We can't find the internet
Attempting to reconnect
Something went wrong!
Hang in there while we get back on track
Nonlinear dynamic response of heavy particles in rotational vortices
Summary
Scientists built a mathematical model to predict how tiny particles—like microplastics—get trapped, spun around, or flung out of swirling water or air currents, depending on their size and density. This matters because it helps explain where pollutants like microplastics are likely to accumulate in oceans and atmosphere, which could ultimately inform predictions about where these particles build up in environments humans depend on for food and water. The research is theoretical (based on math models, not real-world testing yet), but it lays groundwork for better forecasting pollutant hotspots.
Abstract The transport of inertial particles in vortical flows underpins a wide range of environmental processes, from the dispersion of microplastics in the ocean to aerosol clustering in the atmosphere. Yet, understanding their dynamics is limited due to the nonlinear interplay of drag, lift, buoyancy, and rotational forces. Here, we analyse particle motion in an analytically prescribed three-dimensional vortex flow, employing bifurcation theory and time series analysis to uncover the mechanism governing clustering, oscillations, and escape. We show that neutrally buoyant particles undergo a transition from stable to unstable equilibrium via a limit point bifurcation, while slightly negatively buoyant particles remain stable across a broad range of Stokes numbers. Inclusion of the Magnus lift is shown to be essential, as its omission conceals critical equilibrium branches and oscillatory states. Hopf bifurcation marks the onset of oscillatory motion, with codimension-two bifurcation analysis revealing a stability boundary separating supercritical and subcritical regimes by a Generalised Hopf bifurcation Point. In the supercritical case, particles exhibit pronounced axial oscillations at low Stokes numbers, reflecting the enhanced role of Magnus lift and vortex forcing. By contrast, the subcritical regime is restricted to a narrow vicinity in parameter space, where small perturbations trigger immediate divergence from equilibrium and particle escape. Further, the basin of attraction in the ( $$St-\bar{ ho }$$ S t - ρ ¯ ) plane signifies the robustness of the bifurcation structure by showing the existence of three attractors in the stable region. These results provide a framework for predicting particle fate in vortical environments and extend to pollutant dispersion.