Stability of a Lamb-Oseen vortex in two-way coupled particle-laden flows

We investigate the stability of a columnar vortex tube loaded with inertial particles in Eulerian-Lagrangian simulations. The vortex tube is represented as a Lamb-Oseen vortex with a circulation-based Reynolds number equal to $\mathrm{Re}_\Gamma=50$. The particles considered have a small, yet non-zero, circulation Stokes number $\mathrm{St}=0.01$, and are dispersed at a volume fraction $10^{-3}$. We show that when the particle feed-back on the fluid is neglected, the flow is stable to all infinitesimal perturbations. However, when the two-way coupling is taken in account, a centrifugal Rayleigh-Taylor instability may develop leading to the destruction of the vortical structure.