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Global vorticity shedding for a shrinking cylinder

Published online by Cambridge University Press:  07 June 2012

G. D. Weymouth  and
M. S. Triantafyllou
G. D. Weymouth*
Affiliation:
Singapore–MIT Alliance for Research and Technology Centre, S16-05-08 3 Science Drive 2, Singapore 117543
M. S. Triantafyllou
Affiliation:
Center for Ocean Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: weymouth@mit.edu
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Abstract

We study numerically the viscous flow around a steadily moving two-dimensional cylinder undergoing a rapid reduction in its diameter as a model problem for force production through shape change which is encountered in the locomotion of certain animals. We consider first the case of a rapidly collapsing circular cylinder in steady translation, starting from an original diameter and reaching a final, smaller diameter under prescribed kinematics. We show that the difference in added mass energy is recovered by the body, and the boundary layer vorticity is reduced through annihilation with opposite-sign vorticity generated during the reduction phase. Next we consider a steadily moving circular cylinder which undergoes rapid but orderly melting, resulting in the same reduction of its diameter but which exhibits radically different flow patterns compared to the collapsing cylinder. The original vorticity in the boundary layer is shed instantaneously and globally in the fluid at the start of the melting phase, and then rapidly rolls up to form a pair of strong vortices, which contain the energy difference between the original and final cylinder states. The formation of the vortices in the melting cylinder takes less than a third of the time required by a rigid translating cylinder to form such vortices.

JFM classification

Biological Fluid Dynamics: Propulsion Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 702 , 10 July 2012 , pp. 470 - 487
Copyright
Copyright © Cambridge University Press 2012

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References

1. Childress, S., Vandenberghe, N. & Zhang, J. 2006 Hovering of a passive body in an oscillating airflow. Phys. Fluids 18, 117103.CrossRefGoogle Scholar
2. Dabiri, J. O. 2005 On the estimation of swimming and flying forces from wake measurements. J. Expl Biol. 208, 3519–3532.CrossRefGoogle ScholarPubMed
3. Dickinson, M. 2003 Animal locomotion: how to walk on water? Nature 424, 621–622.CrossRefGoogle ScholarPubMed
4. Dong, H., Bozkurttas, M., Mittal, R., Madden, P. & Lauder, G. V. 2010 Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J. Fluid Mech. 645, 345–373.CrossRefGoogle Scholar
5. Drucker, E. G & Lauder, G. V. 2000 A hydrodynamic analysis of fish swimming speed: wake structure and locomotor force in slow and fast labriform swimmers. J. Expl Biol. 203, 2379–2393.CrossRefGoogle ScholarPubMed
6. Eames, I. 2008a Disappearing bodies and ghost vortices. Phil. Trans. R. Soc. Lond. A 366, 2219–3232.Google ScholarPubMed
7. Eames, I. 2008b Rapidly dissolving dense bodies in an inviscid fluid. Proc. R. Soc. Lond. A 464, 2985–3002.Google Scholar
8. Fohl, T. 1968 The creation of vortex rings by impulsive acceleration of a sphere of fluid. J. Appl. Phys. 39, 2470–2471.CrossRefGoogle Scholar
9. Hedenstrom, A., Johansson, L. C. & Spedding, G. R. 2006 Bird or bat: comparing airframe design and flight performance. Bioinsp. Biomim. 4, 015001.CrossRefGoogle Scholar
10. Hsieh, S. T. & Lauder, G. V. 2004 Running on water: three-dimensional force generation by basilisk lizards. Proc. Natl Acad. Sci. 101, 16787.CrossRefGoogle ScholarPubMed
11. Hu, D. L. & Bush, J. W. M. 2010 The hydrodynamics of water-walking arthropods. J. Fluid Mech. 644, 5–33.CrossRefGoogle Scholar
12. Hunt, JCR & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111–132.CrossRefGoogle Scholar
13. Johansson, L. C. & Norberg, U. M. L. 2001 Lift-based paddling in diving grebe. J. Expl Biol. 204, 1687–1696.CrossRefGoogle ScholarPubMed
14. Johansson, L. C. & Norberg, R. A. 2003 Delta-wing function of webbed feet gives hydrodynamic lift for swimming propulsion in birds. Nature 424, 65–68.CrossRefGoogle ScholarPubMed
15. Kanso, E. 2009 Swimming due to transverse shape deformations. J. Fluid Mech. 631, 127–148.CrossRefGoogle Scholar
16. Lentink, D., Müller, U. K., Stamhuis, E. J., de Kat, R., van Gestel, W., Veldhuis, L. L. M., Henningsson, P., Hedenström, A., Videler, J. J. & van Leeuwen, J. L. 2007 How swifts control their glide performance with morphing wings. Nature 446, 1082–1085.CrossRefGoogle ScholarPubMed
17. Lindhe Norberg, U. M. & Winter, Y. 2006 Wing beat kinematics of a nectar-feeding bat, Glossophaga soricina, flying at different flight speeds and Strouhal numbers. J. Expl Biol. 209, 3887–3897.CrossRefGoogle ScholarPubMed
18. Margolin, L. G., Rider, W. J. & Grinstein, F. F. 2006 Modelling turbulent flow with implicit LES. J. Turbul. 7, 1–27.CrossRefGoogle Scholar
19. McHenry, M. J. & Jed, J. 2003 The ontogenic scaling of hydrodynamics and swimming jellyfish (Aurelia aurita). J. Expl Biol. 206, 4125–4137.CrossRefGoogle Scholar
20. Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28, 277–308.CrossRefGoogle Scholar
21. Muller, U. K. & Lentink, D. 2004 Physiology - Turning on a dime. Science 306, 1899–1900.CrossRefGoogle ScholarPubMed
22. Ramamurti, R., Sandberg, W. C., Lohner, R., Walker, J. A. & Westneat, M. W. 2002 Fluid dynamics of aquatic flight in the bird wrasse: three dimensional unsteady computations with fin deformation. J. Expl Biol. 205, 2997–3008.CrossRefGoogle ScholarPubMed
23. Rockwell, D. 1998 Vortex–body interactions. Annu. Rev. Fluid Mech. 30, 199–229.CrossRefGoogle Scholar
24. Spagnolie, S. E. & Shelley, M. J. 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.CrossRefGoogle Scholar
25. Taneda, S. 1977 Visual study of unsteady separated flows around bodies. Prog. Aerosp. Sci. 17, 287–348.CrossRefGoogle Scholar
26. Taylor, G. I. 1953 Formation of a vortex ring by giving an impulse to a circular disk and then dissolving it away. J. Appl. Phys. 24, 104.CrossRefGoogle Scholar
27. Weymouth, G. D., Dommermuth, D. G., Hendrickson, K. & Yue, D. K.-P. 2006 Advancements in Cartesian-grid methods for computational ship hydrodynamics. In Proceedings of the 26th Symposium on Naval Hydrodynamics, Rome, Italy, pp. 17–22 September.Google Scholar
28. Weymouth, G. D. & Yue, D. K.-P. 2011 Boundary data immersion method for Cartesian-grid simulations of fluid–body interaction problems. J. Comput. Phys. 230, 16.CrossRefGoogle Scholar
29. Wibawa, M. S., Steele, S. C., Dahl, J. D., Rival, D. E., Weymouth, G. D. & Triantafyllou, M. S. 2012 Global vorticity shedding for a vanishing wing. J. Fluid Mech. 695, 112–134.CrossRefGoogle Scholar
30. Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar