We investigate high-Reynolds-number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number, which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible, so they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the...

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier-Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec ≈ 2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be indepen...

We combine a discrete-element-method simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical ...