We consider observations and data from live fish and cetaceans, as well as data from engineered flapping foils and fishlike robots, and compare them against fluid mechanics based scaling laws. These laws have been derived on theoretical/numerical/experimental grounds to optimize the power needed for propulsion, or the energy needed for turning and fast starting. The rhythmic, oscillatory motion of fish requires an “impedance matching” between the dynamics of the actively controlled musculature and the fluid loads, to arrive at an optimal motion of the fish’s body. Hence, the degree to which data from live fish, optimized robots, and experimental apparatus are in accordance with, or deviate from these flow-based laws, allows one to assess limitations on performance due to control and sensing choices, and material and structural limitations. This review focuses primarily on numerical and experimental studies of steadily flapping foils for propulsion; three-dimensional effects in flapping foils; multiple foils and foils interacting with bodies; maneuvering and fast-starting foils; the interaction of foils with oncoming, externally-generated vorticity; the influence of Reynolds number on foil performance; scaling effects of flexing stiffness of foils; and scaling laws in fishlike swimming. This review article cites 117 references.
Issue Section:
Review Articles
Keywords:
foils,
reviews,
hydrodynamics,
external flows,
fluid oscillations,
flow instability,
vortices,
biomechanics
1.
Videler
, J.
, 1993, Fish Swimming
, Chapman and Hall
, London.2.
Fish
, F. E.
, and Hui
, C. A.
, 1991, “Dolphin Swimming—A Review
,” Mammal Rev.
, 21
, pp. 181
–195
.3.
Stamhuis
, E.
, and Videler
, J.
, 1995, “Quantitative Flow Analysis Around Aquatic Animals Using Laser Sheet Particle Image Velocimetry
,” J. Exp. Biol.
0022-0949, 198
, pp. 283
–294
.4.
Anderson
, J. M.
, 1996, “Vortex Control for Efficient Propulsion
,” Ph.D. thesis, Joint Program, MIT and WHOI, Cambridge, MA.5.
Mueller
, U.
, van den Heuvel
, B.
, Stamhuis
, E.
, and Videler
, J.
, 1997, “Fish Foot Prints: Morphology and Energetics of the Wake Behind a Continuously Swimming Mullet (Chelon Labrosus Risso)
,” J. Exp. Biol.
0022-0949, 200
, pp. 2893
–2806
.6.
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.
0022-0949, 202
, pp. 2303
–2327
.7.
Drucker
, E. G.
, and Lauder
, G. V.
, 1999, “Locomotor Forces on a Swimming Fish: Three Dimensional Vortex Wake Dynamics Quantified Using DPIV
,” J. Exp. Biol.
0022-0949, 202
, pp. 2393
–2412
.8.
Drucker
, E. G.
, and Lauder
, G. V.
, 2001, “Locomotor Function of the Dorsal Fin in Teleost Fishes: Experimental Analysis of the Wake Forces in Sunfish
,” J. Exp. Biol.
0022-0949, 204
, pp. 2943
–2958
.9.
Lauder
, G. V.
, 2000, “Function of the Caudal Fin During Locomotion in Fishes: Kinematics, Flow Visualization and Evolutionary Patterns
,” Am. Zool.
0003-1569, 40
, pp. 101
–122
.10.
Lighthill
, J.
, 1975, Mathematical Biofluiddynamics
, SIAM
, Philadelphia.11.
Wu
, T.
, 1961, “Swimming of a Waving Plate
,” J. Fluid Mech.
0022-1120, 10
, pp. 321
–344
.12.
Wu
, T.
, 1971, “Hydromechanics of Swimming Propulsion
,” J. Fluid Mech.
0022-1120, 46
, pp. 337
–355
.13.
Liu
, H.
, and Kawachi
, K.
, 1998, “A Numerical Study of Insect Flight
,” J. Comput. Phys.
0021-9991, 146
, pp. 124
–156
.14.
Cheng
, H. K.
, and Murillo
, L. E.
, 1984, “Lunate-Tail Swimming Propulsion as a Problem of Curved Lifting Line in Unsteady Flow, Part 1: Asymptotic Theory
,” J. Fluid Mech.
0022-1120, 143
, pp. 327
–350
.15.
Karpouzian
, G.
