, Springer-Verlag, 2017
