## Abstract

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 language | English (US) |
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Pages (from-to) | 273-302 |

Number of pages | 30 |

Journal | SIAM Journal on Scientific Computing |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - 2008 |

## Keywords

- Equilibria
- Immersed boundary method
- Kirchhoff theory
- Supercoiling

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics