  The influence of an external flow on the relaxation dynamics of a single
polymer is investigated theoretically and numerically. We show that a
pronounced dynamical slowdown occurs in the vicinity of the coil-stretch
transition, especially when the dependence on polymer conformation of the drag
is accounted for. For the elongational flow, relaxation times are exceedingly
larger than the Zimm relaxation time, resulting in the observation of
conformation hysteresis. For random smooth flows hysteresis is not present.
Yet, relaxation dynamics is significantly slowed down because of the large
variety of accessible polymer configurations. The implications of these results
for the modeling of dilute polymer solutions in turbulent flows are addressed.
