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Flow interactions and forward flight dynamics of tandem flapping wings.

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Title: Flow interactions and forward flight dynamics of tandem flapping wings.
Authors: Fang, Fang1 (AUTHOR), Mavroyiakoumou, Christiana1,2 (AUTHOR) mavroyiakoum@maths.ox.ac.uk, Ristroph, Leif1 (AUTHOR), Shelley, Michael J.1,2 (AUTHOR)
Source: Journal of Fluid Mechanics. 5/10/2026, Vol. 1034, p1-42. 42p.
Subjects: Vortex methods, Wakes (Fluid dynamics), Fluid-structure interaction, Ornithopters, Stability theory, Animal locomotion
Abstract: We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex-sheet method to solve for the locomotion of the pair within the collective flow field, and we identify 'schooling states' in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader's wake. Each equilibrium position is stabilised since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust and a weakened collective wake. The equilibria and their stability are also corroborated by a linearised theory for the motion of the leader, the wake it produces and its effect on the follower. We also consider a weakly flapping follower driven with lower heaving amplitude than the leader. We identify 'keep-up' conditions for which the wings may still 'school' together despite their dissimilar kinematics, with the 'freeloading' follower passively assuming a favourable position within the wake that permits it to travel significantly faster than it would in isolation. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193952193
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Flow interactions and forward flight dynamics of tandem flapping wings.
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  Data: <searchLink fieldCode="AR" term="%22Fang%2C+Fang%22">Fang, Fang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mavroyiakoumou%2C+Christiana%22">Mavroyiakoumou, Christiana</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> mavroyiakoum@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Ristroph%2C+Leif%22">Ristroph, Leif</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Shelley%2C+Michael+J%2E%22">Shelley, Michael J.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 5/10/2026, Vol. 1034, p1-42. 42p.
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  Data: <searchLink fieldCode="DE" term="%22Vortex+methods%22">Vortex methods</searchLink><br /><searchLink fieldCode="DE" term="%22Wakes+%28Fluid+dynamics%29%22">Wakes (Fluid dynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid-structure+interaction%22">Fluid-structure interaction</searchLink><br /><searchLink fieldCode="DE" term="%22Ornithopters%22">Ornithopters</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Animal+locomotion%22">Animal locomotion</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex-sheet method to solve for the locomotion of the pair within the collective flow field, and we identify 'schooling states' in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader's wake. Each equilibrium position is stabilised since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust and a weakened collective wake. The equilibria and their stability are also corroborated by a linearised theory for the motion of the leader, the wake it produces and its effect on the follower. We also consider a weakly flapping follower driven with lower heaving amplitude than the leader. We identify 'keep-up' conditions for which the wings may still 'school' together despite their dissimilar kinematics, with the 'freeloading' follower passively assuming a favourable position within the wake that permits it to travel significantly faster than it would in isolation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2026.11521
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      – Code: eng
        Text: English
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        PageCount: 42
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      – SubjectFull: Vortex methods
        Type: general
      – SubjectFull: Wakes (Fluid dynamics)
        Type: general
      – SubjectFull: Fluid-structure interaction
        Type: general
      – SubjectFull: Ornithopters
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: Animal locomotion
        Type: general
    Titles:
      – TitleFull: Flow interactions and forward flight dynamics of tandem flapping wings.
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            NameFull: Fang, Fang
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            NameFull: Mavroyiakoumou, Christiana
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            NameFull: Ristroph, Leif
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            NameFull: Shelley, Michael J.
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            – D: 10
              M: 05
              Text: 5/10/2026
              Type: published
              Y: 2026
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