Heavy Particle Motion in Rotational Vortices

TL;DR

This paper investigates how spherical inertial particles move within a three-dimensional rotating vortex, revealing the complex interplay of forces that influence particle stability, aggregation, and orbital behavior in geophysical and industrial flows.

Contribution

It introduces an analytical model combined with simulations to analyze the effects of various forces on particle dynamics in rotating vortices, highlighting the role of rotational lift forces.

Findings

Rotational lift forces can dominate at moderate Stokes numbers.

Particle stability depends on a balance of multiple forces.

Multiple equilibrium states and bifurcations are identified.

Abstract

This study examines the motion of spherical inertial particles in a three-dimensional rotating cylindrical vortex - a simplified model of geophysical flow structures such as oceanic eddies. The analytical vortex formulation enables the isolation of the key mechanisms that govern particle transport in rotating flows. Using Lagrangian particle tracking simulations, we investigate the influence of drag, buoyancy, virtual mass, Coriolis, and Magnus lift forces across a range of particle sizes, densities, and vortex rotation rates. Results show that particle aggregation and periodic stability depend on both particle inertia and flow parameters. Rotational lift forces, though often neglected for spherical particles, become dominant at moderate particle Stokes numbers and introduce slow vertical oscillations in both particle position and spin. The balance of forces determines whether particles settle into stable periodic orbits or escape the vortex. Our analysis reveals unique equilibrium positions that exhibit bifurcations, with multiple or vanishing steady states depending on particle and flow characteristics. Our results demonstrate how particle aggregation and orbital stability stem from the complex coupling between rotational lift, Coriolis, drag, buoyancy, and virtual mass forces. This model may promote informed modeling of dispersed phase transport in marine flows and industrial mixing processes.