Skip to main content

The unsteady three-dimensional wake produced by a trapezoidal pitching panel

  • Melissa A. Green (a1), Clarence W. Rowley (a1) and Alexander J. Smits (a1)

Particle image velocimetry (PIV) is used to investigate the three-dimensional wakes of rigid pitching panels with a trapezoidal geometry, chosen to model idealized fish caudal fins. Experiments are performed for Strouhal numbers from 0.17 to 0.56 for two different trailing edge pitching amplitudes. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von Kármán vortex street pattern is observed along the mid-span of the near wake, but the vortices realign and exhibit strong interactions near the spanwise edges of the wake. At higher Strouhal numbers, the complexity of the wake increases downstream of the trailing edge as the spanwise vortices spread transversely and lose coherence as the wake splits. This wake transition is shown to correspond to a qualitative change in the LCS pattern surrounding each vortex core, and can be identified as a quantitative event that is not dependent on arbitrary threshold levels. The location of this transition is observed to depend on both the pitching amplitude and free stream velocity, but is not constant for a fixed Strouhal number. On the panel surface, the trapezoidal planform geometry is observed to create additional vortices along the swept edges that retain coherence for low Strouhal numbers or high sweep angles. These additional swept-edge structures are conjectured to add to the complex three-dimensional flow near the tips of the panel.

Corresponding author
Email address for correspondence:
Hide All

Present address: Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC 20375, USA.

Hide All
1. Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J. Expl Biol. 212, 576592.
2. Brunton, S. L. & Rowley, C. W. 2010 Fast computation of finite-time Lyapunov exponent fields for unsteady flows. Chaos 20, 017503.
3. Buchholz, J. H. J. 2006 The flowfield and performance of a low aspect ratio unsteady propulsor. PhD the, Princeton University.
4. Buchholz, J. H. J., Green, M. A. & Smits, A. J. 2011 Circulation of vortices generated by a pitching panel. J. Fluid Mech. (in press).
5. Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331365.
6. Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765777.
7. Clark, R. P. & Smits, A. J. 2006 Thrust production and wake structure of a batoid-inspired oscillating fin. J. Fluid Mech. 562, 415429.
8. Dabiri, J. O. 2009 Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41, 1733.
9. Dong, H., Mittal, R., Bozhurttas, M. & Najjar, F. 2005 Wake structure and performance of finite aspect-ratio flapping foils. In 43rd AIAA Aerospace Sciences Meeting and Exhibit. AIAA.
10. Eldredge, J. D. & Chong, K. 2010 Fluid transport and coherent structures of translating and flapping wings. Chaos 20, 017509.
11. von Ellenrieder, K. D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129138.
12. Ghovardhan, R. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 1147.
13. Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111120.
14. Green, M. A., Rowley, C. W. & Smits, A. J. 2010 Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows. Chaos 20, 017510.
15. Green, M. A. & Smits, A. J. 2008 Effects of three-dimensionality on thrust production by a pitching panel. J. Fluid Mech. 615, 211220.
16. Guglielmini, L. 2004 Modeling of thrust generating foils. PhD thesis, University of Genoa.
17. Haller, G. 2002 Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14 (6), 18511861.
18. Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 126.
19. Haller, G. 2010 A variational theory of hyperbolic Lagrangian coherent structures. Physica D (in press).
20. Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two dimensional turbulence. Physica D 147, 352370.
21. Huang, H., Dabiri, D. & Gharib, M. 1997 On errors of digital particle image velocimetry. Meas. Sci. Technol. 8, 14271440.
22. Hultmark, M., Leftwich, M. & Smits, A. J. 2007 Flowfield measurements in the wake of a robotic lamprey. Exp. Fluids 43, 683690.
23. Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Rep. CTR-S88.
24. Jeong, J. & Hussein, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
25. Jiménez, J. M. 2002 Low reynolds number studies in the wake of a submarine model using particle image velocimetry. Master’s thesis, Princeton University.
26. Koochesfahani, M. M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27 (9), 12001205.
27. Lapeyre, G. 2002 Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos 12 (3), 688698.
28. Lauder, G. V. & Tytell, E. D. 2006 Hydrodynamics of undulatory propulsion. In Fish Biomechanics (ed. Shadwick, R. E. & Lauder, G. V. ). Fish Physiology, vol. 23 . pp. 425468. Academic.
29. Lekien, F. & Leonard, N. 2004 Dynamically consistent Lagrangian coherent structures. In American Inst. of Physics: 8th Experimental Chaos Conference, CP 742, pp. 132–139.
30. Lipinski, D., Cardwell, B. & Mohseni, K. 2008 A Lagrangian analysis of a two-dimensional airfoil with vortex shedding. J. Phys. A: Math. Theor. 41, 122.
31. O’Farrell, C. & Dabiri, J. O. 2010 A Lagrangian approach to identifying vortex pinch-off. Chaos 20, 017513.
32. Sarkar, S. & Venkatraman, K. 2006 Numerical simulation of thrust generating flow past a pitching aerofoil. Comput. Fluids 35, 1642.
33. Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105–1–047105–11.
34. Shadden, S. C., Lekien, F. & Marsden, J. E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensinal aperiodic flows. Physica D 212, 271304.
35. Shadden, S. C., Astorino, M. & Gerbeau, J.-F. 2010 Computational analysis of an aortic valve jet with Lagrangian coherent structures. Chaos 20, 017512.
36. Shadden, S. C., Katija, K., Rosenfeld, M., Marsden, J. E. & Dabiri, J. O. 2007 Transport and stirring induced by vortex formation. J. Fluid Mech. 593, 315331.
37. Shadden, S. C. & Taylor, C. A. 2008 Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Engng 36 (7), 11521162.
38. Tang, W., Chan, P. W. & Haller, G. 2010 Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport. Chaos 20, 017502.
39. Triantafyllou, G., Triantafyllou, M. & Grosenbaugh, M. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7 (2), 205224.
40. Tytell, E. D., Borazjani, I., Sotiropoulos, F., Baker, T. V., Anderson, E. J. & Lauder, G. V. 2010 Disentangling the functional roles of morphology and motion in the swimming of fish. Integr. Compar. Biol. 50 (6), 11401154.
41. Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355381.
42. Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
43. Zhu, Q. & Shoele, K. 2008 Propulsion performance of a skeleton-strengthened fin. J. Expl Biol. 211, 20872100.
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? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 92 *
Loading metrics...

Abstract views

Total abstract views: 206 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th March 2018. This data will be updated every 24 hours.