The myth and reality of Gray's paradox: implication of dolphin drag reduction for technology

The inconsistency for the calculated high drag on an actively swimming dolphin and underestimated muscle power available resulted in what has been termed Gray's paradox. Although Gray's paradox was flawed, it has been the inspiration for a variety of drag reduction mechanisms. This review examines the present state of knowledge of drag reduction specific to dolphins. Streamlining and special behaviors provide the greatest drag reduction for dolphins. Mechanisms to control flow by maintaining a completely laminar boundary layer over the body have not been demonstrated for dolphins.

[1]  John T. Beneski,et al.  Examination of the three‐dimensional geometry of cetacean flukes using computed tomography scans: Hydrodynamic implications , 2007, Anatomical record.

[2]  Kwing-So Choi,et al.  Experiments on the effects of aging on compliant coating drag reduction , 2005 .

[3]  D. A. Pabst,et al.  Structural fiber reinforcement of keel blubber in harbor porpoise (Phocoena phocoena) , 2004, Journal of morphology.

[4]  D. Weihs The hydrodynamics of dolphin drafting , 2004, Journal of biology.

[5]  Terrie M. Williams,et al.  Swimming by sea otters: adaptations for low energetic cost locomotion , 1989, Journal of Comparative Physiology A.

[6]  Yoshimichi Hagiwara,et al.  Turbulence modification by compliant skin and strata-corneas desquamation of a swimming dolphin , 2004 .

[7]  Vadim V Pavlov,et al.  Wing design and morphology of the harbor porpoise dorsal fin , 2003, Journal of morphology.

[8]  V. Babenko Hydrobionic Principles of Drag Reduction , 2003 .

[9]  Christopher Davies,et al.  Hydrodynamics and compliant walls: does the dolphin have a secret? , 2000 .

[10]  J Calambokidis,et al.  Sink or swim: strategies for cost-efficient diving by marine mammals. , 2000, Science.

[11]  T. Williams,et al.  The diving physiology of bottlenose dolphins (Tursiops truncatus). II. Biomechanics and changes in buoyancy at depth. , 1999, The Journal of experimental biology.

[12]  M. J. Wolfgang,et al.  Drag reduction in fish-like locomotion , 1999, Journal of Fluid Mechanics.

[13]  Frank E. Fish,et al.  Review of Dolphin Hydrodynamics and Swimming Performance , 1999 .

[14]  F. Fish,et al.  Comparative kinematics and hydrodynamics of odontocete cetaceans: morphological and ecological correlates with swimming performance. , 1998, The Journal of experimental biology.

[15]  Jennifer C. Nauen,et al.  Experimental approaches towards interpreting dolphin-stimulated bioluminescence. , 1998, The Journal of experimental biology.

[16]  S. Vogel,et al.  Life in Moving Fluids , 2020 .

[17]  R. Marsh,et al.  The effects of length trajectory on the mechanical power output of mouse skeletal muscles. , 1997, The Journal of experimental biology.

[18]  K. Kawachi,et al.  The three-dimensional hydrodynamics of tadpole locomotion. , 1997, The Journal of experimental biology.

[19]  Mehmet Atlar,et al.  Turbulent drag reduction using compliant surfaces , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  David S. Barrett,et al.  A new paradigm of propulsion and maneuvering for marine vehicles. Discussion. Authors' closure , 1996 .

[21]  William M. Carey,et al.  Blubber and compliant coatings for drag reduction in water II. Matched shear impedance for compliant layer drag reduction , 1995 .

[22]  W. Wayt Gibbs Turning Back the Clock , 1995 .

[23]  M. Triantafyllou,et al.  An Efficient Swimming Machine , 1995 .

[24]  Romanenko Ev Swimming of dolphins: experiments and modelling. , 1995 .

[25]  Anthony D. Lucey,et al.  Optimization of viscoelastic compliant walls for transition delay , 1994 .

[26]  F. Fish Influence of Hydrodynamic Design and Propulsive Mode on Mammalian Swimming Energetics , 1994 .

