Stochastic analysis of vortex-induced vibrations by means of a randomized wake-oscillator model

The influence of wind turbulence on the vortex-induced response of a single cylinder is not well understood yet. It also appears that there is no commonly accepted model to represent the influence of a turbulent flow. In this paper, a low-order phenomenological model, inspired by the smooth flow VIV model derived by Facchinetti et al., is described and analyzed. The main features of this model are presented. In particular, the topology of the limit cycle of the coupled wake-oscillator system is analyzed in the presence of noise. The extent of the so-called lock-in domain is interpreted, in the stochastic version of the problem, by means of the statistics of the phase between the two degrees-of-freedom. Based on the slow phase model of the problem, it is shown that both the turbulence intensity and the frequency content of the turbulence play a significant role in the statistical distributions of the magnitudes of fluid and structure oscillations. The derivation is proposed in a dimensionless version so that the major scalings driving the problem naturally come out of the analysis.