The dynamics of small, heavy, rigid spherical particles in a periodic Stuart vortex flow

Abstract

The equation of motion of small, heavy, rigid spherical particles in a periodic Stuart vortex flow is studied as a four-dimensional nonlinear dynamical system with a parametric space of five dimensions. The five parameters are a scaled Reynolds number, the Stokes number, the fluid-to-particle density ratio, the vorticity distribution in the flow, and a gravitational parameter. Depending on the values of these parameters, heavy particles may either settle or remain indefinitely suspended against gravity. When suspension occurs, suspended particles asymptotically collect along periodic, quasiperiodic, or chaotic open trajectories located above or below the vortices. The nature of these asymptotic paths is investigated using the standard tools of power spectrum and bifurcation diagram (Poincaré sections). Furthermore, the basins of attraction in the physical and parametric spaces are also computed for both types of suspensions (above and below the vortices). In addition to the two types of upper and lower asymptotic orbits, the dynamical system of this study also exhibits the phenomenon of intermittency, whereby a particle remains suspended alternately above and below the vortices. Apart from open trajectories, closed orbits encircling one or several vortices are also observed in this work.