Garrick, I. E. Propulsion of a Flapping and Oscillating Airfoil, vol. 567 of National Advisory Committee for Aeronautics: Report (NACA, 1936).
Fernandez-Feria, R. Note on optimum propulsion of heaving and pitching airfoils from linear potential theory. J. Fluid Mech. 826, 781–796 (2017).
Google Scholar
Jones, K. & Platzer, M. Numerical computation of flapping-wing propulsion and power extraction. AIAA Paper 97, 0826 (1997).
Young, J. & Lai, J. C. S. Mechanisms influencing the efficiency of oscillating airfoil propulsion. AIAA J. 45, 1695–1702 (2007).
Google Scholar
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72 (1998).
Google Scholar
Floryan, D., Van Buren, T., Rowley, C. W. & Smits, A. J. Scaling the propulsive performance of heaving and pitching foils. J. Fluid Mech. 822, 386–397 (2017).
Google Scholar
Gray, J. Studies in animal locomotion i. J. Experim. Biol. 10, 88–104 (1933).
Google Scholar
Bale, R., Hao, M., Bhalla, A. P. S., Patel, N. & A.Patankar, N. Gray’s paradox a fluid mechanical perspective. Sci. Rep. 4, 5904 (2014).
Lucas, K. N., Lauder, G. V. & Tytell, E. D. Airfoil-like mechanics generate thrust on the anterior body of swimming fishes. PNAS 117, 10585–10592 (2020).
Google Scholar
Lighthill, J. Note on the swimming of slender fish. J. Fluid Mech. 9, 305–317 (1960).
Google Scholar
Wu, T. Y. Swimming of a waving plate. J. Fluid Mech. 10, 321–344 (1961).
Google Scholar
Carling, J., Williams, T. L. & Bowtell, G. Self-propelled anguilliform swimming simultaneous solution of the two-dimensional Navier–Stokes equations and newtons laws of motion. J. Experim. Biol. 201, 3143–3166 (1998).
Google Scholar
Kern, S. & Koumoutsakos, P. Simulations of optimized anguilliform swimming. J. Experim. Biol. 209, 4841–4857 (2006).
Google Scholar
Yang, Y., Wu, G. H., Yu & Tong, B. G. Two-dimensional self-propelled fish motion in medium: An integrated method for deforming body dynamics and unsteady fluid dynamics. Chin. Phys. Lett. 25, 597–600 (2008).
Borazjani, I. & Sotiropoulos, F. On the role of form and kinematics on the hydrodynamics of self-propelled body-caudal fin swimming. J. Experim. Biol. 213, 89–107 (2010).
Google Scholar
Gabrielli, G. & von Kármán, T. What price speed? Specific power required for propulsion. J. Am. Soc. Naval Eng. 63, 188–200 (1951).
Bale, R., Hao, M., Bhalla, A. P. S. & Patankar, N. A. Energy efficiency and allometry of movement of swimming and flying animals. PNAS 111, 7517–7521 (2014).
Google Scholar
Smits, A. J. Undulatory and oscillatory swimming. J. Fluid Mech. 874, 1–70 (2019).
Google Scholar
Akoz, E. & Moored, K. W. Unsteady propulsion by an intermittent swimming gait. J. Fluid Mech. 834, 149–172 (2018).
Google Scholar
Schultz, W. W. & Webb, P. W. Power requirements of swimming: Do new methods resolve old questions?. Integr. Comp. Biol. 42, 1018–25 (2002).
Google Scholar
Gazzola, M., Argentina, M. & Mahadevan, L. Energy gait and speed selection in slender inertial swimmers. PNAS 112, 3874–3879 (2015).
Google Scholar
Alben, S. & Shelley, M. Coherent locomotion as an attracting state for a free flapping body. PNAS 102, 11163–11166 (2005).
Google Scholar
X, Zhang, Ni Wang, S. & He, G. Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil. Phys. Fluids 21, 103302 (2009).