, Spedding
, G.
, and Cheng
, H. K.
, 1990, “Lunate-Tail Swimming Propulsion, Part 2: Performance Analysis
,” J. Fluid Mech.
0022-1120, 210
, pp. 329
–351
.16.
McCune
, J. E.
, and Tavares
, T. S.
, 1993, “Perspective: Unsteady Wing Theory—The Kármán/Sears Legacy
,” ASME J. Fluids Eng.
0098-2202, 115
(4
), pp. 548
–560
.17.
Streitlien
, K.
, and Triantafyllou
, M. S.
, 1995, “Force and Moment on a Joukowski Profile in the Presence of Point Vortices
,” AIAA J.
0001-1452, 33
(4
), pp. 603
–610
.18.
Streitlien
, K.
, Triantafyllou
, G. S.
, and Triantafyllou
, M. S
, 1996, “Efficient Foil Propulsion Through Vortex Control
,” AIAA J.
0001-1452, 34
(11
), pp. 2315
–2319
.19.
Ramamurti
, R.
, and Sandberg
, W. C.
, 2001, “Simulation of Flow About Flapping Airfoils Using a Finite Element Incompressible Flow Solver
,” AIAA J.
0001-1452, 39
, pp. 253
–260
.20.
Ramamurti
, R.
, and Sandberg
, W. C.
, 2002, “A Three-dimensional Computational Study of the Aerodynamic Mechanisms of Insect Flight
,” J. Exp. Biol.
0022-0949, 205
, pp. 1507
–1518
.21.
Guglielmini
, L.
, and Blondeaux
, P.
, 2004, “Propulsive Efficiency of Oscillating Foils
,” European Journal of Mechanics/B Fluids
(in the press).22.
Guglielmini
, L.
, Blondeaux
, P.
, and Vittori
, G.
, 2004, “A Simple Model of Propulsive Oscillating Foils
,” Ocean Eng.
0029-8018 31
(7
), pp. 883
–899
.23.
Lewin
, G. C.
, and Haj-Hariri
, H.
, 2003, “Modeling Thrust Generation of a Two-Dimensional Heaving Airfoil in a Viscous Flow
,” J. Fluid Mech.
0022-1120, 492
, pp. 339
–362
.24.
Von Ellenrieder
, K. D.
, Parker
, K.
, and Soria
, J.
, 2003, “Flow Structures Behind a Heaving and Pitching Finite-Span Wing
,” J. Fluid Mech.
0022-1120, 490
, pp. 129
–138
.25.
Scherer
, J. O.
, 1968, “Experimental and Theoretical Investigation of Large Amplitude Oscillating Foil Propulsion Systems
,” U.S. Army Engineering Research and Development Laboratories
.26.
DeLaurier
, J. D.
, and Harris
, J. M.
, 1982, “Experimental Study of Oscillating Wing Propulsion
,” J. Aircr.
0021-8669, 19
(5
), pp. 368
–373
.27.
Lai
, P. S. K.
, Bose
, N.
, and McGregor
, R. C.
, 1993, “Wave Propulsion From a Flexible-Armed, Rigid-Foil Propulsor
,” Mar. Technol. Soc. J.
0025-3324, 30
(1
), pp. 28
–36
.28.
Anderson
, J. M.
, Streitlien
, K.
, Barrett
, D. S.
, and Triantafyllou
, M. S.
, 1998, “Oscillating Foils of High Propulsive Efficiency
,” J. Fluid Mech.
0022-1120, 360
, pp. 41
–72
.29.
Read
, D. A.
, 2001, “Oscillating Foils for Propulsion and Maneuvering of Ships and Underwater Vehicles
,” SM thesis, MIT, Cambridge, MA.30.
Ohashi
, H.
, and Ishikawa
, N.
, 1972, “Visualization Study of Flow Near the Trailing Edge of an Oscillating Airfoil
,” Bull. JSME
0021-3764, 15
(85
), pp. 840
–847
.31.
Oshima
, Y.
, and Oshima
, K.
, 1980, “Vortical Flow Behind an Oscillating Foil
,” in Proc. 15th Int. Congress
, Int. Union Theor. Applied Mech.
, North Holland, Amsterdam, pp. 357
–368
.32.
