Memory effects in chaotic advection of inertial particles

A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be comparable with the Stokes drag. As an illustrative example, a pa...

Authors: Daitche, Anton
Tél, Tamás
Document types:Article
Media types:Text
Publication date:2014
Date of publication on miami:11.12.2014
Modification date:16.04.2019
Edition statement:[Electronic ed.]
Source:New Journal of Physics 16 (2014) 7, 1-30, 073008
DDC Subject:530: Physik
License:CC BY 3.0
Language:English
Notes:Finanziert durch den Open-Access-Publikationsfonds 2014/2015 der Deutschen Forschungsgemeinschaft (DFG) und der Westfälischen Wilhelms-Universität Münster (WWU Münster).
Format:PDF document
ISSN:1367-2630
URN:urn:nbn:de:hbz:6-91319457739
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-91319457739
Other Identifiers:DOI: doi:10.1088/1367-2630/16/7/073008
Digital documents:1367-2630_16_7_073008.pdf

A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be comparable with the Stokes drag. As an illustrative example, a paradigmatic two-dimensional flow, the von Kármán flow is taken. For small (but not extremely small) particles all investigated dynamical properties turn out to heavily depend on the presence of memory when compared to the memoryless case: the history force generates a rather non-trivial dynamics that appears to weaken (but not to suppress) inertial effects, it enhances the overall contribution of viscosity. We explore the parameter space spanned by the particle size and the density ratio, and find a weaker tendency for accumulation in attractors and for caustics formation. The Lyapunov exponent of transients becomes larger with memory. Periodic attractors are found to have a very slow, ${{t}^{-1/2}}$ type convergence towards the asymptotic form. We find that the concept of snapshot attractors is useful to understand this slow convergence: an ensemble of particles converges exponentially fast towards a snapshot attractor, which undergoes a slow shift for long times.