Google Scholar
Arora, N., Gupta, A., Sanghi, S., Aono, H. & Shyy, W. Flow patterns and efficiency-power characteristics of a self-propelled, heaving rigid flat plate. J. Fluid Struct. 66, 517–542 (2016).
Google Scholar
Lin, X., Wu, J. & Zhang, T. Performance investigation of a self-propelled foil with combined oscillating motion in stationary fluid. Ocean. Eng. 174, 33–49 (2019).
Google Scholar
Lighthill, J. Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44, 265–301 (1970).
Google Scholar
Wu, T. Y. Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43, 25–58 (2011).
Google Scholar
Paniccia, D., Graziani, G., Lugni, C. & Piva, R. The relevance of recoil and free swimming in aquatic locomotion. J. Fluids Struct. 103, 103290. https://doi.org/10.1016/j.jfluidstructs.2021.103290 (2021).
Google Scholar
Maertens, A. P., Gao, A. & Triantafyllou, M. S. Optimal undulatory swimming for single fish-like body and for pair of interacting swimmers. J. Fluid Mech. 813, 301–345 (2017).
Google Scholar
Bainbridge, R. The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat. J. Experim. Biol. 35, 109–133 (1958).
Google Scholar
Paniccia, D., Graziani, G., Lugni, C. & Piva, R. On the role of added mass and vorticity release for self propelled aquatic locomotion. J. Fluid Mech. 918, A45. https://doi.org/10.1017/jfm.2021.375 (2021).
Google Scholar
White, C. H., Lauder, G. V. & Bart-Smith, H. Tunabot flex: a tuna-inspired robot with body flexibility improves high-performance swimming. Bioinspir. Biomim. 16, 026019 (2021).
Google Scholar
Zhang, D., Pan, G., Chao, L. & Yan, G. Mechanisms influencing the efficiency of aquatic locomotion. Mod. Phys. Lett. B 32, 1850299 (2018).
Google Scholar
Floryan, D., Van Buren, T. & Smits, A. J. Efficient cruising for swimming and flying animals is dictated by fluid drag. PNAS 115, 8116–8118 (2018).
Google Scholar
Di Santo, V., Kenaley, C. P. & Lauder, G. V. High postural costs and anaerobic metabolism during swimming support the hypothesis of a u-shaped metabolism-speed curve in fishes. PNAS 114, 13048–13053 (2017).
Google Scholar
Zhu, J. et al. Tuna robotics: A high-frequency experimental platform exploring the performance space of swimming fishes. Sci. Robot. 4, eaax4615 (2019).
Google Scholar
Li, N., Liu, X. & Su, Y. Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion. PLOS One 12, e0174740 (2017).
Google Scholar
Akoz, E., Han, P., Liu, G., Dong, H. & Moored, K. W. Large-amplitude intermittent swimming in viscous and inviscid flows. AIAA J. 57, 1–8 (2019).
Google Scholar
Van Buren, T., Floryan, D., Wei, N. & Smits, A. J. Flow speed has little impact on propulsive characteristics of oscillating foils. Phys. Rev. Fluids 3, 013103 (2018).
Google Scholar
Noca, F. On the evaluation of time-dependent fluid dynamic forces on bluff bodies. Ph.D. thesis, California Institute of Technology (1997).
Wu, J. Z., Ma, H. Y. & Zhou, M. D. Vortical Flows (Springer, 2015).
Landau, L. D. & Lifschitz, E. M. Fluid Mechanics, vol. 6 (Pergamon Press, 1986), 2 edn.
Childress, S. An Introduction to Theoretical Fluid Dynamics (Courant Lecture Notes, vol. 19, AMS, 2009).
Graziani, G., Ranucci, M. & Piva, R. From a boundary integral formulation to a vortex method for viscous flows. Comput. Mech. 15(4), 301–314 (1995).
Google Scholar
