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.

References

References
1.
Lighthill
,
M. J.
,
1960
, “
Note on the Swimming of Slender Fish
,”
J. Fluid Mech.
,
9
, pp.
305
317
.10.1017/S0022112060001110
2.
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
.10.1017/S0022112071000697
3.
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
4.
Triantafyllou
,
M. S.
,
Triantafyllou
,
G. S.
, and
Yue
,
D. K. P.
,
2000
, “
Hydrodynamics of Fishlike Swimming
,”
Annu. Rev. Fluid Mech.
,
32
, pp.
33
53
.10.1146/annurev.fluid.32.1.33
5.
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
.10.1006/jfls.1993.1012
6.
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
.
7.
Kern
S.
, and
Koumoutsakos
,
P.
,
2006
, “
Simulations of Optimized Anguilliform Swimming
,”
J. Exp. Biol.
,
209
, pp.
4841
4857
.10.1242/jeb.02526
8.
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
.10.1016/j.ijnonlinmec.2010.12.007
9.
Tokic
,
G.
, and
Yue
,
D. K. P.
,
2012
, “
Optimal Shape and Motion of Undulatory Swimming Organisms
,”
Proc. R. Soc. B
,
279
, pp.
3065
3074
.10.1098/rspb.2012.0057
10.
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
.10.1115/1.483251
11.
Kowalik
,
J.
, and
Osborne
,
M. R.
,
1968
,
Methods for Unconstrained Optimization Problems
,
American Elsevier Publishing Company
,
New York
.
12.
Fiacco
,
A.
, and
McCormick
,
G. P.
,
1968
,
Nonlinear Programming Sequential Unconstrained Minimization Techniques
,
John Wiley & Sons
,
New York
.
13.
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
.10.1017/S0022112086000976
14.
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
15.
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
.
You do not currently have access to this content.