Fig. 1. Schematic diagram of a vortex boundary in a flow. (A) 3-D sketch of a vortex ring; (B) the vortex ring on its median-symmetry plane. Circles with inscribed arrows indicate vortex cores and their rotational sense. Two fluid particles close to but on different sides of the vortex boundary separate from each other faster than other arbitrary pairs of fluid particles, giving a larger value of the finite-time Lyapunov exponent field (FTLE) at the boundary. Adapted from Peng et al. (Peng et al., 2007).