Characteristics of clustered particles in skimming flows on a stepped spillway

Air–water flows at hydraulic structures are commonly observed and called white waters. The free-surface aeration is characterised by some intense exchanges of air and water leading to complex air–water structures including some clustering. The number and properties of clusters may provide some measure of the level of particle-turbulence and particle–particle interactions in the high-velocity air–water flows. Herein a re-analysis of air–water clusters was applied to a highly aerated free-surface flow data set (Chanson and Carosi, Exp Fluids 42:385–401, 2007). A two-dimensional cluster analysis was introduced combining a longitudinal clustering criterion based on near-wake effect and a side-by-side particle detection method. The results highlighted a significant number of clustered particles in the high-velocity free-surface flows. The number of bubble/droplet clusters per second and the percentage of clustered particles were significantly larger using the two-dimensional cluster analysis than those derived from earlier longitudinal detection techniques only. A number of large cluster structures were further detected. The results illustrated the complex interactions between entrained air and turbulent structures in skimming flow on a stepped spillway, and the cluster detection method may apply to other highly aerated free-surface flows.