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Skin friction on a moving wall and its implications for swimming animals

  • Uwe Ehrenstein (a1) and Christophe Eloy (a1) (a2)
Abstract
Abstract

Estimating the energetic costs of undulatory swimming is important for biologists and engineers alike. To calculate these costs it is crucial to evaluate the drag forces originating from skin friction. This topic has been controversial for decades, some claiming that animals use ingenious mechanisms to reduce the drag and others hypothesizing that undulatory swimming motions induce a drag increase because of the compression of the boundary layers. In this paper, we examine this latter hypothesis, known as the ‘Bone–Lighthill boundary-layer thinning hypothesis’, by analysing the skin friction in different model problems. First, we study analytically the longitudinal drag on a yawed cylinder in a uniform flow by using the approximation of the momentum equations in the laminar boundary layers. This allows us to demonstrate and generalize a result first observed semi-empirically by G.I. Taylor in the 1950s: the longitudinal drag scales as the square root of the normal velocity component. This scaling arises because the fluid particles accelerate as they move around the cylinder. Next we propose an analogue two-dimensional problem where the same scaling law is recovered by artificially accelerating the flow in a channel of finite height. This two-dimensional problem is then simulated numerically to assess the robustness of the analytical results when inhomogeneities and unsteadiness are present. It is shown that spatial or temporal changes in the normal velocity usually tend to increase the skin friction compared with the ideal steady case. Finally, these results are discussed in the context of swimming energetics. We find that the undulatory motions of swimming animals increase their skin friction drag by an amount that closely depends on the geometry and the motion. For the model problem considered in this paper the increase is of the order of 20 %.

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Email address for correspondence: ehrenstein@irphe.univ-mrs.fr
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Y. G. Aleyev 1977 Nekton. Junk Publishers.

D. S. Barrett , M. S. Triantafyllou , D. K. P. Yue , M. A. Grosenbaugh & M. J. Wolfgang 1999 Drag reduction in fish-like locomotion. J. Fluid Mech. 392, 183212.

D. W. Bechert , M. Bruse , W. Hage , J. G. T. van Der Hoeven & G. Hoppe 1997 Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 5987.

B. Bhushan 2009 Biomimetics: lessons from nature – an overview. Phil. Trans. R. Soc. A 367, 14451486.

I. Borazjani & F. Sotiropoulos 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Exp. Biol. 211, 1541.

H. Choi , P. Moin & J. Kim 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503539.

S. W. Churchill & M. Bernstein 1977 A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. J. Heat Transfer 99, 300.

C. Eloy 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 205218.

F. E. Fish 2006 The myth and reality of grey’s paradox: implication of dolphin drag reduction for technology. Bioinspir. Biomim. 1, R17R25.

F. E. Fish & C. A. Hui 1991 Dolphin swimming – a review. Mammal Rev. 21, 181195.

F. E. Fish & G. V. Lauder 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193224.

M.-L. Gobert , U. Ehrenstein , J. A. Astolfi & P. Bot 2010 Nonlinear disturbance evolution in a two-dimensional boundary-layer along an elastic plate and induced radiated sound. Eur. J. Mech. B/Fluids 29, 105118.

W. A. Khan , J. R. Culham & M. M. Yovanovich 2005 Fluid flow around and heat transfer from elliptical cylinders: analytical approach. J. Thermophys. Heat Transfer 19 (2), 178185.

M. J. Lighthill 1971 Large-amplitude elongated-body theory of fish locomotion. Proc. R. Soc. Lond. B 179, 125138.

M. Marquillie & U. Ehrenstein 2003 On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169188.

R. Peyret 2002 Spectral Methods for Incompressible Flows. Springer.

K. Pohlhausen 1921 Zur näherungsweisen integration der differentialgleichung der laminaren grenzschicht. Z. Angew. Math. Mech. 1, 252290.

D. I. A. Poll 1985 Some observations of the transition process on the windward face of a long yawed cylinder. J. Fluid Mech. 150, 329356.

M. W. Rosen & N. E. Cornford 1971 Fluid friction of fish slimes. Nature 234, 4951.

W. W. Schultz & P. W. Webb 2002 Power requirements of swimming: Do new methods resolve old questions?. Integr. Comp. Biol. 42, 10181025.

W. R. Sears 1948 The boundary layer of yawed cylinders. J. Aeronaut. Sci. 15, 4952.

A. A. Shirgaonkar , M. A. MacIver & N. A. Patankar 2009 A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion. J. Comput. Phys. 228, 23662390.

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

A. Žukauskas & J. Žiugžda 1985 Heat Transfer of a Cylinder in Crossflow. Hemisphere Publishing.

D. Weihs 1974 Energetic advantages of burst swimming of fish. J. Theor. Biol. 48 (1), 215229.

D. Weihs 2004 The hydrodynamics of dolphin drafting. J. Biol. 3 (2), 816.

J. M. Wild 1949 The boundary layer of yawed infinite wings. J. Aeronaut. Sci. 16, 4145.

T. M. Williams , W. A. Friedl , M. L. Fong , R. M. Yamada , P. Sedivy & J. E. Haun 1992 Travel at low energetic cost by swimming and wave-riding bottlenose dolphins. Nature 355, 821823.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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