Simulations of the Whirling Instability by the Immersed Boundary Method

When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. 16--23]. We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier--Stokes equations. This allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state.