The process of turbulent mixing across an ideal model of a meandering Gulf Stream is studied considering particle motion in two dimensions. The turbulent motion is modeled using a “random flight” model that assumes that the evolution of the turbulent velocity along trajectories is a Markov process, with the velocity at one time step depending linearly on the velocity at the previous step. This turbulent field is superimposed on a meandering jet (similar to the one considered by Bower (1991)) propagating steadily eastward. In Bower's model the particles are constrained to move along streamlines in the translating frame; in our model the turbulent motion allows the particles to cross streamlines, resulting in an exchange between the different regions of the flow. The major exchange occurs between the “jet core” region and the “recirculating” regions moving with the meanders. Particles launched in the jet core tend to be lost from the jet in plumes at the extrema of the meanders and to be entrained in successive recirculation regions. When in the recirculation regions, particles tend to be trapped and homogenized. The exchange between the jet and the “far field” depends only on diffusion mechanisms and is small for the short integration time considered. An application of the kinematic techniques considers the distribution of biological species across the jet. The tendency for “patches” of organisms to develop in the recirculation regions is observed. In a two-species case, where the species have affinities for the environment on opposite sides of the jet, there is a linear change in species composition across the jet. Patches forming on either side of the jet consist of an admixture of the two species, with the population for the crest or trough environment dominating.