  The transition to turbulence in a plane Poiseuille flow of dilute polymer
solutions is studied by direct numerical simulations of a FENE-P fluid. A range
of Reynolds number ($Re$) in $2000 \le Re \le 5000$ is studied but with the
same level of elasticity in viscoelastic flows. The evolution of a
finite-amplitude perturbation and its effects on transition dynamics are
investigated. A viscoelastic flow begins transition at an earlier time than its
Newtonian counterparts, but the transition time appears to be insensitive to
polymer concentration at dilute or semi-dilute regimes studied. Increasing
polymer concentration, however, decreases the maximum attainable energy growth
during the transition process. The critical or minimum perturbation amplitude
required to trigger transition is computed. Interestingly, both Newtonian and
viscoelastic flows follow almost the same power-law scaling of $Re^\gamma$ with
the critical exponent $\gamma \approx -1.25$, which is in close agreement with
previous studies. However, a shift downward is observed for viscoelastic flow,
suggesting that smaller perturbation amplitudes are required for the
transition. A mechanism of the early transition is investigated by the
evolution of wall-normal and spanwise velocity fluctuations and flow structure.
The early growth of these fluctuations and formation of quasi-streamwise
vortices around low-speed streaks are promoted by polymers, hence causing an
early transition. These vortical structures are found to support the critical
exponent $\gamma \approx -1.25$. Once the transition process is completed,
polymers play a role in dampening the wall-normal and spanwise velocity
fluctuations and vortices to attain a drag-reduced state in viscoelastic
turbulent flows.
