  Two examples for the interplay between chaotic dynamics and stochastic forces
within hydrodynamical systems are considered. The first case concerns the
relaxation to equilibrium of a concentration field subject to both chaotic
advection and molecular diffusion. The concentration field develops filamentary
structures and the decay rate depends non-monotonically on the diffusion
strength. The second example concerns polymers, modelled as particles with an
internal degree of freedom, in a chaotic flow. The length distribution of the
polymers turns out to follow a power law with an exponent that depends on the
difference between Lyapunov exponent and internal relaxation rate.
