Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness

We explore a new application of the quadrant method in the context of the double-averaged Navier-Stokes equations for studying open channel flow near rough beds. Quadrant analysis is applied to spatial disturbances of time-averaged velocity components, using the experimental data from flow over two-dimensional regular transverse square-bar roughness. The spatial velocity disturbances change periodically performing a full cycle over a single roughness element, so that the quadrant diagrams are regular closed orbits. A colour code is used to produce a quadrant map of the flow cross-section, which reveals contributions from each quadrant to the time-averaged momentum transfer.