Oshima
, Y.
, and Natsume
, A.
, 1980, “Flow Field Around an Oscillating Foil
,” in Flow Visualization II, Proc. 2nd Int. Symp. on Flow Visualization
, Bochum, Germany, W.
Merzkirch
(ed.), Hemisphere Publishing
, New York, pp. 295
–299
.33.
Koochesfahani
, M.
, 1989, “Vortical Patterns in the Wake of an Oscillating Foil
,” AIAA J.
0001-1452, 27
, pp. 1200
–1205
.34.
Freymuth
, P.
, 1988, “Propulsive Vortical Signature of Plunging and Pitching Airfoils
,” AIAA J.
0001-1452, 26
, pp. 881
–883
.35.
Freymuth
, P.
, 1989, “Visualizing the Connectivity of Vortex Systems for Pitching Wings
,” ASME J. Fluids Eng.
0098-2202, 111
, pp. 217
–220
.36.
Freymuth
, P.
, 1990, “Thrust Generation by an Airfoil in Hover Modes
,” Exp. Fluids
0723-4864, 9
, pp. 17
–24
.37.
Freymuth
, P.
, 1991, “Physical Vortex Visualization as a Reference for Computer Simulation
,” in Vortex Methods and Vortex Motion
, K. E.
Gustafson
and J. A.
Sethian
(eds.), SIAM
, Philadelphia, pp. 65
–94
.38.
Jones
, K. D.
, Dohring
, C. M.
, and Platzer
, M. F.
, 1998, “Experimental and Computational Investigation of the Knoller-Betz Effect
,” AIAA J.
0001-1452, 36
(7
), pp. 1240
–1246
.39.
Triantafyllou
, M. S.
, Triantafyllou
, G. S.
, and Gopalkrishnan
, R.
, 1991, “Wake Mechanics for Thrust Generation in Oscillating Foils
,” Phys. Fluids
0031-9171, 3
(12
), pp. 2835
–2837
.40.
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.
0889-9746, 7
, pp. 205
–224
.41.
Triantafyllou
, M. S.
, Triantafyllou
, G. S.
, and Yue
, D. K. P.
, 2000, “Hydrodynamics of Fish Swimming
,” Annu. Rev. Fluid Mech.
0066-4189, 32
, pp. 33
–53
.42.
Fish
, F. E.
, 1997, “Biological Designs for Enhanced Maneuverability: Analysis of Marine Mammal Performance
,” 10th Int. Symp. Unmanned Untethered Submersible Technology
, Special Session on Bio-Engineering Research Related to AUV
, Durham, NH, pp. 109
–117
.43.
Rohr
, J. J.
, and Fish
, F. E.
, 2004, “Strouhal Numbers and optimization by Odontocete Cetaceans
,” J. Exp. Biol.
0022-0949, 207
, pp. 1633
–1642
.44.
Nauen
, J. C.
, and Lauder
, G. V.
, 2002, “Hydrodynamics of Caudal Fin Locomotion by Chub Mackerel Scomber Japonicus (Scombridae)
,” J. Exp. Biol.
0022-0949, 205
, pp. 1709
–1724
.45.
Motani
, R.
, 2002, “Scaling Effects in Caudal Fin Propulsion and the Speed of Ichthyosaurs
,” Nature (London)
0028-0836, 415
, pp. 309
–312
.46.
Taylor
, G. K.
, Nudds
, R. L.
, and Thomas
, A. L. R.
, 2003, “Flying and Swimming Animals Cruise at a Strouhal Number Tuned for High Power Efficiency
,” Nature (London)
0028-0836, 425
, pp. 707
–711
.47.
Reynolds
, W. C.
, and Carr
, L. W.
, 1985, “Review of Unsteady, Driven, Separated Flows
,” AIAA Paper No. 85-0527.48.
McCroskey
, W. J.
, 1982, “Unsteady Airfoils
,” Annu. Rev. Fluid Mech.
0066-4189, 14
, pp. 285
–311
.49.
Maxworthy
, T.
, 1981, “The Fluid Dynamics of Insect Flight
,” Annu. Rev. Fluid Mech.
0066-4189, 13
, pp. 329
–350
.50.
Ellington
, C. P.
