Chaotic particle sedimentation in a rotating flow with time-periodic strength

TL;DR

This paper investigates how particles can exhibit chaotic sedimentation behavior in a rotating flow with a time-varying vortex strength, revealing a mechanism similar to blinking vortex chaos but driven by gravity and particle inertia.

Contribution

It introduces an asymptotic analysis of particle motion under oscillating vortex strength, demonstrating the potential for homoclinic bifurcations and chaos in sedimenting particles.

Findings

Chaotic particle trajectories can occur due to vortex unsteadiness and gravity.

Asymptotic analysis reveals homoclinic bifurcations in particle phase space.

Particle inertia influences the onset of chaos through bifurcation mechanisms.

Abstract

Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and fold" mechanism is close to the so-called blinking vortex effect, which is responsible for chaotic transport of perfect tracers, except that in the present case the vortex motion is replaced by gravitational settling. In the present work this phenomenon is analyzed for heavy Stokes particles moving under the sole effect of gravity and of a linear drag. The vortex is taken to be a fixed isolated point vortex the intensity of which varies under the effect of either boundary conditions or volume force. When the unsteadiness of the vortex is weak and the free-fall velocity is of the order of the fluid velocity, and the particle response time is small, the particle motion equation can be written asymptotically as a perturbed hamiltonian system the phase portrait of which displays a homoclinic trajectory. A homoclinic bifurcation is therefore likely to occur, and the contribution of particle inertia to the occurrence of this bifurcation is analyzed asymptotically by using Melnikov's method.