Schooling fish exhibit captivating biological behaviors that have garnered interest from both biologists and engineers. While the undulatory motion of fish in schools has been extensively studied, rapid turning within these schools remains underexplored. This paper presents a three-dimensional computational fluid dynamics (CFD) model of a fast-start scenario involving two fish to investigate the influence of spatial and phase differences on swimming performance. Our findings indicate that, by leveraging the wake of the upstream fish, a downstream fish can enhance its travel distance by up to 34.4% and its rotational angle by up to 41.6%. The optimal travel distance is achieved when the starting jet of the front fish aligns with the center of mass (COM) of the downstream fish. Conversely, the largest rotational angle is observed when this jet precedes the center of mass. The research further identifies a vortex phase matching phenomenon in fish schools during rapid turns. The phase difference, or the downstream fish's delayed response, allows it to harness the wake for improved transitional and rotational movement. However, this approach might decrease the average angular velocity, which represents the rotational angle divided by the total duration of turning and waiting. Our study concludes that, with a specific phase difference, this delayed action facilitates faster fish turns by utilizing the wake created by the neighboring fish.
REFERENCES
1.
J. R.
Usherwood
et al, “
Flying in a flock comes at a cost in pigeons
,” Nature
474
(7352
), 494
–497
(2011
).2.
D.
Pavlov
and
A.
Kasumyan
, “
Patterns and mechanisms of schooling behavior in fish: a review
,” J. Ichthyol.
40
(2
), S163
(2000
).3.
P. B.
Lissaman
and
C. A.
Shollenberger
, “
Formation flight of birds
,” Science
168
(3934
), 1003
–1005
(1970
).4.
H.
Weimerskirch
et al, “
Energy saving in flight formation
,” Nature
413
(6857
), 697
–698
(2001
).5.
D.
Weihs
, “
Hydromechanics of fish schooling
,” Nature
241
(5387
), 290
–291
(1973
).6.
V.
Belyayev
and
G.
Zuyev
, “
Hydrodynamic hypothesis of school formation in fishes
,” Probl. Ichthyol.
9
, 578
–584
(1969
).7.
E.
Burgerhout
et al, “
Schooling reduces energy consumption in swimming male European eels, Anguilla anguilla L.
,” J. Exp. Mar. Biol. Ecol.
448
, 66
–71
(2013
).8.
S.
Marras
et al, “
Fish swimming in schools save energy regardless of their spatial position
,” Behav. Ecol. Sociobiol.
69
, 219
–226
(2015
).9.
J.
Herskin
and
J.
Steffensen
, “
Energy savings in sea bass swimming in a school: measurements of tail beat frequency and oxygen consumption at different swimming speeds
,” J. Fish Biol.
53
(2
), 366
–376
(1998
).10.
S. S.
Killen
et al, “
Aerobic capacity influences the spatial position of individuals within fish schools
,” Proc. R. Soc. B
279
(1727
), 357
–364
(2012
).11.
R.
Gopalkrishnan
et al, “
Active vorticity control in a shear flow using a flapping foil
,” J. Fluid Mech.
274
, 1
–21
(1994
).12.
J. C.
Liao
, “
A review of fish swimming mechanics and behaviour in altered flows
,” Philos. Trans. R. Soc., B
362
(1487
), 1973
–1993
(2007
).13.
C.
Hemelrijk
et al, “
The increased efficiency of fish swimming in a school
,” Fish Fish.
16
(3
), 511
–521
(2015
).14.
L.
Li
et al, “
Vortex phase matching as a strategy for schooling in robots and in fish
,” Nat. Commun.
11
(1
), 1
–9
(2020
).15.
L.
Li
et al, “
Energy saving of schooling robotic fish in three-dimensional formations
,” IEEE Robot. Autom. Lett.
6
(2
), 1694
–1699
(2021
).16.
Y.
Pan
and
H.
Dong
, “
Computational analysis of hydrodynamic interactions in a high-density fish school
,” Phys. Fluids
32
(12
), 121901
(2020
).17.
Y.
Pan
and
H.
Dong
, “
Effects of phase difference on hydrodynamic interactions and wake patterns in high-density fish schools
,” Phys. Fluids
34
(11
), 111902
(2022
).18.
S.
Verma
,
G.
Novati
, and
P.
Koumoutsakos
, “
Efficient collective swimming by harnessing vortices through deep reinforcement learning
,” Proc. Natl. Acad. Sci. USA
115
(23
), 5849
–5854
(2018
).19.