, 1984, “The Aerodynamics of Hovering Insect Flight
,” Philos. Trans. R. Soc. London, Ser. B
0962-8436, 305
, pp. 17
–181
.51.
Ellington
, C. P.
, Vanderberg
, C.
, Wilmott
, A.
, and Thomas
, A.
, 1996, “Leading Edge Vortices in Insect Flight
,” Nature (London)
0028-0836, 384
, pp. 626
–630
.52.
Dickinson
, M. H.
, 1994, “The Effect of Wing Rotation on Unsteady Aerodynamic Performance at Low Reynolds Numbers
,” J. Exp. Biol.
0022-0949, 192
, pp. 179
–206
.53.
Dickinson
, M. H.
, Lehmann
, F. O.
, and Sane
, S. P.
, 1999, “Wing Rotation and the Aerodynamic Basis Insect Flight
,” Science
0036-8075, 284
, pp. 1954
–1960
.54.
Walker
, J. A.
, 2003, “Rotational Lift: Something Different or More of the Same?
,” J. Exp. Biol.
0022-0949, 205
, pp. 3783
–3792
.55.
Maresca
, C.
, Favier
, D.
, and Rebont
, J.
, 1979, “Experiments on an Airfoil at High Angle of Incidence in Longitudinal Oscillations
,” J. Fluid Mech.
0022-1120, 92
, pp. 671
–690
.56.
Ohmi
, K.
, Coutanceau
, M.
, Loc
, T. P.
, and Dulieu
, A.
, 1990, “Vortex Formation Around an Oscillating and Translating Airfoil at Large Incidences
,” J. Fluid Mech.
0022-1120, 211
, pp. 37
–60
.57.
Ohmi
, K.
, Coutanceau
, M.
, Daube
, O.
, and Loc
, T. P.
, 1991, “Further Experiments on Vortex Formation Around an Oscillating and Translating Airfoil at Large Incidences
,” J. Fluid Mech.
0022-1120, 225
, pp. 607
–630
.58.
Hart
, D. P.
, Acosta
, A.
, and Leonard
, A.
, 1992, “Observations of Cavitation and Wake Structure of Unsteady Tip Vortex Flows
,” Proc. Int. STG Symp. Propulsors and Cavitation
, Hamburg, Germany, pp. 121
–127
.59.
Ahlborn
, B.
, Harper
, D.
, Blake
, R.
, Ahlborn
, D.
, and Cam
, M.
, 1991, “Fish Without Footprints
,” J. Theor. Biol.
0022-5193, 148
, pp. 521
–533
.60.
Lai
, J. C. S.
, and Platzer
, M. F.
, 1998, “The Jet Characteristics of a Plunging Airfoil
,” Paper AIAA-98-0101, 36th AIAA Aerospace Sciences Meeting
, Reno, NV.61.
Guglielmini
, L.
, 2004, “Modeling of Thrust Generating Foils
,” Ph.D. thesis, University of Genova, Italy.62.
Strouhal
, V.
, 1878, “Uber Eine Besondere Art der Tonerregung
,” Ann. Phys. Chem.
0003-3804, 5
(10
), pp. 216
–251
.63.
Zhu
, Q.
, Wolfgang
, M. J.
, Yue
, D. K. P.
, and Triantafyllou
, M. S.
, 2002, “Three-Dimensional Flow Structures and Vorticity Control in Fish-Like Swimming
,” J. Fluid Mech.
0022-1120, 468
, pp. 1
–28
.64.
Hover
, F. S.
, Haugsdal
, O.
, and Triantafyllou
, M. S.
, 2003, “Control of Angle of Attack Profiles in Flapping Foil Propulsion
,” J. Fluids Struct.
0889-9746, 19
, pp. 37
–47
.65.
Gursul
, I.
, Lin
, H.
, and Ho
, C. M.
, 1991, “Vorticity Dynamics of 2D and 3D Wings in Unsteady Free Stream
,” AIAA Paper 91-0010, Reno, NV.66.
Cheng
, J.-Y.
, Zhuang
, L.-X.
, and Tong
, B.-G.
, 1991, “Analysis of Swimming Three-Dimensional Waving Plates
,” J. Fluid Mech.
