Having discussed the current understanding of the fluid mechanics of both swimming and flight, van Leeuwen and Biewener's collection of articles concludes with three papers considering general fluid dynamic approaches. David Lentink and colleagues from Wageningen University and Delft University of Technology describe a soap-film technique(p. 267), which allows the team to directly visualise wake vortices generated by a flapping structure. Designing a small 2D wing, the team move it through a thin flowing soap film, generating eddies and vortices that can be visualised by light diffraction. Using this form of direct visualisation, the team have revealed the range of wake complexity found for a variety of wing beat patterns. Describing the wing beats in terms of `dimensionless wavelengths', the team have derived general principles that can be applied across all flapping structures, revealing the relatively simple wakes generated at high dimensionless wavelengths and the increasingly complex vortex interactions that are generated as the dimensionless wavelength declines.
Returning to robotic techniques in flapping motion simulation, Alexandra Techet has been inspired to understand the fluid dynamics of flapping-fin locomotion with the intention of designing highly manoeuvrable aquatic vehicles. Basing her fin's design on turtle and aquatic penguin fins(p. 274), Techet controls the fin's roll and pitch motions over a range of flapping frequencies while measuring the the hydrodynamic efficiency and forces acting on it. Her intention is to find combinations of kinematic parameters that maximise lift and efficiency.
Concluding the collection, Jifeng Peng and John Dabiri introduce the Lagrangian approach to analysing digital PIV(p. 280). By tracking individual particle trajectories, Dabiri and Peng determine the boundary of the vortex associated with a flapping fin, the momentum of the wake vortex and its added mass in order to determine instantaneous locomotive forces. Dabiri and Peng explain that when a fin or flipper moves through a fluid and generates an attached vortex, the vortex also displaces fluid as the limb is moved. The inertia of the surrounding fluid imparts an `added-mass' to the vortex, and this must also be considered when calculating instantaneous locomotive forces. Applying the method to the two dimensional wake of the bluegill sunfish, the team emphasise that the accuracy of the technique will improve when applied to three dimensional DPIV recordings.