Abstract
Locomotion is essential for the survival of fish because it influences the success rate of avoiding danger and predation. In particular, differences in the hydrodynamic properties of the caudal fin have a significant impact on swimming, since the caudal fin is the primary propulsion organ. The hydrodynamic characteristics of shark caudal fins have been studied. However, comparisons have been limited to a few species, and more caudal fin morphologies need to be investigated to determine the relationship between caudal fin morphology and hydrodynamic characteristics in sharks with diverse morphologies. Therefore, we performed computational fluid dynamics analysis on the caudal fin morphologies of 30 species in 9 orders of sharks to investigate the relationship between caudal fin morphology and hydrodynamic characteristics. We found that caudal fin morphologies with large ARL (ratio of vertical to the horizontal length of caudal fin) had higher thrust and swimming costs and caudal fin morphologies with small ARS (ratio of the product of the length and height of the caudal fin to the surface area) had higher propulsive efficiency. The results of this study will help in selecting caudal fin morphology for fish-like underwater robots and in studying the relationship between shark ecology and caudal fin morphology.
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24 November 2023
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References
Airfoil Tools (2023) NACA 0012 AIRFOILS (n0012-il). Electronic version, updated 22 Jun 2023. http://airfoiltools.com/airfoil/details?airfoil=n0012-il. Accessed 22 Jun 2023
Bamba T, Fukui T, Morinishi K (2021) Numerical study on the effects of aspect ratio of two types of fin folds on the propulsion performance by fish larvae’s swimming simulation. J Fluid Sci Technol 16:21-00018
Blender Foundation (2023) Blender.org. Electronic version, updated 22 Jun 2023. https://www.blender.org/. Accessed 22 Jun 2023
Borazjani I, Sotiropoulos F, Tytell ED, Lauder GV (2012) Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data. J Exp Biol 215:671–684
Bottom RGII, Borazjani I, Blevins EL, Lauder GV (2016) Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex. J Fluid Mech 788:407–443
Caiger PE, Croq C, Clements KD (2021) Environmentally induced morphological variation in the temperate reef fish, Forsterygion lapillum (F. Tripterygiidae). Mar Biol 168:131
Crofts SB, Shehata R, Flammang BE (2019) Flexibility of heterocercal tails: what can the functional morphology of shark tails tell us about ichthyosaur swimming? Integr Org Biol 1:obz002
Cui Z, Yang Z, Shen L, Jiang HZ (2018) Complex modal analysis of the movements of swimming fish propelled by body and/or caudal fin. Wave Motion 78:83–97
Di Santo V, Elsa G, Dylan KW, Otar A, James CL, Theodore CS, Lauder GV (2021) Convergence of undulatory swimming kinematics across a diversity of fishes. Proc Natl Acad Sci U S A 118:e2113206118
Downie AT, Leis JM, Cowman PF, McCormick MI, Rummer JL (2021) The influence of habitat association on swimming performance in marine teleost fish larvae. Fish Fish (Oxf) 22:1187–1212
FishBase (2023a) Search FishBase. Electronic version, updated 29 March 2023. https://fishbase.mnhn.fr/search.php?lang=Japanese. Accessed 22 Jun 2023
FishBase (2023b) Ginglymostoma cirratum summary page. Electronic version, updated 29 March 2023. https://www.fishbase.se/summary/Ginglymostoma-cirratum.html. Accessed 22 Jun 2023
Flammang BE, Lauder GV, Troolin DR, Strand T (2011) Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure. Proc R Soc B 278:3670–3678
Freudiger A, Josi D, Thünken T, Herder F, Flury JM, Marques DA, Taborsky M, Frommen JG (2021) Ecological variation drives morphological differentiation in a highly social vertebrate. Funct Ecol 35:2266–2281
Gabler-Smith MK, Dylan KW, Greta AW, Lauder GV (2021) Dermal denticle diversity in sharks: novel patterns on the interbranchial skin. Integr Org Biol 3:obab034
Ingley SJ, Camarillo H, Willis H, Johnson JB (2016) Repeated evolution of local adaptation in swimming performance: population-level trade-offs between burst and endurance swimming in Brachyrhaphis freshwater fish. Biol J Linn Soc Lond 119:1011–1026
Iosilevskii G, Papastamatiou YP (2016) Relations between morphology, buoyancy and energetics of requiem sharks. R Soc Open Sci 3:160406
Kim SH, Shimada K, Rigsby CK (2013) Anatomy and evolution of heterocercal tail in lamniform sharks. Anat Rec 296:433–442
Krishnadas A, Ravichandran S, Rajagopal P (2018) Analysis of biomimetic caudal fin shapes for optimal propulsive efficiency. Ocean Eng 153:132–142
Langerhans RB (2009) Morphology, performance, fitness: functional insight into a post-Pleistocene radiation of mosquitofish. Biol Lett 5:488–491
Langerhans RB, Layman CA, Shokrollahi AM, DeWitt TJ (2004) Predator-driven phenotypic diversification in Gambusia affinis. Evolution 58:2305–2318
Lauder GV (2000) Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns 1. Am Zool 40:101–122