0022-1120, 232
, pp. 341
–355
.67.
Martin
, C. B.
, 2001, “Propulsive Performance of a Rolling and Pitching Wing
,” MS thesis, Massachusetts Institute of Technology.68.
Martin
, C. B.
, Hover
, F. S.
, and Triantafyllou
, M. S.
, 2001, “Propulsive Performance of a Rolling and Pitching Wing
,” Proc. UUST
, Durham, NH.69.
Kato
, N.
, 1998, “Locomotion by Mechanical Pectoral Fins
,” J. Mar. Sci. Technol.
, 3
, pp. 113
–121
.70.
Kato
, N.
, and Inaba
, T.
, 1997, “Hovering Performance of Fish Robot With Apparatus o Pectoral Fin Motion
,” 10th Int. Symp. on Unmanned Untethered Submersible Technology
, University of New Hampshire.71.
Kato
, N.
, 2000, “Control Performance of Fish Robot With Mechanical Pectoral Fins in Horizontal Plane
,” IEEE J. Ocean. Eng.
0364-9059, 25
(1
), pp. 121
–129
.72.
Walker
, J. A.
, and Westneat
, M. W.
, 2000, “Mechanical Performance of Aquatic Rowing and Flying
,” Proc. R. Soc. London, Ser. B
0962-8452, 267
, pp. 1875
–1881
.73.
Culik
, B. M.
, Wilson
, R. P.
, and Bannasch
, R.
, 1994, “Underwater Swimming at Low Energetic Cost by Pygoscelid Penguins
,” J. Exp. Biol.
0022-0949, 197
, pp. 65
–78
.74.
Bandyopadhyay
, P.
, Donnelly
, M. J.
, Nedderman
, W. H.
, and Castano
, J. M.
, 1997b, “A Dual Flapping Foil Maneuvering Device for Low-Speed Rigid Bodies
,” Third Int. Symp. Performance Enhancement for Marine Vehicles
, Newport, RI.75.
Czarnowski
, J. T.
, 1997, “Exploring the Possibility of Placing Traditional Marine Vessels Under Oscillating Foil Propulsion
,” SM thesis, Dept. Ocean Eng., Massachusetts Institute of Technology, Cambridge, MA.76.
Tsuhara
, M.
, and Kimura
, T.
, 1987, “An Application of the Weis-Fogh Mechanism to Ship Propulsion
,” ASME J. Fluids Eng.
0098-2202, 109
, pp. 107
–13
.77.
Weis-Fogh
, T.
, 1973, “Quick Estimates of Flight Fitness in Hovering Animals Including Novel Mechanisms for Lift Production
,” J. Exp. Biol.
0022-0949, 59
, pp. 169
–230
.78.
Bandyopadhyay
, P. R.
, Castano
, J. M.
, Donnelly
, M. J.
, Nedderman
, W. H.
, and Donnelly
, M. J.
, 2000, “Experimental Simulation of Fish-Inspired Unsteady Vortex Dynamics on a Rigid Cylinder
,” ASME J. Fluids Eng.
0098-2202, 122
, pp. 219
–238
.79.
Webb
, P. W.
, 1997, “Designs for Stability and Maneuverability in Aquatic Vertebrates: What Can We Learn
,” Proc. 10th Int. Symp. Unmanned Untethered Submersible Technology
, Durham, NH, pp. 86
–108
.80.
Webb
, P. W.
, 2000, “Maneuverability Versus Stability: Do Fish Perform Well in Both?
,” Proc. 1st Int. Symp. On Aqua Bio-Mechanisms (ISBMEC 2000)
, Honolulu, Hawaii.81.
Harper
, D. G.
, and Blake
, R. W.
, 1991, “Prey Capture and the Fast-Start Performance of Northern Pike (Esox Lucius)
,” J. Exp. Biol.
0022-0949, 155
, pp. 175
–192
.82.
Frith
, H. R.
, and Blake
, R. W.
, 1995, “Mechanical Power Output and Hydrodynamical Efficiency of Northern Pike (Esox Lucius) Fast-Starts
,” J. Exp. Biol.
0022-0949, 198
, pp. 1863
–1873
.83.
Triantafyllou
, M. S.
, Techet
, A. H.
