Resolvent and dynamic mode analysis of flow past a square cylinder at subcritical Reynolds numbers

Flow-induced vibration (FIV) of bluff bodies can occur at subcritical Reynolds numbers (i.e., below the Re of the vortex shedding from fixed bodies). To analyze the mechanism of this subcritical FIV phenomenon, resolvent and dynamic mode analyses are introduced in this work. For laminar flow past a square cylinder, both resolvent and dynamic modes are extracted and investigated. The results indicate that the dominant dynamic mode decomposition mode and the leading response mode are similar. Both modes lead to vortex shedding at supercritical Reynolds numbers, and they vanish below Re = 19 along with the dominant forcing mode. In addition, the first and second resolvent gains separate near the characteristic flow frequency and overlap at Re = 19, indicating the disappearance of the first-order resolvent mode. The disappearance of these critical modes indicates the lowest Reynolds number of FIV instability for flow past a square cylinder.