  This study presents a numerical investigation of how fluid viscoelasticity
influences the flow dynamics past a transversely forced oscillating cylinder in
the laminar vortex shedding regime at a fixed Reynolds number of 100. In
particular, we examine how fluid viscoelasticity influences the boundary
between the lock-in and no lock-in zones and the associated wake topology
compared to that seen in a simple Newtonian fluid. All in all, we find that the
fluid viscoelasticity facilitates the synchronization of the vortex street with
the cylinder motion at lower oscillation frequencies than that required for a
Newtonian fluid. Consequently, the boundary of the lock-in region for a
viscoelastic fluid differs from the Newtonian one and broadens in the
non-dimensional cylinder oscillation amplitude and frequency plane.
Furthermore, we propose that excess strain generated due to the stretching of
polymer molecules in a viscoelastic fluid results in a marked difference in the
wake structure from that seen in a Newtonian fluid. For a Newtonian fluid, only
2S (two single vortices) and P+S (a pair and a single vortex) vortex shedding
modes are detected in the primary synchronization region. However, a 2P(two
pairs of vortices) vortex mode is detected for a viscoelastic fluid in this
region. We also employ the data-driven dynamic mode decomposition (DMD) reduced
order modeling technique to extract and analyze underlying coherent flow
structures and their associated frequencies to understand the differences in
the flow dynamics of Newtonian and viscoelastic fluids past an oscillating
cylinder.
