Nonlocal flow sampling enables vortex trapping of heavy particles
Most analyses of inertial particle motion in vortical flows rely on the point-particle approximation, in which the fluid velocity is assumed to be linear at the scale of the particle, and for heavy particles inertia typically leads to centrifugal expulsion from vortex cores. Here, we show that a spatially extended particle, modeled as a rigid symmetric dumbbell of two identical inertial point particles connected by a massless rod that samples the flow at two points, can converge to a vortex-centered spinning state. We study the dynamics of this inertial dumbbell in a steady two-dimensional Lamb-Oseen vortex and identify three qualitatively distinct long-time behaviors controlled by the Stokes number. In the weak-inertia limit, the motion remains bounded and traces spirographic-like trajectories around the vortex center, while at sufficiently large inertia centrifugal effects dominate and trajectories spiral outward, approaching inertial point-particle behavior. Between these limits, the dumbbell can reach a trapped spinning state in which the center-of-mass converges to the vortex center and spins steadily, with accessibility determined by the initial conditions. Basin-of-attraction maps and ensemble statistics reveal a non-monotonic dependence of the accessibility of the spinning state on inertia, with basins of finite measure occurring only over an intermediate range of Stokes numbers. Linear stability is governed by the logarithmic slope of the vortex angular-velocity profile, and for the Lamb-Oseen vortex the spinning state is stable for all Stokes numbers. These results highlight how nonlocal flow sampling by spatially extended inertial particles can fundamentally alter transport and long-time behavior in vortical flows.