Control mechanisms for the global structure of scalar dispersion in chaotic flows

Scalar dispersion has complex interactions between advection and diffusion that depend on the values of the scalar diffusivity and of the (possibly large) set of parameters controlling the flow. Using a spectral method which is three to four orders of magnitude faster than traditional methods, we calculate the fine-scale structure of the global solution space of the advection-diffusion equation for a physically realizable chaotic flow. The solution space is rich: spatial pattern locking, an order-disorder transition, and optima in dispersion rates that move discontinuously with Peclet number and boundary condition type are some of the discoveries. We uncover the mechanisms which control pattern locking and govern the global structure of dispersion across the parameter space and Peclet number spectrum.