Experiments in Fluids

, Volume 51, Issue 1, pp 23–35 | Cite as

Swimming hydrodynamics: ten questions and the technical approaches needed to resolve them

Research Article


Recent experimental and computational studies of swimming hydrodynamics have contributed significantly to our understanding of how animals swim, but much remains to be done. Ten questions are presented here as an avenue to discuss some of the arenas in which progress still is needed and as a means of considering the technical approaches to address these questions. 1. What is the three-dimensional structure of propulsive surfaces? 2. How do propulsive surfaces move in three dimensions? 3. What are the hydrodynamic effects of propulsor deformation during locomotion? 4. How are locomotor kinematics and dynamics altered during unsteady conditions? 5. What is the three-dimensional structure of aquatic animal vortex wakes? 6. To what extent are observed propulsor deformations actively controlled? 7. What is the response of the body and fins of moving animals to external perturbations? 8. How can robotic models help us understand locomotor dynamics of organisms? 9. How do propulsive surfaces interact hydrodynamically during natural motions? 10. What new computational approaches are needed to better understand locomotor hydrodynamics? These ten questions point, not exclusively, toward areas in which progress would greatly enhance our understanding of the hydrodynamics of swimming organisms, and in which the application of new technology will allow continued progress toward understanding the interaction between organisms and the aquatic medium in which they live and move.



This work was supported by an ONR-MURI Grant N00014-03-1-0897, and by ONR grant N00014-09-1-0352. We thank Drs. Rajat Mittal for many helpful discussions on bio-inspired propulsion. Many thanks to members of the Lauder and Tangorra Laboratories for numerous helpful discussions, and to Timo Gericke for constructing the vortex generator.


  1. Akhtar I, Mittal R, Lauder GV, Drucker E (2007) Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theor Comput Fluid Dyn 21:155–170MATHCrossRefGoogle Scholar
  2. Alben S (2008) Optimal flexibility of a flapping appendage in an inviscid fluid. J Fluid Mech 614:355–380MATHMathSciNetCrossRefGoogle Scholar
  3. Alben S, Shelley M, Zhang J (2004) How flexibility induces streamlining in a two-dimensional flow. Phys Fluids 16:1694CrossRefGoogle Scholar
  4. Alben S, Madden PGA, Lauder GV (2007) The mechanics of active fin-shape control in ray-finned fishes. J Roy Soc Interface 4:243–256CrossRefGoogle Scholar
  5. Bainbridge R (1963) Caudal fin and body movements in the propulsion of some fish. J Exp Biol 40:23–56Google Scholar
  6. Bandyopadhyay PR (2002) Maneuvering hydrodynamics of fish and small underwater vehicles. Int Comp Biol 42:102–117CrossRefGoogle Scholar
  7. Bartol IK, Gharib M, Webb PW, Weihs D, Gordon MS (2005) Body-induced vortical flows: a common mechanism for self-corrective trimming control in boxfishes. J Exp Biol 208:327–344CrossRefGoogle Scholar
  8. Birch JM, Dickinson MH (2003) The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight. J Exp Biol 206:2257–2272CrossRefGoogle Scholar
  9. Blondeaux P, Fornarelli F, Guglielmini L, Triantafyllou MS, Verzicco R (2005) Numerical experiments on flapping foils mimicking fish-like locomotion. Phys Fluids 17:113601CrossRefGoogle Scholar
  10. Borazjani I, Sotiropoulos F (2008) Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J Exp Biol 211:1541–1558CrossRefGoogle Scholar
  11. Borazjani I, Sotiropoulos F (2009) Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J Exp Biol 212:576–592CrossRefGoogle Scholar
  12. Bowtell G, Williams TL (1991) Anguilliform body dynamics—modelling the interaction between muscle activation and body curvature. Phil Trans R Soc Lond B 334:385–390CrossRefGoogle Scholar
  13. Bowtell G, Williams TL (1994) Anguilliform body dynamics—a continuum model for the interaction between muscle activation and body curvature. J Math Biol 32:83–91MATHCrossRefGoogle Scholar
