  Polymer stretching in random smooth flows is investigated within the
framework of the FENE dumbbell model. The advecting flow is Gaussian and
short-correlated in time. The stationary probability density function of
polymer extension is derived exactly. The characteristic time needed for the
system to attain the stationary regime is computed as a function of the
Weissenberg number and the maximum length of polymers. The transient relaxation
to the stationary regime is predicted to be exceptionally slow in the proximity
of the coil-stretch transition.
