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

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

2010-03-21

arxiv.org/abs/1003.3983v1

J.R. Angilella. Chaotic particle sedimentation in a rotating flow with time-periodic strength. Physical Review E 78(6) 066310

Physics

Fluid Dynamics

8 figures

Scientific paper

10.1103/PhysRevE.78.066310

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.

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