Files in this Data Supplement:

• Supplemental Movie 1 -

  Movie 1. Three flapping kinematics used in the study. Red, kinematics 1 listed in Table 1; black, kinematics 2; green, kinematics 3.

• Supplemental Movie 2 -

  Movie 2. The locomotion of the model swimmer and the velocity field (vector plot) and the vortex sheet (blue curve).

• Supplemental Movie 3 -

  Movie 3. Temporal evolution of the FTLE fields and corresponding LCS curves. Blue, backward-time FTLE; red, forward-time FTLE.

• Supplemental Movie 4 -

  Movie 4. Temporal evolution of the upstream wake. Fluid particles in each of three adjacent repelling LCS are labeled magenta or green in order to track their evolution. Fluid particles initially separated by the repelling LCS do not mix and are only moderately deformed. Plotted in the reference frame attached to the model swimmer.

• Supplemental Movie 5 -

  Movie 5. Temporal evolution of upstream adjacent fluid parcels with a horizontal interface. After interaction with the swimmer, the particles in the adjacent parcels exhibit substantial deformation and mixing in the vicinity of the attracting LCS. Plotted in the reference frame attached to the model swimmer.

• Supplemental Movie 6 -

  Movie 6. Temporal evolution of upstream adjacent fluid parcels with a vertical interface. After interaction with the swimmer, the particles in the adjacent parcels exhibit substantial deformation and mixing in the vicinity of the attracting LCS. Plotted in the reference frame attached to the model swimmer.

• Supplemental Movie 7 -

  Movie 7. Fluid structure in the empiriemcally measured flow about a free-swimming Aurelia aurita jellyfish. The red curve is an repelling LCS computed from the DPIV flow field. The LCS bounds upstream fluid which is entrained into the subumbrellar region of the jellyfish, as shown in the movie. From (Shadden et al., 2006).