Lattice BGK Simulation of Multipolar Vortex Formation (Advances in Applied Mathematics and Mechanics, 2021)
Analytical and numerical studies have shown that multipolar vortices canemerge in two-dimensional flow due to azimuthal normal mode perturbations ofshielded vortices. It has been found that mode 2 and 3 perturbations canlead to the formation of stable tripoles and quadrapoles, respectively,while higher order modes result in more complex unstable compound vortices.We have used the lattice Boltzmann method to simulate the effect of azimuthalperturbations on shielded vortices at moderate Reynolds numbers. We have found thatazimuthal normal mode perturbations result in the formation of multipoles, whichdecay due to viscous dissipation. We could also observe that the outcome of such simulations is very sensitive to the displacement of perturbations above wavenumber-3 excitations,in spite of the significant viscosity we used.