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Particle sedimentation in the vicinity of a fixed horizontal vortex withtime-dependent intensity can be chaotic, provided gravity is sufficient todisplace 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 inthe present case the vortex motion is replaced by gravitational settling. Inthe present work this phenomenon is analyzed for heavy Stokes particles movingunder the sole effect of gravity and of a linear drag. The vortex is taken tobe a fixed isolated point vortex the intensity of which varies under the effectof either boundary conditions or volume force. When the unsteadiness of thevortex is weak and the free-fall velocity is of the order of the fluidvelocity, and the particle response time is small, the particle motion equationcan be written asymptotically as a perturbed hamiltonian system the phaseportrait of which displays a homoclinic trajectory. A homoclinic bifurcation istherefore likely to occur, and the contribution of particle inertia to theoccurrence of this bifurcation is analyzed asymptotically by using Melnikov'smethod.

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