, Zhu
, Q.
, Beal
, D. N.
, Hover
, F. S.
, and Yue
, D. K. P.
, 2003, “Vorticity Control in Fish-Like Propulsion and Maneuvering
,” Integr. Comp. Biol.
1540-7063, 42
(5
), pp. 1026
–1031
.84.
Read
, D. A.
, Hover
, F. S.
, and Triantafyllou
, M. S.
, 2003, “Forces on Oscillating Foils for Propulsion and Maneuvering
,” J. Fluids Struct.
0889-9746, 17
, pp. 163
–183
.85.
Kato
, N.
, 1999, “Hydrodynamic Characteristics of Mechanical Pectoral Fin
,” ASME J. Fluids Eng.
0098-2202, 121
, pp. 605
–613
.86.
Kato
, N.
, 1999, “Three-Motor-Driven Mechanical Pectoral Fin
,” Proc. 11th Int. Symp. Unmanned Untethered Submersible Technology
, Durham, NH, pp. 467
–476
.87.
Hertel
, H.
, 1966, Structure Form and Movement
, Reinhold
, New York.88.
Flores
, M. D.
, 2003, “Flapping Motion of a Three-Dimensional Foil for Propulsion and Maneuvering of Underwater Vehicles
,” S.M. thesis, Dept. Ocean Engineering, MIT, Cambridge, MA.89.
Triantafyllou
, M. S.
, Zhu
, Q.
, Techet
, A. H.
, and Yue
, D. K. P.
, 2003, “Scaling Law in Rapidly-Maneuvering Fish
,” 56th Annual Meeting, Division of Fluid Dynamics, American Physical Society
, East Rutherford, NJ.90.
Daigh
, S.
, and Techet
, A. H.
, 2003, “Experimental Visualization of Rapidly Maneuvering Fish
,” 56th Annual Meeting, Division of Fluid Dynamics
, E. Rutherford, NJ.91.
Gharib
, M.
, Rambod
, E.
, Dabiri
, D.
, and Hammache
, M.
, 1994, “Pulsatile Heart Flow: A Universal Time Scale
,” Proc. 2nd Int. Conf. Experimental Fluid Mech.
, M.
Onorato
, (ed.) Torino, Italy.92.
Gharib
, M.
, Rambod
, E.
, and Shariff
, K.
, 1998, “A Universal Time Scale for Vortex Ring Formation
,” J. Fluid Mech.
0022-1120, 360
, pp. 121
–140
.93.
Rosenfeld
, M.
, Gharib
, M.
, and Rambod
, E.
, 1998, “Circular and Formation Number of Laminar Vortex Rings
,” J. Fluid Mech.
0022-1120, 376
, pp. 297
–318
.94.
Isshiki
, H.
, and Murakami
, M.
, 1984, “A Theory of Wave Devouring Propulsion
,” J. Soc. Naval Arch. Jpn
, 156
, pp. 102
–114
.95.
Sparenberg
, J. A.
, and Wiersma
, A. K.
, 1975, “On the Efficiency Increasing Interaction of Thrust Producing Lifting Surfaces
,” in Swimming and Flying in Nature
, Plenum Press, T.
Wu
, C. J.
Brokaw
, and C.
Brennen
, (eds.) Vol. 2
, pp. 891
–917
.96.
Koochesfahani
, M.
, and Dimotakis
, P.
, 1998, “A Cancellation Experiment in a Forced Turbulent Shear Layer
,” AIAA Technical Paper 88-3713-CP.97.
Gopalkrishnan
, R.
, Triantafyllou
, M. S.
, Triantafyllou
, G. S.
, and Barrett
, D. S.
, 1994, “Active Vorticity Control in a Shear Flow Using a Flapping Foil
,” J. Fluid Mech.
0022-1120, 274
, pp. 1
–21
.98.
Beal
, D. N.
, Hover
, F. S.
, and Triantafyllou
, M. S.
, 2001, “The Effect on Thrust and Efficiency of an Upstream Karman Wake on an Oscillating Foil
,” Proc. UUST
, Durham, NH.99.
Liao
, J. C.
, Beal
, D. N.
, Lauder
, G. V.
, and Triantafyllou
, M. S.
