Dynamics of a closed rod with twist and bend in fluid

Sookkyung Lim, Anca Ferent, X. Sheldon Wang, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


We investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous, incompressible fluid. A new version of the immersed boundary (IB) method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid. An important feature of the IB method in this context is that self-crossing of the rod is automatically avoided because the rod moves in a continuous (interpolated) velocity field. A rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition, with the fluid initially at rest. If the twist in the rod is sufficiently small, the rod simply returns to its circular equilibrium configuration, but for larger twists that equilibrium configuration becomes unstable, and the rod undergoes large excursions before relaxing to a stable coiled configuration.

Original languageEnglish (US)
Pages (from-to)273-302
Number of pages30
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2008


  • Equilibria
  • Immersed boundary method
  • Kirchhoff theory
  • Supercoiling

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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