Three-dimensional transition of the flow past an elastically mounted circular cylinder

Floquet stability analysis and direct simulations of a circular cylinder undergoing vortex-induced vibration (VIV) are presented. Simulation predictions are examined for the reduced velocity range over which there is a strong and periodic resonant response: U-r is an element of[4.0, 8.0], focusing on a mass ratio of m* = 2.546 matching a number of previous investigations. Over most of this range, the dominant wake modes present are analogous to modes A, B and QP (quasi-periodic) observed in a stationary circular cylinder wake. However, at U-r = 4.5, the dominant modes are B, QP and a subharmonic mode (SH), whereas at Ur = 4.0, the two-dimensional base state switches to a P + S wake. The critical Reynolds number for two- to three-dimensional transition is observed to decrease with an increase of Ur, in line with a decreasing response amplitude. Over this range, the minimum Re for which the wake remains two-dimensional is 202, which occurs at Ur = 7.5, but this increases to Re-cr = 300 at U-r = 4.5, noting the critical Reynolds number for a stationary circular cylinder is Re-cr = 189. The corresponding critical spanwise wavelengths for U-r = 4.5 and 8 are 1.4D (mode B) and 4.0D (mode A), respectively. Simulations indicate that even at Re = 300, flow three-dimensionality increases the amplitude of the lower branch considerably. The investigation establishes the role of oscillation amplitude and reduced velocity in three-dimensional transition for elastically mounted systems.