Geometry of twist transport in a rotating elastic rod

An elastic rod rotating in a viscous fluid undergoes a shape transition from a twirling (axial spinning) to a whirling state (crankshafting motion) at a certain critical frequency [Wolgemuth et al., Phys. Rev. Lett. 84, 1623 (2000)]. The physical properties of such whirling rods are largely unknown, owing to their strongly nonlinear character. We analytically and numerically demonstrate that this dynamical transition occurs to reduce the viscous energy dissipation. A simple geometric interpretation underlying this observation is also given. These results provide a fundamental scenario for viscous twist transport in flexible filaments and are potentially important in the analysis of biopolymer dynamics such as DNA supercoiling during transcriptions.