Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows

In this paper we intend to predict the magnitude of the contribution to the Reynolds stress of bursting events: ‘ejections’, ‘sweeps’, ‘inward interactions’ and ‘outward interactions’. We shall do this by making use of the conditional probability distribution of the Reynolds stress − uv , which can be derived by applying the cumulant-discard method to the Gram-Charlier probability distribution of the two variables u and v . The Reynolds-stress fluctuations in openchannel flows over smooth and rough beds are measured by dual-sensor hot-film anemometers, whose signals are conditionally sampled and sorted into the four quadrants of the u, v plane by using a high-speed digital data processing system. We shall verify that even the third-order conditional probability distribution of the Reynolds stress shows fairly good agreement with the experimental results and that the sequence of events in the bursting process, i.e. ejections, sweeps and interactions, is directly related to the turbulent energy budget in the form of turbulent diffusion. Also, we shall show that the roughness effect is marked in the area from the wall to the middle of the equilibrium region, and that sweeps appear to be more important than ejections as the roughness increases and as the distance from the wall decreases.