Symbolic dynamics applied to a numerical simulation of a perturbed Hill's spherical vortex.

3D homotopic lobe dynamics (HLD) is a new symbolic method of describing topological dynamics for fully 3D systems. Here we apply this new method to a numerically computed perturbed Hill's spherical vortex flow. We consider the scattering of passive tracers that are drawn into and then ejected from the vortex. We focus on the numerical computation of fractal scattering functions—the time advected particles are trapped within the vortex as a function of two impact parameters. We compare the fractal self-similarity of these scattering functions to those predicted by 3D HLD. Our new method also produces a lower bound on the topological entropy of our system which approaches the true topological entropy as we add more numerical data.