A linear stability approach to vortex-induced vibrations and waves

The motion induced by vortex shedding on slender flexible structures subjected to cross-flow is considered here. This phenomenon of vortex-induced vibration (VIV) is analysed by considering the linear stability of a coupled system that includes the structure dynamics and the wake dynamics. The latter is modelled by a continuum of wake oscillators, distributed along the span of the structure. In the case of uniform flows over a straight tensioned cable, VIV are found to arise as an instability related to the merging of two waves. In the case of a cable of finite length, the selection of modes that experience lock-in with the wake is found using the same stability argument. In non-uniform flows, several unstable wave systems are identified, and competition between them is discussed. Comparison is then made with existing experimental and computational data of VIV of slender structures under uniform and non-uniform flows. Phenomena previously identified in these systems, such as mode switching when the flow velocity is varied, time sharing of the response between two frequencies, or the coexistence of several regions of VIV with different dynamics in the same structure, are discussed with the help of the proposed model.