E. D.
Tytell
and
G. V.
Lauder
, “
Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus
,” J. Exp. Biol.
211
(21
), 3359
–3369
(2008
).20.
D. G.
Harper
and
R. W.
Blake
, “
Fast-start performance of rainbow trout Salmo gairdneri and northern pike Esox lucius
,” J. Exp. Biol.
150
(1
), 321
–342
(1990
).21.
H.
Frith
and
R.
Blake
, “
Mechanics of the startle response in the northern pike, Esox lucius
,” Can. J. Zool.
69
(11
), 2831
–2839
(1991
).22.
J.
Song
et al, “
Tail shapes lead to different propulsive mechanisms in the body/caudal fin undulation of fish
,” Proc. Inst. Mech. Eng., Part C
235
(2
), 351
–364
(2021
).23.
Y.
Li
et al, “
Hydrodynamics and musculature actuation of fish during a fast start
,” Appl. Sci.
13
(4
), 2365
(2023
).24.
P. B.
Moyle
and
J. J.
Cech
, Fishes: An Introduction to Ichthyology (Pearson Prentice-Hall, 2000).25.
M.
Larsson
, “
Why do fish school?
,” Curr. Zool.
58
(1
), 116
–128
(2012
).26.
I.
Ashraf
et al, “
Simple phalanx pattern leads to energy saving in cohesive fish schooling
,” Proc. Natl. Acad. Sci. USA
114
(36
), 9599
–9604
(2017
).27.
J. E.
Herbert-Read
et al, “
Inferring the rules of interaction of shoaling fish
,” Proc. Natl. Acad. Sci. USA
108
(46
), 18726
–18731
(2011
).28.
Y.
Katz
et al, “
Inferring the structure and dynamics of interactions in schooling fish
,” Proc. Natl. Acad. Sci. USA
108
(46
), 18720
–18725
(2011
).29.
S. B.
Rosenthal
et al, “
Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion
,” Proc. Natl. Acad. Sci. USA
112
(15
), 4690
–4695
(2015
).30.
J.
Song
et al, “
Hydrodynamics of larval fish quick turning: a computational study
,” Proc. Inst. Mech. Eng., Part C
232
(14
), 2515
–2523
(2018
).31.
Y.
Zhong
et al, “
Hydrodynamic effects of the caudal fin shape of fish in carangiform undulatory swimming
,” Proc. Inst. Mech. Eng., Part C
236
, 6385
(2022
).32.
J.
Song
,
H.
Luo
, and
T. L.
Hedrick
, “
Three-dimensional flow and lift characteristics of a hovering ruby-throated hummingbird
,” J. R. Soc. Interface
11
(98
), 20140541
(2014
).33.
J.
Song
et al, “
Three-dimensional simulation for fast forward flight of a calliope hummingbird
,” R Soc. Open Sci.
3
(6
), 160230
(2016
).34.
R.
Mittal
et al, “
A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries
,” J. Comput. Phys.
227
(10
), 4825
–4852
(2008
).35.
P.
Webb
, “
Body and fin form and strike tactics of four teleost predators attacking fathead minnow (Pimephales promelas) prey
,” Can. J. Fish. Aquat. Sci.
41
(1
), 157
–165
(1984
).36.
P.
Domenici
and
R. W.
Blake
, “
The effect of size on the kinematics and performance of angelfish (Pterophyllum eimekei) escape responses
,” Can. J. Zool.
71
(11
), 2319
–2326
(1993
).37.
I.
Borazjani
et al, “
Hydrodynamics of the bluegill sunfish C-start escape response: three-dimensional simulations and comparison with experimental data
,” J. Exp. Biol.
215
(4
), 671
–684
(2012
).38.
T.
Inagaki
et al, “
Studies on the schooling behavior of fish-III
,” Nippon Suisan Gakkaishi
42
, 1083
–1091
(1976
).39.
B.
Partridge
, “
Internal dynamics and the interrelations of fish in schools
,” J. Comp. Physiol.
144
, 313
–325
(1981
).40.
J. M.
Cullen
,
E.
Shaw
, and
H. A.
Baldwin
, “
Methods for measuring the three-dimensional structure of fish schools
,” Anim. Behav.
13
(4
), 534
(1965
).41.
I.
Aoki
,
T.
Inagaki
, and
L. V.
Long
, “
Measurements of the three-dimensional structure of free-swimming pelagic fish schools in a natural environment
,” Bull. Jpn. Soc. Sci. Fish.
52
, 2069
–2077
(1986
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
