Nonlinear elastic polymers in random flow

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.