| The motion of isolated tiny heavy Stokes particles can be very complex, even in laminar flows. Under the effect of gravity and of particle inertia, chaotic motion can occur, leading to unpredictable trajectories and efficient mixing properties. In the limit of vanishing particle Reynolds number this complexity is mainly due to the gradients of the unperturbed fluid flow which make the particle motion equation non-linear. For solid particles these equations form a dissipative dynamical system in a phase space of dimension at most twelve. Classical asymptotic approaches, based on the fact that the particle response time is much smaller than the unperturbed flow time scales, enable to approximate this system as a non-dissipative dynamical system plus a perturbation containing the dissipative terms of the particle dynamics. This approach is applied here to two elementary and widely met flow structures : the upward streamline and the horizontal vortex. The former has retained the attention of the marine research community in the last century, since it has been observed that particles (plankton) settling in a lake could be trapped in the vicinity of the upward vertical streamlines of Langmuir cells. In this talk we will derive the simplest criterion leading to the formation of such trapping zones (Stommel cells), and analyze the conditions leading to the breaking of the separatrices of these cells and to chaotic particle settling. The latter flow (horizontal vortex) will be analyzed by using the same asymptotic approach. We will show how an unsteady fixed horizontal vortex can induce chaotic particle settling through some kind of gravitational "blinking vortex" effect. |
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