Point vortex dynamics in the post-Aref era

Three vortices move in a plane You can solve that with limited pain But add in a speck And all goes to heck Its motion is really insane! (H Aref) Hassan Aref's many contributions to the field of vorticity dynamics were highlighted in a dedicated lecture at the IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function, Fukuoka Japan, 10−14 March 2013. Here we present a background discussion of the pleasures and challenges associated with working with discrete vorticity representations of fluid flows, one of the areas to which Professor Aref devoted his scientific career. This will lead to a discussion of several interesting problems that remain to be analyzed for the N-point vortex equations, including (i) dynamics and equilibria on curved surfaces; (ii) energy minimizing configurations (large N, general ); (iii) equilibria with defects; and (iv) formation of equilibria (in the presence of noise and other background flow). We finish with some final thoughts on the impact of Professor Aref's style and contributions to the field of low-dimensional discrete vortex modeling of fluid flows.