  The effects induced by long temporal correlations of the velocity gradients
on the dynamics of a flexible polymer are investigated by means of theoretical
and numerical analysis of the Hookean and FENE dumbbell models in a random
renewing flow. For Hookean dumbbells, we show that long temporal correlations
strongly suppress the Weissenberg-number dependence of the power-law tail
characterising the probability density function (PDF) of the elongation. For
the FENE model, the PDF becomes bimodal, and the coil-stretch transition occurs
through the simultaneous drop and rise of the two peaks associated with the
coiled and stretched configurations, respectively.
