Memory effects in chaotic advection of inertial particles

Abstract

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.

The joy of transient chaos

“…They are thus natural candidates for characterizing Lagrangian coherent structures, 19 and other environment-related phenomena. 49 Transient chaos theory can also be used to understand the origin of transients and extreme events in excitable systems, 50,51 long spatiotemporal transients in chimera states, 52,53 memory effects in particle dispersion in open flows, 54 and to gain a deeper insight into the nature of turbulence. 55 Recent developments in classical chaotic scattering include the investigation of the ray dynamics in optical metamaterials, 56 of escape in celestial mechanics 57,58 and in medically relevant fluid flows, 59,60 and a basic understanding of the structure of chaotic saddles underlying scattering in higher dimensions.…”

On the role of the history force for inertial particles in turbulence

“…It was shown that memory can be quite important, for example the experimental studies showed that the history force is necessary (in these cases) for a match between experiment and theory. Chaotic dynamics of inertial particles have been studied by Yannacopoulos et al (1997); Daitche & Tél (2011); Guseva et al (2013); Daitche & Tél (2014) showing that the history force can qualitatively change the dynamics, for example, the history force reduces the tendency for accumulation and can change the nature of attractors from non-chaotic to chaotic and vice versa. Reeks & McKee (1984); Mei et al (1991); van Aartrijk & Clercx (2010) have shown that memory can affect the dispersion of particles in turbulence.…”

History effects in the sedimentation of light aerosols in turbulence: The case of marine snow

“…There is an increasing evidence, both theoretical and experimental, pointing out the relevance of memory effects in the advection of inertial particles (see e.g. [1][2][3][4][5][6][7][8][9][10]). Several further studies concerning these effects in turbulence are reviewed in [11].…”