Whirling instability of an elastic filament by the immersed boundary method
Mathematical Biosciences Institute, The Ohio State University
(February 26, 2004 11:30 AM - 12:30 PM)
When an elastic filament spins in a viscous incompressible fluid at varying angular frequency it may undergo a whirling instability and a bifurcation occurs, as studied asymptotically by Wolgemuth, Powers, Goldstein. We use the Immersed Boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous incompressible fluid as governed by the Navier-Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical. This allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state. The numerical method shows two dynamical motions of the rotating elastic filament depending on the angular frequency and also on the initial bend. These are in which the filament rotates in place around a straight axis, and in which the axis of the filament becomes drastically bent and precesses about the symmetry axis of the system.