Simulations of a single vortex ring using an unbounded, regularized particle-mesh based vortex method

In resent work we have developed a new FFT based Poisson solver, which uses regularized Greens functions to obtain arbitrary high order convergence to the unbounded Poisson equation. The high order Poisson solver has been implemented in an unbounded particle-mesh based vortex method which uses a re-meshing of the vortex particles to ensure the convergence of the method. Furthermore, we use a re-projection of the vorticity field to include the constraint of a divergence-free stream function which is essential for the underlying Helmholtz decomposition and ensures a divergence free vorticity field. The high order, unbounded particle-mesh based vortex method is used to simulate the instability, transition to turbulence and eventual destruction of a single vortex ring. From the simulation data a novel method on analyzing the dynamics of the enstrophy is presented based on the alignment of the vorticity vector with the principal axis of the strain rate tensor. We find that the dynamics of the enstrophy density is dominated by the local flow deformation and axis of rotation, which is used to infer some concrete tendencies related to the topology of the vorticity field.