Steady-state solutions to the advection-diffusion equation and ghost coordinates for a chaotic flow

Steady-state solutions to the advection-diffusion equation for a passive scalar, with a chaotic divergence-free flow, are determined using a discrete-time, finite-difference model. The physical system studied is a density of particles diffusing across a chaotic layer. The impact of the advective structures on the solutions is illustrated, with special attention given to the cantori. It is argued that cantori play an important role in restricting transport and that coordinates adapted to cantori, called ghost coordinates, provide a natural framework about which the dynamics may be organized; for example, the averaged density profile becomes a smoothed devil's staircase in ghost coordinates.