  14. Bozkurttas M, Dong H, Mittal R, Madden P, Lauder GV (2006) Hydrodynamic performance of deformable fish fins and flapping foils. AIAA paper 2006-1392Google Scholar
  15. Bozkurttas M, Mittal R, Dong H, Lauder GV, Madden P (2009) Low-dimensional models and performance scaling of a highly deformable fish pectoral fin. J Fluid Mech 631:311–342MATHCrossRefGoogle Scholar
  16. Brücker C, Bleckmann H (2007) Vortex dynamics in the wake of a mechanical fish. Exp Fluids 43:799–810CrossRefGoogle Scholar
  17. Carling JC, Williams TL, Bowtell G (1998) Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional Navier–Stokes equations and Newton’s laws of motion. J Exp Biol 201:3143–3166Google Scholar
  18. Collin SP, Marshall NJ (2003) Sensory processing in aquatic environments. Springer Verlag, New YorkCrossRefGoogle Scholar
  19. Coombs SA, Van Netten SM (2006) The hydrodynamics and structural mechanics of the lateral line system. In: Shadwick RE, Lauder GV (eds) Fish biomechanics volume 23 in fish physiology. Academic Press, San Diego, pp 103–139Google Scholar
  20. Cooper LN, Sedano N, Johansson S, May B, Brown JD, Holliday CM, Kot BW, Fish FE (2008) Hydrodynamic performance of the minke whale (Balaenoptera acutorostrata) flipper. J Exp Biol 211:1859–1867CrossRefGoogle Scholar
  21. Dabiri JO (2005) On the estimation of swimming and flying forces from wake measurements. J Exp Biol 208:3519–3532CrossRefGoogle Scholar
  22. Dabiri JO (2009) Optimal vortex formation as a unifying principle in biological propulsion. Ann Rev Fluid Mech 41:17–33MathSciNetCrossRefGoogle Scholar
  23. Dabiri JO, Colin SP, Costello JH, Gharib M (2005) Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses. J Exp Biol 208:1257–1265CrossRefGoogle Scholar
  24. Dabiri JO, Colin SP, Costello JH (2006) Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake. J Exp Biol 209:2025–2033CrossRefGoogle Scholar
  25. Drucker EG, Lauder GV (1999) Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J Exp Biol 202:2393–2412Google Scholar
  26. Drucker EG, Lauder GV (2000) A hydrodynamic analysis of fish swimming speed: wake structure and locomotor force in slow and fast labriform swimmers. J Exp Biol 203:2379–2393Google Scholar
  27. Drucker EG, Lauder GV (2001) Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J Exp Biol 204:2943–2958Google Scholar
  28. Dubois AB, Ogilvy CS (1978) Forces on the tail surface of swimming fish: thrust, drag and acceleration in bluefish (Pomatomus saltatrix). J Exp Biol 77:225–241Google Scholar
  29. DuBois AB, Cavagna GA, Fox RS (1976) Locomotion of bluefish. J Exp Zool 195:223–235CrossRefGoogle Scholar
  30. Epps B, Techet A (2007) Impulse generated during unsteady maneuvering of swimming fish. Exp Fluids 43:691–700CrossRefGoogle Scholar
  31. Fish F (2004) Structure and mechanics of nonpiscine control surfaces. IEEE J Oceanic Eng 29:605–621CrossRefGoogle Scholar
  32. Fish F, Lauder GV (2006) Passive and active flow control by swimming fishes and mammals. Ann Rev Fluid Mech 38:193–224MathSciNetCrossRefGoogle Scholar
  33. Fish FE, Howle LE, Murray MM (2008) Hydrodynamic flow control in marine mammals. Integr Comp Biol 48:788–800CrossRefGoogle Scholar
  34. Flammang BE, Lauder GV (2008) Speed-dependent intrinsic caudal fin muscle recruitment during steady swimming in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:587–598CrossRefGoogle Scholar
  35. Flammang BE, Lauder GV (2009) Caudal fin shape modulation and control during acceleration, braking and backing maneuvers in bluegill sunfish, Lepomis macrochirus. J Exp Biol 212:277–286CrossRefGoogle Scholar
  36. Fontaine EI, Zabala F, Dickinson MH, Burdick JW (2009) Wing and body motion during flight initiation in Drosophila revealed by automated visual tracking. J Exp Biol 212:1307–1323CrossRefGoogle Scholar
  37. Geerlink PJ, Videler JJ (1987) The relation between structure and bending properties of teleost fin rays. Neth J Zool 37:59–80CrossRefGoogle Scholar
  38. Hain R, Kähler C, Michaelis D (2008) Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate. Exp Fluids 45:715–724CrossRefGoogle Scholar
