Abstract
We summarize the geometric treatment of locomotion in an ideal fluid in the absence of vorticity and link this work to a planar model incorporating localized vortex shedding evocative of vortex shedding from the caudal fin of a swimming fish. We present simulations of open-loop and closed-loop navigation and energy-harvesting by a Joukowski foil with variable camber shedding discrete vorticity from its trailing tip.
The work of all three authors was supported in part by NSF grant CMMI 04-49319.
AMS(MOS) subject classifications. Primary 70H33, 76B47, 93C10
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Notes
- 1.
Specifically, the swimmer’s effective mass in the horizontal direction.
- 2.
Planar Stokes flow requires a modified treatment due to Stokes’ paradox[1].
- 3.
Compare the role of of IV  − 1 here to that of the Reynolds number in the Navier-Stokes equations, which become the equations for creeping flow as Re → 0 [3].
- 4.
In the context of Stokes flow, this is the famous scallop theorem [13].
- 5.
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Kelly, S.D., Pujari, P., Xiong, H. (2012). Geometric Mechanics, Dynamics, and Control of Fishlike Swimming in a Planar Ideal Fluid. In: Childress, S., Hosoi, A., Schultz, W., Wang, J. (eds) Natural Locomotion in Fluids and on Surfaces. The IMA Volumes in Mathematics and its Applications, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3997-4_7
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