Although potential flows are irrotational, Lagrangian chaos can occur when these are unsteady, with rapid global mixing observed upon flow parameter optimization. What is unknown is whether Lagrangian chaos in potential flows results in accelerated scalar dispersion, to what magnitude, how robustly, and via what mechanisms. We consider scalar dispersion in a model unsteady potential flow, the Lagrangian topology of which is well understood. The asymptotic scalar dispersion rate $q$ and corresponding scalar distribution (strange eigenmode) are calculated over the flow parameter space $\mathcal{Q}$ for Peclét numbers $\text{Pe}={10}^1–{10}^4$. The richness of solutions over $\mathcal{Q}$ increases with Pe, with pattern mode locking, symmetry breaking transitions to chaos and fractally distributed maxima observed. Such behavior suggests detailed global resolution of $\mathcal{Q}$ is necessary for robust optimization, however localization of local optima to bifurcations between periodic and subharmonic eigenmodes suggests novel efficient means of optimization. Acceleration rates of 150 fold at $\text{Pe}={10}^4$ are observed; significantly greater than corresponding values for chaotic Stokes flows, suggesting significant scope for dispersion acceleration in potential flows in general.

• Received 12 November 2009

DOI:https://doi.org/10.1103/PhysRevE.81.046319