  We present direct numerical simulations of turbulent channel flow with
passive Lagrangian polymers. To understand the polymer behavior we investigate
the behavior of infinitesimal line elements and calculate the probability
distribution function (PDF) of finite-time Lyapunov exponents and from them the
corresponding Cramer's function for the channel flow. We study the statistics
of polymer elongation for both the Oldroyd-B model (for Weissenberg number $\Wi
<1$) and the FENE model. We use the location of the minima of the Cramer's
function to define the Weissenberg number precisely such that we observe
coil-stretch transition at $\Wi\approx1$. We find agreement with earlier
analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon
and Lebedev [Phys. Rev. Lett., 84, 4765 (2000).] for linear polymers (Oldroyd-B
model) with $\Wi<1$ and by Chertkov [Phys. Rev. Lett., 84, 4761 (2000).] for
nonlinear FENE-P model of polymers. For $\Wi>1$ (FENE model) the polymer are
significantly more stretched near the wall than at the center of the channel
where the flow is closer to homogenous isotropic turbulence. Furthermore near
the wall the polymers show a strong tendency to orient along the stream-wise
direction of the flow but near the centerline the statistics of orientation of
the polymers is consistent with analogous results obtained recently in
homogeneous and isotropic flows.
