Vortex Flow Simulations by Lagrangian Particle/Panel Methods

I'll present three vortex flow simulations from incompressible fluid dynamics. The numerical method uses Lagrangian particles and panels to represent the flow map, and velocities are computed using the Biot-Savart integral. The first example is the Kelvin-Helmholtz instability and spiral roll-up of a vortex sheet in 2D. The second example is the azimuthal instability of a vortex ring using a vortex sheet model in 3D. The third example concerns smooth vorticity distributions on a rotating sphere.