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:
$U_r \in [4.0, 8.0]$, 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
$U_r = 4.0$, 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
$U_r$, in line with a decreasing response amplitude. Over this range, the minimum
${\textit {Re}}$ for which the wake remains two-dimensional is 202, which occurs at
$U_r = 7.5$, but this increases to
${\textit {Re}}_{cr} = 300$ at
$U_r = 4.5$, noting the critical Reynolds number for a stationary circular cylinder is
${\textit {Re}}_{cr}=189$. 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.