  39. Hertel H (1966) Structure, form and movement. Reinhold, New York, NYGoogle Scholar
  40. Hoerner SF (1965) Fluid-dynamic drag. Hoerner Fluid Dynamics, Bakersfield, CaliforniaGoogle Scholar
  41. Horner AM, Jayne BC (2008) The effects of viscosity on the axial motor pattern and kinematics of the African lungfish (Protopterus annectens) during lateral undulatory swimming. J Exp Biol 211:1612–1622CrossRefGoogle Scholar
  42. Hunt von Herbing I, Keating K (2003) Temperature-induced changes in viscosity and its effects on swimming speed in larval haddock. In: Browman HI, Skiftesvik A (eds) The big fish bang. Institute of Marine Research, Bergen, pp 23–34Google Scholar
  43. Johnson TP, Cullum AJ, Bennett AF (1998) Partitioning the effects of temperature and kinematic viscosity on the c-start performance of adult fishes. J Exp Biol 201:2045–2051Google Scholar
  44. Kato N (2000) Control performance in the horizontal plane of a fish robot with mechanical pectoral fins. IEEE J Oceanic Eng 25:121–129CrossRefGoogle Scholar
  45. Lauder GV (1989) Caudal fin locomotion in ray-finned fishes: historical and functional analyses. Amer Zool 29:85–102Google Scholar
  46. Lauder GV (2000) Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns. Amer Zool 40:101–122CrossRefGoogle Scholar
  47. Lauder GV (2006) Locomotion. In: Evans DH, Claiborne JB (eds) The physiology of fishes, 3rd edn. CRC Press, Boca Raton, pp 3–46Google Scholar
  48. Lauder GV, Drucker EG (2002) Forces, fishes, and fluids: hydrodynamic mechanisms of aquatic locomotion. News Physiol Sci 17:235–240Google Scholar
  49. Lauder GV, Madden PGA (2006) Learning from fish: kinematics and experimental hydrodynamics for roboticists. Int J Automat Comput 4:325–335CrossRefGoogle Scholar
  50. Lauder GV, Madden PGA (2007) Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins. Exp Fluids 43:641–653CrossRefGoogle Scholar
  51. Lauder GV, Madden PGA (2008) Advances in comparative physiology from high-speed imaging of animal and fluid motion. Ann Rev Physiol 70:143–163CrossRefGoogle Scholar
  52. Lauder GV, Tytell ED (2006) Hydrodynamics of undulatory propulsion. In: Shadwick RE, Lauder GV (eds) Fish biomechanics volume 23 in fish physiology. Academic Press, San Diego, pp 425–468Google Scholar
  53. Lauder GV, Madden PGA, Mittal R, Dong H, Bozkurttas M (2006) Locomotion with flexible propulsors I: experimental analysis of pectoral fin swimming in sunfish. Bioinsp Biomimet 1:S25–S34CrossRefGoogle Scholar
  54. Lauder GV, Anderson EJ, Tangorra J, Madden PGA (2007) Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J Exp Biol 210:2767–2780CrossRefGoogle Scholar
  55. Lehmann F-O (2008) When wings touch wakes: understanding locomotor force control by wake wing interference in insect wings. J Exp Biol 211:224–233CrossRefGoogle Scholar
  56. Lehmann F-O (2009) Wing–wake interaction reduces power consumption in insect tandem wings. Exp Fluids 46:765–775Google Scholar
  57. Lehmann F-O, Sane SP, Dickinson M (2005) The aerodynamic effects of wing-wing interaction in flapping insect wings. J Exp Biol 208:3075–3092CrossRefGoogle Scholar
  58. Liao J (2004) Neuromuscular control of trout swimming in a vortex street: implications for energy economy during the Karman gait. J Exp Biol 207:3495–3506CrossRefGoogle Scholar
  59. Liao J, Beal DN, Lauder GV, Triantafyllou MS (2003a) Fish exploiting vortices decrease muscle activity. Science 302:1566–1569CrossRefGoogle Scholar
  60. Liao J, Beal DN, Lauder GV, Triantafyllou MS (2003b) The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street. J Exp Biol 206:1059–1073CrossRefGoogle Scholar
  61. Liu H, Wassersug RJ, Kawachi K (1997) The three-dimensional hydrodynamics of tadpole locomotion. J Exp Biol 200:2807–2819Google Scholar
  62. Long J (1998) Muscles, elastic energy, and the dynamics of body stiffness in swimming eels. Amer Zool 38:771–792Google Scholar
  63. Long JH, Nipper KS (1996) The importance of body stiffness in undulatory propulsion. Amer Zool 36:678–694Google Scholar
