On the use of the pulsed-convection approach for modelling advection-diffusion in chaotic flows—A prototypical example and direct numerical simulations

This article addresses the application of pulsed system models (in which the advection operator is decoupled from the diffusion operator) for investigating the physics of dispersion/homogenization in deterministic chaotic flows. The analysis is organized along to main directions: (i) the development of a simplified time-continuous model which can be viewed as a generalization in a time-continuous frame of the baker's transformation, and which is amenable to analytical investigation, and (ii) the comparison of the results deriving from several typical pulsed-system models with the direct numerical simulation of the advection-diffusion equation. Both these approaches reveal the intrinsic ambiguity of the pulsed system approach in describing advection-diffusion problems.