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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.

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Figures

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Fig. 1

The assumed instantaneous lateral displacement of a swimming object

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Fig. 2

Optimum shape of an object swimming with U=5ℓ

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Fig. 3

Reduction of an objective function in the optimization process

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Fig. 4

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

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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)

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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)

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Fig. 5

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

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Fig. 8

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

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Fig. 9

Effect of the constraint on minimum volume

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