  64. Long JH Jr, Koob TJ, Irving K, Combie K, Engel V, Livingston N, Lammert A, Schumacher J (2006) Biomimetic evolutionary analysis: testing the adaptive value of vertebrate tail stiffness in autonomous swimming robots. J Exp Biol 209:4732–4746CrossRefGoogle Scholar
  65. Mittal R, Dong H, Bozkurttas M, Lauder GV, Madden PGA (2006) Locomotion with flexible propulsors II: computational modeling and analysis of pectoral fin swimming in sunfish. Bioinsp Biomimet 1:S35–S41CrossRefGoogle Scholar
  66. Müller UK, Smit J, Stamhuis EJ, Videler JJ (2001) How the body contributes to the wake in undulatory fish swimming: flow fields of a swimming eel (Anguilla anguilla). J Exp Biol 204:2751–2762Google Scholar
  67. Nauen JC, Lauder GV (2002a) Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae). J Exp Biol 205:1709–1724Google Scholar
  68. Nauen JC, Lauder GV (2002b) Quantification of the wake of rainbow trout (Oncorhynchus mykiss) using three-dimensional stereoscopic digital particle image velocimetry. J Exp Biol 205:3271–3279Google Scholar
  69. Peng J, Dabiri JO (2008a) An overview of a Lagrangian method for analysis of animal wake dynamics. J Exp Biol 211:280–287CrossRefGoogle Scholar
  70. Peng J, Dabiri JO (2008b) The ‘upstream wake’ of swimming and flying animals and its correlation with propulsive efficiency. J Exp Biol 211:2669–2677CrossRefGoogle Scholar
  71. Pereira F, Gharib M, Dabiri D, Modarress D (2000) Defocusing digital particle image velocimetry: a 3-component 3-dimensional DPIV measurement technique. Application to bubbly flows. Exp Fluids 29:S78–S84CrossRefGoogle Scholar
  72. Ramamurti R, Sandberg WC, Lohner R, Walker JA, Westneat M (2002) Fluid dynamics of flapping aquatic flight in the bird wrasse: three-dimensional unsteady computations with fin deformation. J Exp Biol 205:2997–3008Google Scholar
  73. Sakakibara J, Nakagawa M, Yoshida M (2004) Stereo-PIV study of flow around a maneuvering fish. Exp Fluids 36:282–293CrossRefGoogle Scholar
  74. Shadwick RE, Lauder GV (2006) Fish biomechanics. In: Hoar WS, Randall DJ, Farrell AP (eds) Fish physiology, vol 23. Academic Press, San DiegoGoogle Scholar
  75. Shen L, Zhang X, Yue D, Triantafyllou MS (2003) Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J Fluid Mech 484:197–221MATHCrossRefGoogle Scholar
  76. Shirgaonkar AA, Curet OM, Patankar NA, MacIver MA (2008) The hydrodynamics of ribbon-fin propulsion during impulsive motion. J Exp Biol 211:3490–3503CrossRefGoogle Scholar
  77. Shoele K, Zhu Q (2009) Fluid–structure interactions of skeleton-reinforced fins: performance analysis of a paired fin in lift-based propulsion. J Exp Biol 212:2679–2690CrossRefGoogle Scholar
  78. Standen EM (2008) Pelvic fin locomotor function in fishes: three-dimensional kinematics in rainbow trout (Oncorhynchus mykiss). J Exp Biol 211:2931–2942CrossRefGoogle Scholar
  79. Standen EM, Lauder GV (2005) Dorsal and anal fin function in bluegill sunfish (Lepomis macrochirus): three-dimensional kinematics during propulsion and maneuvering. J Exp Biol 205:2753–2763CrossRefGoogle Scholar
  80. Standen EM, Lauder GV (2007) Hydrodynamic function of dorsal and anal fins in brook trout (Salvelinus fontinalis). J Exp Biol 210:325–339CrossRefGoogle Scholar
  81. Svizher A, Cohen J (2006) Holographic particle image velocimetry measurements of hairpin vortices in a subcritical air channel flow. Phys Fluids 18:014105–014114CrossRefGoogle Scholar
  82. Taft N, Lauder GV, Madden PG (2008) Functional regionalization of the pectoral fin of the benthic longhorn sculpin during station holding and swimming. J Zool Lond 276:159–167CrossRefGoogle Scholar
  83. Tan G-K, Shen G-X, Huang S-Q, Su W–H, Ke Y (2007) Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement. Exp Fluids 43:811–821CrossRefGoogle Scholar
  84. Tangorra J, Anquetil P, Fofonoff T, Chen A, Del Zio M, Hunter I (2007) The application of conducting polymers to a biorobotic fin propulsor. Bioinsp Biomimet 2:S6–S17CrossRefGoogle Scholar
