  In this work, we investigate the dynamics of vortex-induced vibration of an
elastically mounted cylinder with very low values of mass and damping. We use
two methods to investigate this canonical problem: first we calculate the
instantaneous phase between the cylinder motion and the fluid forcing; second
we decompose the total hydrodynamic force into drag and lift components that
act along and normal to, respectively, the instantaneous effective angle of
attack. We focus on the phase dynamics in the large-amplitude-response range,
consisting of the initial, upper and lower branches of response. The
instantaneous phase between the transverse force and displacement shows
repeated phase slips separating periods of constant, or continuous-drifting,
phase in the second half of the upper branch. The phase between the lift
component and displacement shows strong phase locking throughout the
large-amplitude range - the average phase varies linearly with the primary
frequency - however the modulation of this phase is largest in the second half
of the upper branch. These observations suggest that the
large-amplitude-response dynamics is driven by two distinct limit cycles - one
that is stable over a very small range of reduced velocity at the beginning of
the upper branch, and another that consists of the lower branch. The chaotic
oscillation between them - the majority of the upper branch - occurs when
neither limit cycle is stable. The transition between the upper and lower
branches is marked by intermittent switching with epochs of time where
different states exist at a constant reduced velocity. These different states
are clearly apparent in the phase between the lift and displacement,
illustrating the utility of the force decomposition employed.
