Dispersion of particles in two-dimensional monopolar and dipolar vortices using a Lagrangian stochastic model

Abstract

The dispersion of particles in two-dimensional vortices, two circular monopoles, and the Chaplygin–Lamb dipole is studied numerically with a Lagrangian stochastic model. The monopoles are the Rankine and the steady Oseen vortex, whose azimuthal velocity profile is irrotational at a long radial distance. The total velocity of each particle is divided into two parts: the deterministic field due to the vortex plus a stochastic velocity representing homogeneous turbulence. The experiments are carried out with thousands of particles to calculate the dispersion as a function of time. The dispersion in the monopoles grows rapidly and then increases at a lower rate as the particles transit toward the potential region. This transition occurs more quickly in the Rankine vortex, so the Oseen vortex has a wider time-lapse to generate a more significant dispersion. In the case of the Chaplygin–Lamb dipole, having an internal and external flow, the dispersion has different behavior depending on which region the particles depart. The dispersion curves describe the exchange of particles between the poles and the outer flow as the dipole drifts. We discuss the capacity of the dipole to transport particles through long distances.