Form-induced stress in non-uniform steady and unsteady open channel flow over a static rough bed

This paper presents a series of 18 steady and 45 unsteady flow experiments over an artificial, rough surface, obtained by a novel molding technique for gravel beds. Velocity data are obtained by a Particle Image Velocimetry (PIV) system. The vertical distributions of the form-induced stresses 〈u˜2〉 and −〈u˜w˜〉 are compared for all experiments. Furthermore, quadrant maps are drawn to analyze the near bed spatial velocity fluctuations u˜ and w˜ in a vertical plane parallel to the flow direction. All experiments were done under non-uniform flow. It is shown that (1) the qualitative shape of the vertical form-induced stress distributions 〈u˜2〉 and −〈u˜w˜〉 is independent from the discharge, as stated in the literature, as well as from the unsteadiness of the flow. (2) The magnitude of the form-induced stress 〈u˜2〉 and −〈u˜w˜〉 in the roughness layer increases with increasing discharge for non-uniform flow, while uniform flow experiments in the literature report the form-induced stresses to be independent from the discharge. A hypothesis is, therefore, proposed, that the independence of the form-induced stress magnitude from the discharge is only valid for uniform flow. (3) Quadrant maps, describing the distribution of the spatial fluctuations u˜ and w˜ in a two-dimensional plane are independent from discharge and unsteadiness of the flow.