DMD analysis of lock-in and lock-out zones of a transversely vibrating circular cylinder in the wake of a stationary square cylinder

The complex fluid-structure interactions during vortex-induced vibrations are difficult to explain analytically because of the high-dimensional nature of the fluid. We use Dynamic Mode Decomposition (DMD) to analyze the underlying coupled fluid-structure modes and quantify their bifurcation between the observed 'lock-in' and 'lock-out' behavior for a damped transversely oscillating circular cylinder (mass ratio = 10) in the wake of a stationary square cylinder. Simulations are performed at a Reynolds number of 100, and the gap ratio (S/D) between cylinder centers vary from 2 to 5. The circular cylinder oscillates negligibly in the envelope of the wake of the upstream square cylinder until S/D = 4. The vortices shed in the gap at S/D = 5 and interact strongly with the downstream cylinder, resulting in increased oscillations. For such a tandem arrangement, the lock-in zone expands. To characterize the flow dynamics, Koopman modes computed from pressure data in the flow field are used. To describe the original flow in a lock-out situation, a number of Koopman modes must be retained, whereas the first few Koopman modes retain the total energy of the flow in the lock-in case.