Lauder GV, Di Santo V (2015) 6 - Swimming mechanics and energetics of elasmobranch fishes. Academic Press, Cambridge
Li G, Liu H, Müller UK, Voesenek, CJ, van Leeuwen JL (2021) Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport. Proc R Soc B 288:20211601
Li N, Liu H, Su Y (2017) Numerical study on the hydrodynamics of thunniform bio-inspired swimming under self-propulsion. PLoS One 12(3):e0174740
Lowe C (1996) Kinematics and critical swimming speed of juvenile scalloped hammerhead sharks. J Exp Biol 199:2605–2610
Menter F, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. Heat Mass Transf 4:625–632
Moran CJ, Gerry SP, O’Neill MW, Rzucidlo CL, Gibb AC (2018) Behavioral and physiological adaptations to high-flow velocities in Southwestern native chubs (Gila spp.). J Exp Biol 221:jeb158972
OpenCFD (2021) OpenFOAM® - Official home of The Open Source Computational Fluid Dynamics (CFD) Toolbox. Electronic version, updated 8 march 2021. https://www.openfoam.com/. Accessed 8 March 2021
Payne NL, Iosilevskii G, Barnett A, Fischer C, Graham RT, Gleiss AC, Watanabe YY (2016) Great hammerhead sharks swim on their side to reduce transport costs. Nat Commun 7:12289
Riedeberger D, Rist U (2012) Numerical simulation of laminar–turbulent transition on a dolphin using the γ-Reθ model. In: Nagel W, Kröner D, Resch M (eds) High performance computing in science and engineering '11. Springer, Berlin, Heidelberg, pp 379–391
Scaradozzi D, Palmieri G, Costa D, Pinelli A (2017) BCF swimming locomotion for autonomous underwater robots: a review and a novel solution to improve control and efficiency. Ocean Eng 130:437–453
scikit-learn (2023a) sklearn.linear_model.LinearRegression. Electronic version, updated 20 August 2023. https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html. Accessed 21 August 2023
scikit-learn (2023b) sklearn.preprocessing.PolynomialFeatures. Electronic version, updated 20 August 2023. https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html. Accessed 21 August 2023
Simons JR (1970) The direction of the thrust produced by the heterocercal tails of two dissimilar elasmobranchs: the Port Jackson shark, Heterodontus portusjacksoni (Meyer), and the piked dogfish, Squalus Megalops (Macleay). J Exp Biol 52:95–107
Sternes PC, Shimada K (2020) Body forms in sharks (Chondrichthyes: Elasmobranchii) and their functional, ecological, and evolutionary implications. Zoology 140:125799
Sumikawa H, Naraoka Y, Fukue T, Miyoshi T (2022) Changes in rays’ swimming stability due to the phase difference between left and right pectoral fin movements. Sci Rep 12:2362
Thomson KS, Simanek DE (1977) Body form and locomotion in sharks. Integr Comp Biol 17:343–354
Tytell ED, Standen EM, Lauder GV (2008) Escaping flatland: three-dimensional kinematics and hydrodynamics of median fins in fishes. J Exp Biol 211:187–195
Wang J, Wainwright DK, Lindengren RE, Lauder GV, Dong H (2020) Tuna locomotion: a computational hydrodynamic analysis of finlet function. J R Soc Interface 17:20190590
Wilga CD, Lauder GV (2002) Function of the heterocercal tail in sharks: quantitative wake dynamics during steady horizontal swimming and vertical maneuvering. J Exp Biol 205:2365–2374
Wilga CD, Lauder GV (2004) Biomechanics: hydrodynamic function of the shark’s tail. Nature 430:850
Witt WC, Wen L, Lauder GV (2015) Hydrodynamics of C-start escape responses of fish as studied with simple physical models. Integr Comp Biol 55:728–739
Yeh PD, Alexeev A (2016) Effect of aspect ratio in free-swimming plunging flexible plates. Comput Fluids 124:220–225
Zhang J-D, Sung HJ, Huang W-X (2020) Specialization of tuna: a numerical study on the function of caudal keels. Phys Fluids 32:111902
Zhao Z, Dou L (2019) Effects of the structural relationships between the fish body and caudal fin on the propulsive performance of fish. Ocean Eng 186:106117
Zhou K, Liu J, Chen W (2016) Numerical study on hydrodynamic performance of bionic caudal fin. Appl Sci 6:15
Acknowledgments
Part of the analysis in this study was performed using supercomputing resources at the Cyberscience Center of Tohoku University. This work was supported by JSPS KAKENHI Grant Number JP23KJ0081.
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This study did not use actual fish and was conducted while observing the Guidelines for the use of fish in research published by the Ichthyological Society of Japan in 2003.
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ESM Movie S1 Motion of analytical model A viewed from above at 0.5x speed (MP4 475 KB)
ESM Movie S2 Motion of analytical model A viewed from behind at 0.5x speed (MP4 180 KB)
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Sumikawa, H., Naraoka, Y., Obayashi, Y. et al. Fluid dynamic properties of shark caudal fin morphology and its relationship to habitats. Ichthyol Res 71, 294–304 (2024). https://doi.org/10.1007/s10228-023-00933-1
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DOI: https://doi.org/10.1007/s10228-023-00933-1