Skip to main content
×
Home
    • Aa
    • Aa

Learning to school in the presence of hydrodynamic interactions

  • M. Gazzola (a1), A. A. Tchieu (a2), D. Alexeev (a3), A. de Brauer (a4) and P. Koumoutsakos (a3)...
Abstract

Schooling, an archetype of collective behaviour, emerges from the interactions of fish responding to sensory information mediated by their aqueous environment. A fundamental and largely unexplored question in fish schooling concerns the role of hydrodynamics. Here, we investigate this question by modelling swimmers as vortex dipoles whose interactions are governed by the Biot–Savart law. When we enhance these dipoles with behavioural rules from classical agent-based models, we find that they do not lead robustly to schooling because of flow-mediated interactions. We therefore propose to use swimmers equipped with adaptive decision-making that adjust their gaits through a reinforcement learning algorithm in response to nonlinearly varying hydrodynamic loads. We demonstrate that these swimmers can maintain their relative position within a formation by adapting their strength and school in a variety of prescribed geometrical arrangements. Furthermore, we identify schooling patterns that minimize the individual and collective swimming effort, through an evolutionary optimization. The present work suggests that the adaptive response of individual swimmers to flow-mediated interactions is critical in fish schooling.

Copyright
Corresponding author
Email address for correspondence: petros@ethz.ch
Linked references
Hide All

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.

M. V. Abrahams  & P. W. Colgan 1987 Fish schools and their hydrodynamic function: a reanalysis. Environ. Biol. Fishes 20 (1), 7980.

I. Aoki 1982 A simulation study on the schooling mechanism in fish. Bull. Japan. Soc. Sci. Fisheries 48 (8), 10811088.

H. Aref , P. Newton , M. A. Stremler , T. Tokieda  & D. Vainchtein 2003 Vortex crystals. Adv. Appl. Mech. 39, 179.

B. M. Boschitsch , P. A. Dewey  & A. J. Smits 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26 (5), 051901.

J. F. Brady  & G. Bossis 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111157.

H. Chate , F. Ginelli , G. Gregoire , F. Peruani  & F. Raynaud 2008 Modeling collective motion: variations on the Vicsek model. Eur. Phys. J. B 64 (3–4), 451456.

I. D. Couzin , J. Krause , N. R. Franks  & S. A. Levin 2005 Effective leadership and decision-making in animal groups on the move. Nature 433 (7025), 513516.

I. D. Couzin , J. Krause , R. James , G. D. Ruxton  & N. R. Franks 2002 Collective memory and spatial sorting in animal groups. J. Theoret. Biol. 218 (1), 111.

J. M. Cullen , E. Shaw  & H. A. Baldwin 1965 Methods for measuring the three-dimensional structure of fish schools. Animal Behaviour 13 (4), 534543.

P. A. Dewey , D. B. Quinn , B. M. Boschitsch  & A. J. Smits 2014 Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration. Phys. Fluids 26 (4), 041903.

M. Gazzola , C. J. Burckhardt , B. Bayati , M. Engelke , U. F. Greber  & P. Koumoutsakos 2009 A stochastic model for microtubule motors describes the in vivo cytoplasmic transport of human adenovirus. PLoS Comput. Biol. 5 (12), e1000623.

M. Gazzola , P. Chatelain , W. M. van Rees  & P. Koumoutsakos 2011a Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230 (19), 70937114.

M. Gazzola , B. Hejazialhosseini  & P. Koumoutsakos 2014 Reinforcement learning and wavelet adapted vortex methods for simulations of self-propelled swimmers. SIAM J. Sci. Comput. 36 (3), B622B639.

M. Gazzola , C. Mimeau , A. A. Tchieu  & P. Koumoutsakos 2012a Flow mediated interactions between two cylinders at finite Re numbers. Phys. Fluids 24 (4), 043103.

M. Gazzola , O. V. Vasilyev  & P. Koumoutsakos 2011b Shape optimization for drag reduction in linked bodies using evolution strategies. Comput. Struct. 89 (11–12), 12241231.

