Multiple lock-ins in vortex-induced vibration of a filament

The vortex-induced vibration of a flexible filament attached behind a stationary cylinder is studied in the two-dimensional, laminar flow regime. We explore the response of the filament for a wide range of flexibility and inertia. Lock-in with a large number of normal modes of the filament, each in a different regime of reduced speed, is observed. Reduced speed is the free-stream speed of the incoming flow non-dimensionalized with the first natural frequency of the structure and the diameter of the cylinder. Several branches, based on response of the filament, are identified and the contributions of various structural modes along these branches are quantified. Contribution from a particular structural mode increases significantly during lock-in, accompanied by a large amplitude of vibration. The transition between different branches is found to be hysteretic and intermittent. The flow exhibits a variety of vortex-shedding patterns, including the mode. The modes of shedding show a systematic variation with amplitude and frequency. The map of vortex-shedding patterns in the amplitude-frequency plane resembles the corresponding map for forced vibration of a rigid cylinder. The transformation of wake from one mode of shedding to another is explained phenomenologically. Variation of rate of energy transfer between the fluid and filament with space and time is analysed to determine optimal placement of transducers for harvesting energy.