Skip to main content Accessibility help

Interaction modes of multiple flexible flags in a uniform flow

  • Emad Uddin (a1), Wei-Xi Huang (a2) and Hyung Jin Sung (a1)

Fish schooling is not merely a social behaviour; it also improves the efficiency of movement within a fluid environment. Inspired by the hydrodynamics of schooling, a group of flexible bodies was modelled as a collection of individuals arranged in a combination of tandem and side-by-side formations. The downstream bodies were found to be strongly influenced by the vortices shed from an upstream body, as revealed in the vortex–vortex and vortex–body interactions. To investigate the interactions between flexible bodies and vortices, the present study examined flexible flags in a viscous flow by using an improved version of the immersed boundary method. Three different flag formations were modelled to cover the basic structures involved in fish schooling: triangular, diamond and conical formations. The drag coefficients of the downstream flags could be decreased below the value for a single flag by adjusting the streamwise and spanwise gap distances and the flag bending coefficient. The drag variations were influenced by the interactions between vortices shed from the upstream flexible flags and those surrounding the downstream flags. The interactions between the flexible flags were investigated as a function of both the gap distance between the flags and the bending coefficients. The maximum drag reduction and the trailing flag position were calculated for different sets of conditions. Single-frequency and multifrequency modes were identified and were found to correspond to constructive and destructive vortex interaction modes, which explained the variations in the drag on the downstream flags.