Y. Goto  & H. Tanaka 2015 Purely hydrodynamic ordering of rotating disks at a finite Reynolds number. Nat. Commun. 6.

N. Hansen , S. D. Muller  & P. Koumoutsakos 2003 Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11 (1), 118.

Y. Hatwalne , S. Ramaswamy , M. Rao  & R. A. Simha 2004 Rheology of active-particle suspensions. Phys. Rev. Lett. 92 (11), 118101.

S. Hubbard , P. Babak , S. T. Sigurdsson  & K. G. Magnusson 2004 A model of the formation of fish schools and migrations of fish. Ecol. Model. 174 (4), 359374.

A. Huth  & C. Wissel 1992 The simulation of the movement of fish schools. J. Theoret. Biol. 156 (3), 365385.

H. S. Jiang , T. R. Osborn  & C. Meneveau 2002 The flow field around a freely swimming copepod in steady motion. Part I. Theoretical analysis. J. Plankton Res. 24 (3), 167189.

S. Kern  & P. Koumoutsakos 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209 (24), 48414857.

D. L. Koch  & G. Subramanian 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637659.

L. Landeau  & J. Terborgh 1986 Oddity and the ‘confusion effect’ in predation. Animal Behaviour 34 (5), 13721380.

J. C. Liao , D. N. Beal , G. V. Lauder  & M. S. Triantafyllou 2003 Fish exploiting vortices decrease muscle activity. Science 302 (5650), 15661569.

P. F. Major 1978 Predator–prey interactions in two schooling fishes, Caranx ignobilis and Stolephorus purpureus. Animal Behaviour 26 (0), 760777.

O. A. Misund , A. Aglen  & E. Fronaes 1995 Mapping the shape, size, and density of fish schools by echo integration and a high-resolution sonar. ICES J. Marine Sci. 52 (1), 1120.

H. S. Niwa 1994 Self-organizing dynamic-model of fish schooling. J. Theoret. Biol. 171 (2), 123136.

J. K. Parrish , S. V. Viscido  & D. Grünbaum 2002 Self-organized fish schools: an examination of emergent properties. Biol. Bull. 202 (3), 296305.

B. L. Partridge 1982 The structure and function of fish schools. Sci. Am. 246 (6), 114123.

B. L. Partridge , T. Pitcher , J. M. Cullen  & J. Wilson 1980 The three-dimensional structure of fish schools. Behav. Ecol. Sociobiol. 6 (4), 277288.

T. J. Pitcher , A. E. Magurran  & I. J. Winfield 1982 Fish in larger shoals find food faster. Behav. Ecol. Sociobiol. 10 (2), 149151.

L. Ristroph  & J. Zhang 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.

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

A. A. Tchieu , D. Crowdy  & A. Leonard 2010 Fluid-structure interaction of two bodies in an inviscid fluid. Phys. Fluids 22 (10), 107101.

A. A. Tchieu , E. Kanso  & P. K. Newton 2012 The finite-dipole dynamical system. Proc. R. Soc. Lond. A 468, 30063026.

A. C. H. Tsang  & E. Kanso 2013 Dipole interactions in doubly periodic domains. J. Nonlinear Sci. 23 (6), 971991.

T. Vicsek , A. Czirok , E. Benjacob , I. Cohen  & O. Shochet 1995 Novel type of phase-transition in a system of self-driven particles. Phys. Rev. Lett. 75 (6), 12261229.

S. V. Viscido , J. K. Parrish  & D. Grunbaum 2005 The effect of population size and number of influential neighbors on the emergent properties of fish schools. Ecol. Model. 183 (2–3), 347363.

C. Watkins  & P. Dayan 1992 Q-learning. Mach. Learn. 8 (3–4), 279292.

D. Weihs 1973 Hydromechanics of fish schooling. Nature 241 (5387), 290291.

R. Whittlesey , S. Liska  & J. Dabiri 2010 Fish schooling as a basis for vertical axis wind turbine farm design. Bioinspir. Biomim. 5 (3), 035005.

L. Zhu , E. Lauga  & L. Brandt 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24, 051902.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 1
Total number of PDF views: 97 *
Loading metrics...

Abstract views

Total abstract views: 160 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 27th March 2017. This data will be updated every 24 hours.