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.

References in corpus (9)

• Heavy particle concentration in turbulence at dissipative and inertial scales
• Climate dynamics and fluid mechanics: Natural variability and related uncertainties
• The effect of the Basset history force on particle clustering in Homogeneous and Isotropic Turbulence
• Can aerosols be trapped in open flows?
• Biological activity in the wake of an island close to a coastal upwelling
• Kinematic studies of transport across an island wake, with application to the Canary islands
• Coagulation and fragmentation dynamics of inertial particles
• Inertial particle trapping in an open vortical flow
• Asymptotic analysis of chaotic particle sedimentation and trapping in the vicinity of a vertical upward streamline

Cited by in corpus (15)

• On the role of the history force for inertial particles in turbulence
• Building a Maxey--Riley framework for surface ocean inertial particle dynamics
• Accurate solution method for the Maxey-Riley equation, and the effects of Basset history
• Nonlinear dynamics of inertial particles in the ocean: From drifters and floats to marine debris and Sargassum
• History effects in the sedimentation of light aerosols in turbulence: the case of marine snow
• Turbulence induces clustering and segregation of non-motile, buoyancy-regulating phytoplankton
• Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair
• Transient chaos under coordinate transformations in relativistic systems
• Ergodic decay laws in Newtonian and relativistic chaotic scattering
• Trapping enhanced by noise in nonhyperbolic and hyperbolic chaotic scattering
• Basset-Boussinesq history force and inertia are relevant for unsteady particle settling dynamics
• A map for heavy inertial particles in fluid flows
• Relevance of the Basset history term for Lagrangian particle dynamics
• Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering
• Statistics of relative velocity for particles settling under gravity in a turbulent flow