A one-dimensional discrete random walk is used to model particle dispersion in a turbulent flow containing isolated, coherent vortices. Steps of length zero are allowed, representing trapping of particles in orbits around vortices. The length of each step is dependent on the preceding step; that is, a second-order model is used. If there is a nonzero transition probability for a step of nonzero length following a step of zero length, then the net displacement is asymptotically normally distributed. If a step of zero length is always followed by another such step, then the displacement variance is bounded, and the statistics are not normal.