Corresponding author
Email address for correspondence:
Hide All
Abrahams, M. V. & Colgan, P. W. 1985 Risk of predation, hydrodynamic efficiency and their influence on school structure. Environ. Biol. Fishes 13, 195202.
Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489496.
Alben, S. & Shelley, M. J. 2008 Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. Phys. Rev. Lett. 100, 074301.
Bagheri, S. 2010 Analysis and control of transitional shear flows using global modes. PhD thesis, Department of Mechanics, Royal Institute of Technology, Sweden.
Belyayev, V. V. & Zuyev, G. V. 1969 Hydrodynamic hypothesis of schooling in fish. J. Ichthy 9, 578584.
Breder, C. M. Jr. 1965 Vortices and fish schools. Zoologica 50, 97114.
Breder, C. M. Jr. 1967 On the survival value of fish schools. Zoologica 52, 2540.
Breder, C. M. Jr. 1976 Fish schools as operational structures. Fish. Bull. 74, 471502.
Connell, B. S. H. & Yue, D. K. P. 2007 Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 581, 3367.
Deng, J. & Shao, X. E. 2006 Hydrodynamics in a diamond-shaped fish school. J. Hydrodyn. Ser. B 18, 438442.
Deng, J., Shao, X.-M. & Yu, Z.-X. 2007 Hydrodynamic studies on two travelling wavy foils in tandem arrangement. Phys. Fluids 19, 113104.
Dong, G. J. & Lu, X. Y. 2007 Characteristics of flow over travelling wavy foils in a side-by-side arrangement. Phys. Fluids 19, 057107.
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J. Fluid Mech. 611, 97106.
Farnell, D. J. J., David, T. & Barton, D. C. 2004 Coupled states of flapping flags. J. Fluids Struct. 19, 2936.
Fauci, L. J. 1990 Interaction of oscillating filaments: a computational study. J. Comput. Phys. 86 (2), 294313.
Fish, F. E. 1999 Energetics of swimming and flying in formation. Comments Theor. Biol. 5, 283304.
Glowinski, R., Pana, T.-W., Hesla, T. I. & Joseph, D. D. 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25, 755794.
Gopalkrishnan, R., Triantafyllou, M. S., Triantafyllou, G. S. & Barrett, D. 1994 Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech. 274, 121.
Huang, W.-X., Shin, S. J. & Sung, H. J. 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 22062228.
Huber, G. 2000 Swimming in flatsea. Nature 408, 777878.
James, C. L. 2007 Review of fish swimming mechanics and behaviour in altered flows. Phil. Trans. R. Soc. B 362, 19731993.
Jia, L. B., Li, F., Yin, X. Z. & Yin, X. Y. 2007 Coupling modes between two flapping filaments. J. Fluid Mech. 581, 199220.
Kanso, E., Marsden, J. E., Rowley, C. W. & Mellihuber, J. B. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15 (4), 255289.
Kelly, S. D. & Xiong, H. 2005 Controlled hydrodynamic interactions in schooling aquatic locomotion. In 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference (CDC-ECC ’05), pp. 39043910. IEEE Press.
Kim, S., Huang, W.-X. & Sung, H. J. 2010 Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511521.
Kyle, C. R. 1979 Reduction of wind resistance and power output of racing cyclists and runners travelling in groups. Ergonomics 22, 387397.
Liao, J. C., Beal, D. N., Lauder, G. V. & Triantafyllou, M. S. 2003 Fish exploiting vortices decrease muscle activity. Science 302, 15661569.
Magnuson, J. J. 1978 Locomotion by scombrid fish: hydrodynamics morphology and behaivor. Fish Physiol. Locomotion 7, 239313.
Michelin, S. & Llewellyn Smith, S. G. 2009 Linear stability analysis of coupled parallel flexible plates in an axial flow. J. Fluids Struct. 25, 11361157.
Muller, U. 2003 Fish’n flag. Science 302, 15111512.
Nair, S. & Kanso, E. 2007 Hydrodynamically coupled rigid bodies. J. Fluid Mech. 592, 393411.
Parrish, J. K. & Keshet, L. E. 1999 Complexity, pattern and evolutionary trade-offs in animal aggregation. Science 284, 99101.
Partridge, B. L. & Pitcher, T. J. 1979 Evidence against a hydrodynamic function for fish school. Nature 279, 418419.
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101, 194502.
Romberg, C. F., Chianese, F. Jr. & Lajoie, R. G. 1971 Aerodynamics of race cars in drafting and passing situations. Soc. Auto. Engng 710213.
Rowley, C. W., Colonius, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315346.
Ruhe, A. 1984 Rational Krylov sequence methods for eigenvalue computation. Linear Algebra Appl. 58, 279316.
Schouveiler, L. & Eloy, C. 2009 Coupled flutter of parallel plates. Phys. Fluids 21, 081703.
Shaw, E. 1978 Schooling fish. Am. Sci. 66, 166175.
Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowingwater. Phys. Rev. Lett. 94, 094302.
Shelley, M. J. & Zhang, J. 2011 Flapping and bending bodies interacting with fluid flows. Annu. Rev. Fluid Mech. 43, 449465.
Sparenberg, J. A. 2002 Survey of the mathematical theory of fish locomotion. J. Engng Maths 44, 395448.
Stöker, S. 1999 Models for tuna school formation. Math. Biosci. 156, 167190.
Streitlien, K., Triantafyllou, G. S. & Triantafyllou, M. S. 1996 Efficient foil propulsion through vortex control. AIAA J. 34, 23152319.
Tang, L. & Paidoussis, M. P. 2009 The coupled dynamics of two cantilevered flexible plates in axial flow. J. Sound Vib. 323, 790801.
Tian, F. B., Luo, H. & Zhu, L. 2011a Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23, 111903.
Tian, F. B., Luo, H., Zhu, L., Liao, J. C. & Lu, X. Y. 2011b An efficient immersed boundary–lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 230, 72667283.
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241, 290291.
Weihs, D. 1975 Some hydrodynamical aspects of fish schooling. Swimming Flying Nature 2, 703718.
Zdravkovich, M. M. 1977 Review of flow interference between two circular cylinders in various arrangement. J. Fluids Engng. 99, 618633.
Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835839.
Zhang, X., Zhu, X. J. & He, G. W. 2013 An improved direct-forcing immersed boundary method for fluid-structure interaction simulations. ASME Fluids Engineering Summer Meeting, Nevada, USA. (FEDSM2013-16472).
Zhu, L. 2009 Interaction of two tandem deformable bodies in a viscous incompressible flow. J. Fluid Mech. 635, 455475.
Zhu, L. & Peskin, C. S. 2002 Simulation of a flapping flexible filament in a flowing soap film bythe immersed boundary method. J. Comput. Phys. 179, 452468.
Zhu, L. & Peskin, C. S. 2003 Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15, 19541960.
Zhu, Q. & Peng, Z. 2009 Mode coupling and flow energy harvesting by a flapping foil. Phys. Fluids 21, 033601.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed