Nature showcases many examples of animals moving together as a group within a fluid, such as fish in a school or birds in formation flight. Each individual produces flows as they flap their fins, or wings, in order to propel themselves through the fluid. We are interested in how fluid-mediated interactions between members of a group influence the dynamics of each member.
In order to study these interactions between actively flapping swimmers or flyers we use flapping hydrofoils submerged in a water tank as a mechanical analogue of the fins of fish or the wings of birds. Both foil and fin use energy to flap in order to move through a fluid and, in doing so, they produce qualitatively similar wakes. The foils we employ are free to swim forward, but with prescribed flapping motions, allowing for precise control of the flapping kinematics and measurement of the swimming dynamics.
Our first study looks at actively flapping foils in a tandem formation with a fixed distance between the foils in the swimming direction. The interaction between a foil and the wake of its upstream neighbor results in a slow-swimming mode and a fast-swimming mode that both exist for the same prescribed flapping motion, making the system bi-stable with a steady-state swimming speed that depends on the initial conditions.
Our second study looks at two foils that each have independently prescribed flapping motions but have free-spacing between the foils in the swimming direction. We find that the following foil experiences modified fluid forces when swimming in the leader's wake which creates stable positions whose locations can be controlled by changing the relative flapping phase or relative flapping amplitude of the foils. These wake interactions can force both slower-flapping and faster-flapping followers to keep pace with a leader by surfing on its wake.
Our third study looks at two foils that have free spacing in the swimming direction but with an imposed lateral spacing transverse to the swimming direction. When one foil swims ahead of the other, the follower experiences stable positions in the leader's wake up to twice as far downstream compared to tandem foils.
The side-by-side formation is also stable and yields an increase in the swimming speed of the pair up to ~ 60% faster than an isolated foil with the same flapping kinematics.
Our final study looks at tandem formations of many flapping foils with free spacing in the swimming direction. In this case each foil experiences stable positions in the wake of its upstream neighbor, similar to those in the two-foil problem. The foils in these larger formations oscillate around their stable positions with amplitudes of oscillation that become larger for latter members. This effect is revealed to be the result of the foils having the same resonance frequency about their stable positions and can be mitigated by modifying the spacing between adjacent foils by adding voids or changing their relative flapping phase.
We are able to explain the dynamics that result from these flow-interactions using a model with the fundamental ingredient that the thrust experienced by a foil swimming in a wake depends on the relative velocity between the foil's flapping motion and the wake-flow. The lessons learned from these experiments and models can be used to make predictions about real animals that move together within a fluid, as well as informing engineering applications such as energy harvesting using flapping foils or groups of vehicles that propel through fluids using flapping foils.
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|Advisor:||Zhang, Jun, Ristroph, Leif|
|Commitee:||Peskin, Charlie, Zidovska, Alexandra, Chaikin, Paul|
|School:||New York University|
|School Location:||United States -- New York|
|Source:||DAI-B 81/5(E), Dissertation Abstracts International|
|Subjects:||Fluid mechanics, Physics, Biomechanics|
|Keywords:||Bird flocking, Collective locomotion, Fish schooling, Fluid dynamics, Fluid-structure interaction, Hydrodynamic interaction|
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