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  • Journal of Fluid Mechanics, Volume 717
  • February 2013, pp. 48-89

On the best design for undulatory swimming

  • Christophe Eloy (a1) (a2)
  • DOI: http://dx.doi.org/10.1017/jfm.2012.561
  • Published online: 01 February 2013
Abstract
Abstract

Most aquatic vertebrates swim by passing a bending wave down their bodies, a swimming mode known as undulatory propulsion. Except for very elongated swimmers like eels and lampreys, these animals have generally evolved to a similar shape: an anterior streamlined region of large volume separated from a caudal fin by a caudal peduncle of reduced cross-section. However, the link between this particular shape and the hydrodynamical constraints remains to be explored. Here, this question is addressed by seeking the optimal design for undulatory swimmers with an evolutionary algorithm. Animals of varying elliptic cross-section are considered whose motions are prescribed by arbitrary periodic curvature laws. In the elongated-body limit, reactive and resistive forces can be formulated at any cross-section, allowing the recoil motion and the mean swimming speed of a given animal to be calculated. A bi-objective optimization problem then consists of finding body shapes and corresponding motions associated with the lowest energetic costs, the highest stride lengths (which is a dimensionless measure of swimming speed) or any trade-offs between the two. For biologically relevant parameters, this optimization calculation yields two distinct ‘species’: one specialized in economical swimming and the other in large stride lengths. By comparing the attributes and performance of these numerically obtained swimmers with data on undulatory-swimming animals, it is argued that evolution is consistent with the selection of species with low energetic costs.

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Corresponding author
Email address for correspondence: Christophe.Eloy@irphe.univ-mrs.fr
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. W. Blake 2004 Fish functional design and swimming performance. J. Fish Biol. 65, 11931222.

I. Borazjani & F. Sotiropoulos 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211, 1541.

J. Branke , K. Deb , K. Miettinen & R. Słowiński  (Eds) 2008 Multiobjective Optimization: Interactive and Evolutionary Approaches. Springer.

J.-Y. Cheng , T. J. Pedley & J. D. Altringham 1998 A continuous dynamic beam model for swimming fish. Phil. Trans. R. Soc. Lond. B 353, 981997.


P. S. Dodds , D. H. Rothman & J. S. Weitz 2001 Re-examination of the ‘$3/ 4$-law’ of metabolism. J. Theor. Biol. 209, 927.

C. Eloy 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 205218.

C. Eloy , O. Doaré , L. Duchemin & L. Schouveiler 2010 A unified introduction to fluid mechanics of flying and swimming at high Reynolds number. Exp. Mech. 50, 13611366.

C. Eloy & L. Schouveiler 2011 Optimisation of two-dimensional undulatory swimming at high Reynolds number. Intl J. Non-Linear Mech. 46, 568576.

F. E. Fish & C. A. Hui 1991 Dolphin swimming – a review. Mammal Rev. 21, 181195.

S. Kern & P. Koumoutsakos 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209, 48414857.

G. V. Lauder & E. D. Tytell 2005 Hydrodynamics of undulatory propulsion. Fish Physiol. 23, 425468.


M. J. Lighthill 1969 Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech. 1, 413446.


M. J. Lighthill 1971 Large-amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179, 125138.

C. C. Lindsey 1978 Form, function and locomotory habits in fish. In Fish Physiology VII (ed. W. S. Hoar & D. J. Randall), pp. 1100. Academic.

M. W. Rosen & N. E. Cornford 1971 Fluid friction of fish slimes. Nature 234, 4951.

G. I. Taylor 1952 Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214, 158183.

G Tokić & D. K. P. Yue 2012 Optimal shape and motion of undulatory swimming organisms. Proc. R. Soc. Lond. B 279 (1740), 30653074.

G. S. Triantafyllou , M. S. Triantafyllou & M. A. Grosenbaugh 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205224.

M. S. Triantafyllou , G. S. Triantafyllou & D. K. P. Yue 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32 (1), 3353.

V. A. Tucker 1970 Energetic cost of locomotion in animals. Comp. Biochem. Physiol. 34 (4), 841846.

E. D. Tytell , C. Y. Hsu , T. L. Williams , A. H. Cohen & L. J. Fauci 2010 Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proc. Natl Acad. Sci. USA 107, 1983219837.

E. D. Tytell & G. V. Lauder 2004 The hydrodynamics of eel swimming. I. Wake structure. J. Expl Biol. 207, 18251841.

J. J. Videler 1993 Fish Swimming, Fish and Fisheries Series, vol. 10. Chapman & Hall.

D. Weihs 1973 Optimal fish cruising speed. Nature (London) 245, 4850.

C. R. White & R. S. Seymour 2005 Allometric scaling of mammalian metabolism. J. Expl Biol. 208, 16111619.


T. Y. Wu 2011 Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43, 25.

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