Residence time distributions in unstable channel flow

The transport properties of the plane Poiseuille flow in which a two-dimensional, nonlinearly saturated Tollmien-Schlichting wave is propagating are studied in terms of residence time distributions (RTDs). First, a method for computing RTDs in any type of open flows is developed, making use of a single trajectory over a long period of time, with a controlled level of diffusion. With this method, RTDs of this perturbed flow are computed, along with a quantitative measure of their dispersion through the mean absolute deviation. Depending on the travel distance, RTDs display two kinds of pattern. For short travel distances, a pattern of peaks and valleys is observed for long residence times, originating in regions of negative streamwise velocity produced by the wave. For longer travel distances, a large probability peak is observed at t = 𝜏_wave, the time needed for the wave to travel one section downstream. This peak is attributed to the cat's eye pattern characteristic of this type of traveling wave. It is shown that the increased dispersion of the RTD is mainly due to the nonlinear correction of the mean velocity profile.