Physical Mechanisms of Efficient Biological Propulsion Wake Resonance

Vortex Shedding https://www.pmmh.espci.fr/?Biomimetics-and-Fluid-Structure-Interaction&id_document=191

Why Fluids is Theoretically Difficult Navier-Stokes Equation. $1M bucks if you can solve it, no joke! The other “solution”: DO EXPERIMENTS!

Larger scale vortex street (for fun)

Vortex Shedding Dictated by Strouhal Number Image credit: A.H. Techet, MIT

Strouhal Number 𝑆𝑡= 𝑓𝐴 𝑈 = 𝐴 𝑇 /𝑈 f = flapping frequency = 1/T 𝑆𝑡= 𝑓𝐴 𝑈 = 𝐴 𝑇 /𝑈 f = flapping frequency = 1/T A = displacement at mid- chord U = forward speed. St = Strouhal number Image credit: (http://style.org/strouhalflight/)

Vortex Wake Dynamics Increasing flapping frequency Typical vortex structures of swimming animals (Smits et al, 2012) (Lentink et al, 2008)

Oscillation vs. Undulation Intermediate oscillatory

Vortex Wake Thrust a) Ray-like robotic fin b) vorticity in 2S pattern c) time-averaged velocity field (Moored, 2012)

Wake transitions in batoid-inspired oscillating fin Biological swimmers 2S wake 2P wake (Dewey et al., 2012)

Efficient swimming: Wake Resonance Froude Propulsive Efficiency: Mechanical Power output = avg. thrust x avg swimming speed Mechanical Power input (Moored, 2012)

Wake Resonance: Why it works Initial velocity profile from vortex shedding Final velocity profile after “roll-up” 2P wake 2S wake “When driven at wake resonant frequency, there is increase in entrainment of momentum into the time-averaged velocity jet…” (Moored, 2014)

Efficient Swimming: Be a bit Flexible Most flexible Most rigid (Smits et al., 2012)

References 1. Moored, K. W., Dewey, P. A., Boschitsch, B. M., Smits, A. J., & Haj-Hariri, H. (2014). Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors. Physics of Fluids, 26(4), 041905. 2. Dewey, P. A., Boschitsch, B. M., Moored, K. W., Stone, H. A., & Smits, A. J. (2013). Scaling laws for the thrust production of flexible pitching panels. Journal of Fluid Mechanics, 732, 29-46. 3. Dewey, P. A., Carriou, A., & Smits, A. J. (2012). On the relationship between efficiency and wake structure of a batoid-inspired oscillating fin. Journal of fluid mechanics, 691, 245-266. 4. Moored, K. W., Dewey, P. A., Smits, A. J., & Haj-Hariri, H. (2012). Hydrodynamic wake resonance as an underlying principle of efficient unsteady propulsion. Journal of Fluid Mechanics, 708, 329-348. 5. Smits, A. J., Moored, K. W., & Dewey, P. A., (2012) The Swimming of Manta Rays, Fluid-Structure-Sound-Interactions and Control, Lecture Notes in Mechanical Engineering 6. Lentink, D., Muijres, F. T., Donker-Duyvis, F. J., & van Leeuwen, J. L. (2008). Vortex-wake interactions of a flapping foil that models animal swimming and flight. Journal of Experimental Biology, 211(2), 267-273. 7. Clark, R. P., & Smits, A. J. (2006). Thrust production and wake structure of a batoid-inspired oscillating fin. Journal of fluid mechanics, 562, 415-429. 8. Triantafyllou, G. S., Triantafyllou, M. S., & Grosenbaugh, M. A. (1993). Optimal thrust development in oscillating foils with application to fish propulsion. Journal of Fluids and Structures, 7(2), 205-224.