Scalar transport in closed potential flows is investigated for the specific case of a periodically reoriented dipole flow. Despite the irrotational nature of the flow, the periodic reorientations effectively create heteroclinic and/or homoclinic points arising from the joining of stable and unstable manifolds. For scalar advection, Lagrangian chaos can be achieved with breakdown of the regular Hamiltonian structure, which is governed by symmetry conditions imposed by the dipole flow. Instability envelopes associated with period-doubling bifurcations of fixed points govern which regions of the flow control parameter space admit global chaos. These regions are further refined via calculation of Lyapunov exponents. These results suggest significant scalar transport enhancement is possible within potential flows, given appropriate programming of stirring protocols.
Lester, D. R., Metcalf, G., Trefry, M., Ord, A., Hobbs, B., & Rudman, M. (2009). Lagrangian topology of a periodically reoriented potential flow: Symmetry, optimization, and mixing. Physical Review E, 80(3), Article number 036208, 10pp. https://doi.org/10.1103/PhysRevE.80.036208