[27]  C. Gibbs,et al.  Energetics of fast‐ and slow‐twitch muscles of the mouse. , 1993, The Journal of physiology.

[28]  S.H. Ridgway,et al.  Features of dolphin skin with potential hydrodynamic importance , 1993, IEEE Engineering in Medicine and Biology Magazine.

[29]  T. Williams,et al.  Travel at low energetic cost by swimming and wave-riding bottlenose dolphins , 1992, Nature.

[30]  F. Fish,et al.  Dolphin swimming–a review , 1991 .

[31]  Mohamed Gad-el-Hak,et al.  Separation control - Review , 1991 .

[32]  P. A. Shoemaker,et al.  CUTANEOUS RIDGES IN ODONTOCETES , 1991 .

[33]  D. M. Bushnell,et al.  DRAG REDUCTION IN NATURE , 1991 .

[34]  Neil Bose,et al.  Measurements of the bodies and flukes of several cetacean species , 1990, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[35]  Paul W. Webb,et al.  Locomotion in the Biology of Large Aquatic Vertebrates , 1990 .

[36]  C. A. Hui,et al.  Surfacing Behavior and Ventilation in Free-Ranging Dolphins , 1989 .

[37]  Peter W. Carpenter,et al.  Status of Transition Delay Using Compliant Walls , 1989 .

[38]  Clifford Goodman,et al.  American Society of Mechanical Engineers , 1988 .

[39]  C. P. van Dam,et al.  Efficiency characteristics of crescent-shaped wings and caudal fins , 1987, Nature.

[40]  C. P. van Dam,et al.  Efficiency characteristics of crescent-shaped wings and caudal fins , 1987 .

[41]  Mohamed Gad-el-Hak,et al.  Compliant coatings research: A guide to the experimentalist , 1987 .

[42]  Roland R. Roy,et al.  AXIAL MUSCULATURE IN THE DOLPHIN (TURSIOPS TRUNCATUS): SOME ARCHITECTURAL AND HISTOCHEMICAL CHARACTERISTICS , 1985 .

[43]  W. M. Madigosky,et al.  Acoustic surface wave measurements on live bottlenose dolphins , 1984 .

[44]  J. Ashenberg,et al.  Minimum induced drag of wings with curved planform , 1984 .

[45]  B. D. Hicks,et al.  Epidermal cell proliferation in the bottlenose dolphin (Tursiops truncatus) , 1983 .

[46]  Atsushi Suzuki,et al.  HISTOCHEMICAL PROPERTIES OF MYOFIBERS IN LONGISSIMUS MUSCLE OF COMMON DOLPHINS (DELPHINUS DELPHIS) , 1983 .

[47]  E. Romanenko Distribution of dynamic pressure over the body of an actively swimming dolphin , 1981 .

[48]  Thomas L. Daniel,et al.  FISH MUCUS: IN SITU MEASUREMENTS OF POLYMER DRAG REDUCTION , 1981 .

[49]  D. Au,et al.  At high speeds dolphins save energy by leaping , 1980, Nature.

[50]  S H Ridgway,et al.  Dolphin lung collapse and intramuscular circulation during free diving: evidence from nitrogen washout. , 1979, Science.

[51]  P. Ponganis,et al.  Muscle metabolic profiles and fiber-type composition in some marine mammals. , 1978, Comparative biochemistry and physiology. B, Comparative biochemistry.

[52]  R. McNeill Alexander,et al.  Mechanics and energetics of animal locomotion , 1977 .

[53]  G. Whittow,et al.  Body temperature and heat exchange in the Hawaiian spinner dolphin, Stenella longirostris. , 1976, Comparative biochemistry and physiology. A, Comparative physiology.

[54]  J L Hess,et al.  On the Problem of Shaping an Axisymmetric Body to Obtain Low Drag at Large Reynolds Numbers , 1975 .

[55]  P. Webb Hydrodynamics and Energetics of Fish Propulsion , 1975 .

[56]  J. W. Hoyt,et al.  Hydrodynamic Drag Reduction Due to Fish Slimes , 1975 .

