Research Papers: Flows in Complex Systems

Why do Fish Have a “Fish-Like Geometry”?

[+] Author and Article Information
Hiroshi Kagemoto

The University of Tokyo,
5-1-5 Kashiwanoha,
Kashiwa City, Chiba 277-8563, Japan
e-mail: kagemoto@k.u-tokyo.ac.jp

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 18, 2012; final manuscript received August 1, 2013; published online November 6, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(1), 011106 (Nov 06, 2013) (7 pages) Paper No: FE-12-1450; doi: 10.1115/1.4025646 History: Received September 18, 2012; Revised August 01, 2013

Most fish share a common geometry, a streamlined anterior body and a deep caudal fin, connected to each other at a tail-base neck, where the body almost shrinks to a point. This work attempts to explain the reason that fish exhibit this type of geometry. Assuming that the fish-like geometry is a result of evolution over millions of years, or, that bodies of modern-day fish have been optimized in some manner as a result of evolution, this work investigates the optimum geometry for a swimming object through existing mathematical optimization techniques to check whether the result obtained is the same as the naturally observed fish-like geometry. In this analysis, the work done by a swimming object is taken as the objective function of the optimization. It is found that a fish-like geometry is in fact obtained mathematically, provided that the appropriate constraints are imposed on the optimization process, which, in turn, provides some clues that explain the reason that fish have a fish-like geometry.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Lighthill, M. J., 1960, “Note on the Swimming of Slender Fish,” J. Fluid Mech., 9, pp. 305–317. [CrossRef]
Yao-Tsu Wu, T., 1971, “Hydromechanics of Swimming Propulsion, Part 3. Swimming and Optimum Movements of Slender Fish With Side Fins,” J. Fluid Mech., 46, part 3, pp. 545–568. [CrossRef]
Wolfgang, M. J., Anderson, J. M., Grosenbaugh, M. A., Yue, D. K. P., and Triantafyllou, M. S., 1999, “Near-Body Flow Dynamics in Swimming Fish,” J. Exp. Biol., 202, pp. 2303–2327. Available at: http://jeb.biologists.org/content/202/17/2303.long [PubMed]
Triantafyllou, M. S., Triantafyllou, G. S., and Yue, D. K. P., 2000, “Hydrodynamics of Fishlike Swimming,” Annu. Rev. Fluid Mech., 32, pp. 33–53. [CrossRef]
Triantafyllou, G. S., Triantafyllou, M. S., and Grosenbaugh, M. A., 1993, “Optimal Thrust Development in Oscillating Foils With Application to Fish Propulsion,” J. Fluids Struct., 7, pp. 205–224. [CrossRef]
Kagemoto, H., Yue, D. K. P., and Triantafyllou, M. S., 1997, “Optimization of a Fish-Like Swimming Body,” Bull. Am. Phys. Soc., 42, p. 5533.
KernS., and Koumoutsakos, P., 2006, “Simulations of Optimized Anguilliform Swimming,” J. Exp. Biol., 209, pp. 4841–4857. [CrossRef] [PubMed]
Eloy, C., and Schouveiler, L., 2011, “Optimization of Two-Dimensional Undulatory Swimming at High Reynolds Number,” Int. J. Non-linear Mech., 46, pp. 568–576. [CrossRef]
Tokic, G., and Yue, D. K. P., 2012, “Optimal Shape and Motion of Undulatory Swimming Organisms,” Proc. R. Soc. B, 279, pp. 3065–3074. [CrossRef]
Kagemoto, H., Wolfgang, M. J., Yue, D. K. P., and Triantafyllou, M. S., 2000, “Force and Power Estimation in Fish-Like Locomotion Using a Vortex-Lattice Method,” ASME J. Fluids Eng., 122, pp. 239–253. [CrossRef]
Kowalik, J., and Osborne, M. R., 1968, Methods for Unconstrained Optimization Problems, American Elsevier Publishing Company, New York.
Fiacco, A., and McCormick, G. P., 1968, Nonlinear Programming Sequential Unconstrained Minimization Techniques, John Wiley & Sons, New York.
Triantafyllou, G. S., Triantafyllou, M. S., and Chryssostomidis, C. C., 1986, “On the Formation of Vortex Streets Behind Stationary Cylinders,” J. Fluid Mech., 170, pp. 461–477. [CrossRef]
Bainbridge, R., 1957, “The Speed of Swimming Fish as Related to Size and to the Frequency and Amplitude of the Tail Beat,” J. Exp. Biol., 35, pp. 109–133. Available at: http://jeb.biologists.org/content/35/1/109.full.pdf+html
Pyatetskiy, V. E., 1971, “Kinematic Swimming Characteristics of Some Fast Marine Fish,” Hydrodynamic Problems of Bionics, G. V.Logvinovich, ed., Joint Publications Research Service, Washington, DC, pp. 12–23.


Grahic Jump Location
Fig. 1

The assumed instantaneous lateral displacement of a swimming object

Grahic Jump Location
Fig. 3

Reduction of an objective function in the optimization process

Grahic Jump Location
Fig. 4

Comparison of the optimum shapes identified for U = 2ℓ,5ℓ,10ℓ

Grahic Jump Location
Fig. 5

Comparison of optimum elastic modulus distribution identified for U = 2ℓ,5ℓ,10ℓ

Grahic Jump Location
Fig. 2

Optimum shape of an object swimming with U=5ℓ

Grahic Jump Location
Fig. 6

(a) Optimum shape identified starting from a different initial condition (U = 5ℓ); (b) optimum elastic modulus identified starting from a different initial condition (U = 5ℓ)

Grahic Jump Location
Fig. 7

Comparison of the optimum shape identified while taking the vortex shedding from the edge of the body into consideration (Wu) with that identified while neglecting the vortex shedding from the edge of the body (Lighthill) (U = 10ℓ)

Grahic Jump Location
Fig. 8

(a) Effect of the constraint on recoils; (b) reduction of the objective function in the optimization process

Grahic Jump Location
Fig. 9

Effect of the constraint on minimum volume



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In