Lagrangian Transport Structures in Three-dimensional Incompressible Time-periodic Flow

In this thesis, a closed, 3D incompressible flow is considered that has two invariants in the Stokes regime. First one, and then the second, invariant is destroyed, and the Lagrangian structures in the resulting flows examined. To compute Lagrangian structures accurately, a new divergence-free interpolation method is developed and presented. Here it is shown that global Lagrangian transport structures of one invariant flows can be completely understood and calculated numerically by identifying degenerate points on periodic lines. A new mechanism of 3D chaotic transport that features non-heteroclinic connections of tubular transition regions is observed in the perturbed zero-invariant flow.