Proper orthogonal decomposition analysis of a circular cylinder undergoing vortex-induced vibrations

Proper orthogonal decomposition (POD) is utilized to analyze the wake-dynamics of a low-mass ratio circular cylinder undergoing vortex-induced vibrations in the initial and upper branches (U* = U∞/fND = 4.07, 5.32). POD allows for characterizing dynamics at frequencies which differ from the cylinder oscillation that cannot be captured with conventional phase-averaging. POD modes contributing to the dominant coherent motions are described in detail. Fourier analysis techniques are used to identify relationships between the POD modes describing non-periodic dynamics linked to the slow-varying base flow and result in a modulation in the strength of vortex shedding. Heuristic models based on mean-field theory are proposed for the POD temporal coefficients. The modelled wake dynamics are found to account for a significant contribution to the Reynolds stresses. In the initial branch, it is found that 6 POD modes are required to capture the salient aspects of the flow, while in the upper branch, 7 modes are required.