, 2003, “The Karman Gait: Novel Body Kinematics of Rainbow Trout Swimming in a Vortex Street
,” J. Exp. Biol.
0022-0949, 206
, pp. 1059
–1073
.100.
Liao
, J. C.
, Beal
, D. N.
, Lauder
, G. V.
, Triantafyllou
, M. S.
, 2003, “Fish Exploiting Vortices Use Less Muscle
,” Science
0036-8075, 302
, pp. 1566
–1569
.101.
Hoerner
, S. F.
, 1965, Fluid Dynamic Drag
(published by the author).102.
Bose
, N.
, 1995, “Performance of Chordwise Flexible Oscillating Propulsors Using A Time-Domain Panel Method
,” Int. Shipbuild. Progr.
, 42
(432
), pp. 281
–294
.103.
Castelo
, M. E.
, 2002, “Propulsive Performance of Flexible-Chord Foils
,” B.S. thesis, Department of Ocean Engineering, MIT.104.
Prempraneerach
, P.
, Hover
, F. S.
, and Triantafyllou
, M. S.
, 2003, “The Effect of Chordwise Flexibility on the Thrust and Efficiency of a of Flapping Foil
” Proceedings Unmanned, Untethered Submersible Technology
, Durham, NH, Aug.105.
Liu
, P.
, and Bose
, N.
, 1997, “Propulsive Performance From Oscillating Propulsors With Spanwise Flexibility
,” Proc. R. Soc. London, Ser. A
1364-5021, 453
, pp. 1763
–1770
.106.
Katz
, J.
, and Weihs
, D.
, 1979, “Large Amplitude Unsteady Motion of a Flexible Slender Propulsor
,” J. Fluid Mech.
0022-1120, 90
, pp. 713
–723
.107.
McCutchen
, C. W.
, 1970, “The Trout Tail Fin: A Self-Cambering Hydrofoil
,” J. Biomech.
0021-9290, 3
, 271
–281
.108.
Combs
, S. A.
, and Daniel
, T. L.
, 2001, “Shape, Flapping and Flexion: Wing and Fin Design for Forward Flight
,” J. Exp. Biol.
0022-0949, 204
, pp. 2073
–2085
.109.
Alexander
, R. McN.
, 2003, Principles of Animal Locomotion
, Princeton University Press
, Princeton, N. J.110.
Blake
, R. W.
, 1983, Fish Locomotion
, Cambridge University Press
, London.111.
Clark
, B. D.
, and Bemis
, W.
, 1979, “Kinematics of Swimming of Penguins at the Detroit Zoo
,” J. Zool.
0022-5460, 188
, pp. 411
–428
.112.
Triantafyllou
, M. S.
, and Triantafyllou
, G. S.
, 1995, “An Efficient Swimming Machine
,” Sci. Am.
0036-8733, 272
(3
), pp. 64
–70
.113.
Kumph
, J.
, and Triantafyllou
, M. S.
, 1998, “A Fast-Starting and Maneuvering Vehicle, the Robopike
,” Proc. Int. Symp. Seawater Drag Reduction
, Newport, RI.114.
Techet
, A. H.
, 2001, “Experimental Visualization of the Near-Boundary Hydrodynamics About Fish-Like Swimming Bodies
,” Ph.D. thesis, MIT, Cambridge, MA.115.
Techet
, A. H.
, Anderson
, E. J.
, McGillis
, W. R.
, Grosenbaugh
, M. A.
, and Triantafyllou
, M. S.
, 1999, “Flow Visualization of Swimming Robotic Fish in the Near Boundary Region
,” Third Int. Workshop on Particle Image Velocimetry
, Santa Barbara, CA, September 16
–18
, 1999.116.
Taneda
, S.
, 1977, “Visual Study of Unsteady Separated Flows Around Bodies
,” Prog. Aerosp. Sci.
0376-0421, 17
, pp. 287
–348
.117.
Shen
, L.
, Zhang
, X.
, Yue
, D. K. P.
, and Triantafyllou
, M. S.
, 2003, “Turbulent Flow Over a Flexible Wall Undergoing a Streamwise Traveling Wavy Motion
,” J. Fluid Mech.
0022-1120, 484
, pp. 197
–221
.Copyright © 2005
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