Chaotic advection in a three-dimensional volume preserving potential flow

Scalar transport in a time-periodic 3D incompressible potential flow is studied in the context of Lagrangian chaos in a reoriented 3D dipole flow. A mixture of chaotic dynamics and regular KAM-tubes are observed, and particles reside on adiabatic surfaces rather than invariant surfaces. The factors controlling the adiabatic surfaces are investigated, for instance the presence of hyperbolic periodic points acts as a local accelerant to dynamics, yet also forms a barrier to transport. The adiabatic surfaces provide a mechanism for 3D scalar transport and the possibility of global chaos.