  85. Triantafyllou MS, Triantafyllou GS (1995) An efficient swimming machine. Sci Amer 272:64–70CrossRefGoogle Scholar
  86. Triantafyllou MS, Triantafyllou GS, Yue DKP (2000) Hydrodynamics of fishlike swimming. Ann Rev Fluid Mech 32:33–53MathSciNetCrossRefGoogle Scholar
  87. Triantafyllou M, Hover FS, Techet AH, Yue D (2005) Review of hydrodynamic scaling laws in aquatic locomotion and fish swimming. Transactions of the ASME 58:226–237Google Scholar
  88. Troolin D, Longmire E (2008) Volumetric 3-component velocity measurements of vortex rings from inclined exits. In: 14th international symposium on applications of laser techniques to fluid mechanics. Lisbon, Portugal, pp 1–11Google Scholar
  89. Tytell ED (2004) Kinematics and hydrodynamics of linear acceleration in eels, Anguilla rostrata. Proc Roy Soc Lond B 271:2535–2540CrossRefGoogle Scholar
  90. Tytell ED (2006) Median fin function in bluegill sunfish, Lepomis macrochirus: streamwise vortex structure during steady swimming. J Exp Biol 209:1516–1534CrossRefGoogle Scholar
  91. Tytell ED, Lauder GV (2004) The hydrodynamics of eel swimming. I. Wake structure. J Exp Biol 207:1825–1841CrossRefGoogle Scholar
  92. Tytell ED, Lauder GV (2008) Hydrodynamics of the escape response in bluegill sunfish, Lepomis macrochirus. J Exp Biol 211:3359–3369CrossRefGoogle Scholar
  93. Tytell ED, Standen EM, Lauder GV (2008) Escaping flatland: three-dimensional kinematics and hydrodynamics of median fins in fishes. J Exp Biol 211:187–195CrossRefGoogle Scholar
  94. Usherwood JR, Lehman F-O (2008) Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl. J Roy Soc Interface 5:1303–1307CrossRefGoogle Scholar
  95. Videler JJ (1993) Fish swimming. Chapman and Hall, New YorkGoogle Scholar
  96. Wakeling JM (2006) Fast-start mechanics. In: Shadwick RE, Lauder GV (eds) Fish biomechanics volume 23 in fish physiology. Academic Press, San Diego, pp 333–368Google Scholar
  97. Wang H, Ando N, Kanzaki R (2008) Active control of free flight manoeuvres in a hawkmoth, Agrius convolvuli. J Exp Biol 211:423–432CrossRefGoogle Scholar
  98. Webb PW (1975) Hydrodynamics and energetics of fish propulsion. Bull Fish Res Bd Can 190:1–159Google Scholar
  99. Webb PW (2004a) Maneuverability–general issues. IEEE J Oceanic Eng 29:547–555CrossRefGoogle Scholar
  100. Webb PW (2004b) Response latencies to postural disturbances in three species of teleostean fishes. J Exp Biol 207:955–961CrossRefGoogle Scholar
  101. Webb P (2006) Stability and maneuverability. In: Shadwick RE, Lauder GV (eds) Fish biomechanics volume 23 in fish physiology. Academic Press, San Diego, pp 281–332Google Scholar
  102. Webb JF, Fay RR, Popper A (2008) Fish bioacoustics. Springer Verlag, New YorkCrossRefGoogle Scholar
  103. Weber PW, Howle LE, Murray MM, Fish FE (2009) Lift and drag performance of odontocete cetacean flippers. J Exp Biol 212:2149–2158CrossRefGoogle Scholar
  104. Wieneke B (2008) Volume self-calibration for 3D particle image velocimetry. Exp Fluids 45:549–556CrossRefGoogle Scholar
  105. Wilga CD, Lauder GV (2004) Hydrodynamic function of the shark’s tail. Nature 430:850CrossRefGoogle Scholar
  106. Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas Sci Technol 8:1465–1479CrossRefGoogle Scholar
  107. Wolfgang MJ, Anderson JM, Grosenbaugh M, Yue D, Triantafyllou M (1999) Near-body flow dynamics in swimming fish. J Exp Biol 202:2303–2327Google Scholar
  108. Zhang W, Hain R, Kähler C (2008) Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil. Exp Fluids 45:725–743CrossRefGoogle Scholar
  109. Zhu Q, Shoele K (2008) Propulsion performance of a skeleton-strengthened fin. J Exp Biol 211:2087–2100CrossRefGoogle Scholar
  110. Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou GS (2002) Three-dimensional flow structures and vorticity control in fish-like swimming. J Fluid Mech 468:1–28MATHMathSciNetCrossRefGoogle Scholar

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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Museum of Comparative ZoologyHarvard UniversityCambridgeUSA

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