Flow-induced vibrations in long rows of cylinders and their links to convective instabilities

Flows past rows of elastically mounted cylinders display a number of flow-induced vibration phenomena that hitherto have proven difficult to categorise in a way that is independent of the number of cylinders in the row. Here, we investigate the flow past six equispaced but independent elastically-mounted cylinders at Reynolds number Re = 200 using direct numerical simulations over a wide range of stiffnesses and for three values of the inter-cylinder spacing or pitch p. We make a first attempt at categorising the responses observed in terms of the framework of flow states linked to convective instabilities in rows of rigidly mounted cylinders recently presented in Hosseini, Griffith and Leontini (2020). We show that regardless of pitch, this framework has some success in explaining and collating the flow-induced vibration response for high to moderate stiffnesses (corresponding to low to moderate reduced velocities U*). Among others, one phenomenon observed that fits this framework is the fact that for some cases, the first and last cylinders in an array can vibrate, while the rest are almost stationary. However, at low stiffness/high U*, the arrays behave more like a single flexible structure that exhibits waves, which is an inherent fluid-structure mode with no root in the rigidly mounted case.