[57]  Mats Amundin,et al.  Functional analysis of the surfacing behaviour in the harbour porpoise, Phocoena phocoena (L.) , 1973 .

[58]  F. G. Wood,et al.  Marine Mammals and Man;: The Navy's porpoises and sea lions , 1973 .

[59]  G. Whittow,et al.  Body heat dissipation and conservation in two species of dolphins. , 1972, Comparative biochemistry and physiology. A, Comparative physiology.

[60]  D. Mottram,et al.  Studies on the distribution of acetylcholinesterase (ACHE)-positive and -negative autonomic axons to smooth muscle in the normal and 5-hydroxydopamine-incubated rat iris. , 1972, Journal of anatomy.

[61]  R J Harrison,et al.  Fine structural features of delphinid epidermis. , 1972, Journal of anatomy.

[62]  M. Lighthill Large-amplitude elongated-body theory of fish locomotion , 1971, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[63]  Moe W. Rosen,et al.  Fluid Friction of Fish Slimes , 1971, Nature.

[64]  M. Lighthill Aquatic animal propulsion of high hydromechanical efficiency , 1970, Journal of Fluid Mechanics.

[65]  S H Ridgway,et al.  Respiration and Deep Diving in the Bottlenose Porpoise , 1969, Science.

[66]  V. SOKOLOV,et al.  Interaction of Dolphin Epidermis with Flow Boundary Layer , 1969, Nature.

[67]  P E Purves,et al.  The Structure of the Flukes in Relation to Laminar Flow in Cetaceans , 1967 .

[68]  T. Lang,et al.  Hydrodynamic Analysis of Dolphin Fin Profiles , 1966, Nature.

[69]  Max O. Kramer,et al.  Hydrodynamics of the Dolphin , 1965 .

[70]  D. Lindsley,et al.  Microvibrations in Man and Dolphin , 1964, Science.

[71]  Moe W. Rosen FLOW VISUALIZATION EXPERIMENTS WITH A DOLPHIN , 1963 .

[72]  P. E. PURVES,et al.  Locomotion in Whales , 1963, Nature.

[73]  M. Landahl,et al.  On the stability of a laminar incompressible boundary layer over a flexible surface , 1962, Journal of Fluid Mechanics.

[74]  Max O. Kramer,et al.  BOUNDARY LAYER STABILIZATION BY DISTRIBUTED DAMPING , 1962 .

[75]  V. Walters BODY FORM AND SWIMMING PERFORMANCE IN THE SCOMBROID FISHES , 1962 .

[76]  Charles Harvard Gibbs-Smith,et al.  Sir George Cayley's aeronautics, 1796-1855 , 1962 .

[77]  W. SOKOLOV,et al.  Some Similarities and Dissimilarities in the Structure of the Skin Among the Members of the Suborders Odontoceti and Mystacoceti (Cetacea) , 1960, Nature.

[78]  R. V. Mises Theory of Flight , 1959 .

[79]  P. F. Scholander,et al.  Counter-current vascular heat exchange in the fins of whales. , 1955, Journal of applied physiology.

[80]  H. Schlichting Boundary Layer Theory , 1955 .

[81]  F S Essapian Speed-induced skin folds in the bottle-nosed porpoise, Tursiops truncatus , 1955 .

[82]  D. Küchemann The Distribution of Lift over the Surface of Swept Wings , 1953 .

[83]  D A PARRY,et al.  The structure of whale blubber, and a discussion of its thermal properties. , 1949, The Quarterly journal of microscopical science.

[84]  L. HARRISON MATTHEWS The Swimming of Dolphins , 1948, Nature.

[85]  J. Gray Studies in Animal Locomotion: VI. The Propulsive Powers of the Dolphin , 1936 .

[86]  Yandell Henderson,et al.  THE MAXIMUM OF HUMAN POWER AND ITS FUEL , 1925 .

[87]  D. S. B A R R E T T,et al.  Drag reduction in fish-like locomotion , 2022 .