Analytical solutions for particle dispersion in Taylor–Green vortex flows

Abstract

This study presents new analytical solutions for the dynamics and dispersion of particles laden in two-dimensional Taylor–Green vortex flows. Explicit solutions are found for the temporal evolution of free and forced particles under the viscous decaying vortical flow for low Stokes numbers. When placed in the vicinity of the vortex structure, forced particles may either trap within or escape the vortex cell, for which an explicit criterion is proposed. Using the same methodology, the trajectories of charged particles in a vortex flow in the presence of a magnetic field are solved. All cases are compared to numerical simulations demonstrating the validity of the proposed theoretical solutions. The explicit analytical solutions derived here provide fundamental insights into the complex phenomena of particle-vortex interactions and may be used to predict and control particle dispersion in various engineering and natural systems .